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Sample records for newtonian fluids adopting

  1. Applying Tiab’s direct synthesis technique to dilatant non-Newtonian/Newtonian fluids

    Directory of Open Access Journals (Sweden)

    Javier Andrés Martínez

    2011-09-01

    Full Text Available Non-Newtonian fluids, such as polymer solutions, have been used by the oil industry for many years as fracturing agents and drilling mud. These solutions, which normally include thickened water and jelled fluids, are injected into the formation to enhanced oil recovery by improving sweep efficiency. It is worth noting that some heavy oils behave non-Newtonianly. Non-Newtonian fluids do not have direct proportionality between applied shear stress and shear rate and viscosity varies with shear rate depending on whether the fluid is either pseudoplastic or dilatant. Viscosity decreases as shear rate increases for the former whilst the reverse takes place for dilatants. Mathematical models of conventional fluids thus fail when applied to non-Newtonian fluids. The pressure derivative curve is introduced in this descriptive work for a dilatant fluid and its pattern was observed. Tiab’s direct synthesis (TDS methodology was used as a tool for interpreting pressure transient data to estimate effective permeability, skin factors and non-Newtonian bank radius. The methodology was successfully verified by its application to synthetic examples. Also, comparing it to pseudoplastic behavior, it was found that the radial flow regime in the Newtonian zone of dilatant fluids took longer to form regarding both the flow behavior index and consistency factor.

  2. Revisiting Newtonian and Non-Newtonian Fluid Mechanics Using Computer Algebra

    Science.gov (United States)

    Knight, D. G.

    2006-01-01

    This article illustrates how a computer algebra system, such as Maple[R], can assist in the study of theoretical fluid mechanics, for both Newtonian and non-Newtonian fluids. The continuity equation, the stress equations of motion, the Navier-Stokes equations, and various constitutive equations are treated, using a full, but straightforward,…

  3. Non-Newtonian fluid flow in 2D fracture networks

    Science.gov (United States)

    Zou, L.; Håkansson, U.; Cvetkovic, V.

    2017-12-01

    Modeling of non-Newtonian fluid (e.g., drilling fluids and cement grouts) flow in fractured rocks is of interest in many geophysical and industrial practices, such as drilling operations, enhanced oil recovery and rock grouting. In fractured rock masses, the flow paths are dominated by fractures, which are often represented as discrete fracture networks (DFN). In the literature, many studies have been devoted to Newtonian fluid (e.g., groundwater) flow in fractured rock using the DFN concept, but few works are dedicated to non-Newtonian fluids.In this study, a generalized flow equation for common non-Newtonian fluids (such as Bingham, power-law and Herschel-Bulkley) in a single fracture is obtained from the analytical solutions for non-Newtonian fluid discharge between smooth parallel plates. Using Monte Carlo sampling based on site characterization data for the distribution of geometrical features (e.g., density, length, aperture and orientations) in crystalline fractured rock, a two dimensional (2D) DFN model is constructed for generic flow simulations. Due to complex properties of non-Newtonian fluids, the relationship between fluid discharge and the pressure gradient is nonlinear. A Galerkin finite element method solver is developed to iteratively solve the obtained nonlinear governing equations for the 2D DFN model. Using DFN realizations, simulation results for different geometrical distributions of the fracture network and different non-Newtonian fluid properties are presented to illustrate the spatial discharge distributions. The impact of geometrical structures and the fluid properties on the non-Newtonian fluid flow in 2D DFN is examined statistically. The results generally show that modeling non-Newtonian fluid flow in fractured rock as a DFN is feasible, and that the discharge distribution may be significantly affected by the geometrical structures as well as by the fluid constitutive properties.

  4. Spreading of Non-Newtonian and Newtonian Fluids on a Solid Substrate under Pressure

    Energy Technology Data Exchange (ETDEWEB)

    Choudhury, Moutushi Dutta; Chandra, Subrata; Nag, Soma; Tarafdar, Sujata [Condensed Matter Physics Research Centre, Physics Department, Jadavpur University, Kolkata 700032 (India); Das, Shantanu, E-mail: mou15july@gmail.com [Reactor Control Division, Bhabha Atomic Research Center, Trombay, Mumbai 400085 (India)

    2011-09-15

    Strongly non-Newtonian fluids namely, aqueous gels of starch, are shown to exhibit visco-elastic behavior, when subjected to a load. We study arrowroot and potato starch gels. When a droplet of the fluid is sandwiched between two glass plates and compressed, the area of contact between the fluid and plates increases in an oscillatory manner. This is unlike Newtonian fluids, where the area increases monotonically in a similar situation. The periphery moreover, develops an instability, which looks similar to Saffman Taylor fingers. This is not normally seen under compression. The loading history is also found to affect the manner of spreading. We attempt to describe the non-Newtonian nature of the fluid through a visco-elastic model incorporating generalized calculus. This is shown to reproduce qualitatively the oscillatory variation in the surface strain.

  5. Dynamic characteristics of Non Newtonian fluid Squeeze film damper

    Science.gov (United States)

    Palaksha, C. P.; Shivaprakash, S.; Jagadish, H. P.

    2016-09-01

    The fluids which do not follow linear relationship between rate of strain and shear stress are termed as non-Newtonian fluid. The non-Newtonian fluids are usually categorized as those in which shear stress depends on the rates of shear only, fluids for which relation between shear stress and rate of shear depends on time and the visco inelastic fluids which possess both elastic and viscous properties. It is quite difficult to provide a single constitutive relation that can be used to define a non-Newtonian fluid due to a great diversity found in its physical structure. Non-Newtonian fluids can present a complex rheological behaviour involving shear-thinning, viscoelastic or thixotropic effects. The rheological characterization of complex fluids is an important issue in many areas. The paper analyses the damping and stiffness characteristics of non-Newtonian fluids (waxy crude oil) used in squeeze film dampers using the available literature for viscosity characterization. Damping and stiffness characteristic will be evaluated as a function of shear strain rate, temperature and percentage wax concentration etc.

  6. Experimental and CFD flow studies in an intracranial aneurysm model with Newtonian and non-Newtonian fluids.

    Science.gov (United States)

    Frolov, S V; Sindeev, S V; Liepsch, D; Balasso, A

    2016-05-18

    According to the clinical data, flow conditions play a major role in the genesis of intracranial aneurysms. The disorder of the flow structure is the cause of damage of the inner layer of the vessel wall, which leads to the development of cerebral aneurysms. Knowledge of the alteration of the flow field in the aneurysm region is important for treatment. The aim is to study quantitatively the flow structure in an patient-specific aneurysm model of the internal carotid artery using both experimental and computational fluid dynamics (CFD) methods with Newtonian and non-Newtonian fluids. A patient-specific geometry of aneurysm of the internal carotid artery was used. Patient data was segmented and smoothed to obtain geometrical model. An elastic true-to-scale silicone model was created with stereolithography. For initial investigation of the blood flow, the flow was visualized by adding particles into the silicone model. The precise flow velocity measurements were done using 1D Laser Doppler Anemometer with a spatial resolution of 50 μ m and a temporal resolution of 1 ms. The local velocity measurements were done at a distance of 4 mm to each other. A fluid with non-Newtonian properties was used in the experiment. The CFD simulations for unsteady-state problem were done using constructed hexahedral mesh for Newtonian and non-Newtonian fluids. Using 1D laser Doppler Anemometer the minimum velocity magnitude at the end of systole -0.01 m/s was obtained in the aneurysm dome while the maximum velocity 1 m/s was at the center of the outlet segment. On central cross section of the aneurysm the maximum velocity value is only 20% of the average inlet velocity. The average velocity on the cross-section is only 11% of the inlet axial velocity. Using the CFD simulation the wall shear stresses for Newtonian and non-Newtonian fluid at the end of systolic phase (t= 0.25 s) were computed. The wall shear stress varies from 3.52 mPa (minimum value) to 10.21 Pa (maximum value) for the

  7. Force effects on rotor of squeeze film damper using Newtonian and non-Newtonian fluid

    Science.gov (United States)

    Dominik, Šedivý; Petr, Ferfecki; Simona, Fialová

    2017-09-01

    This article presents the evaluation of force effects on rotor of squeeze film damper. Rotor is eccentric placed and its motion is translate-circular. The amplitude of rotor motion is smaller than its initial eccentricity. The force effects are calculated from pressure and viscous forces which were gained by using computational modeling. Two types of fluid were considered as filling of damper. First type of fluid is Newtonian (has constant viscosity) and second type is magnetorheological fluid (does not have constant viscosity). Viscosity of non-Newtonian fluid is given using Bingham rheology model. Yield stress is a function of magnetic induction which is described by many variables. The most important variables of magnetic induction are electric current and gap width which is between rotor and stator. Comparison of application two given types of fluids is shown in results.

  8. Verification of vertically rotating flume using non-newtonian fluids

    Science.gov (United States)

    Huizinga, R.J.

    1996-01-01

    Three tests on non-Newtonian fluids were used to verify the use of a vertically rotating flume (VRF) for the study of the rheological properties of debris flow. The VRF is described and a procedure for the analysis of results of tests made with the VRF is presented. The major advantages of the VRF are a flow field consistent with that found in nature, a large particle-diameter threshold, inexpensive operation, and verification using several different materials; the major limitations are a lack of temperature control and a certain error incurred from the use of the Bingham plastic model to describe a more complex phenomenon. Because the VRF has been verified with non-Newtonian fluids as well as Newtonian fluids, it can be used to measure the rheological properties of coarse-grained debris-flow materials.

  9. Transport phenomena in Newtonian fluids a concise primer

    CERN Document Server

    Olsson, Per

    2013-01-01

    This short primer provides a concise and tutorial-style introduction to transport phenomena in Newtonian fluids , in particular the transport of mass, energy and momentum.  The reader will find detailed derivations of the transport equations for these phenomena, as well as selected analytical solutions to the transport equations in some simple geometries. After a brief introduction to the basic mathematics used in the text, Chapter 2, which deals with momentum transport, presents a derivation of the Navier-Stokes-Duhem equation describing the basic flow in a Newtonian fluid.  Also provided at

  10. On Laminar Flow of Non-Newtonian Fluids in Porous Media

    KAUST Repository

    Fayed, Hassan E.

    2015-10-20

    Flow of generalized Newtonian fluids in porous media can be modeled as a bundle of capillary tubes or a pore-scale network. In general, both approaches rely on the solution of Hagen–Poiseuille equation using power law to estimate the variations in the fluid viscosity due to the applied shear rate. Despite the effectiveness and simplicity, power law tends to provide unrealistic values for the effective viscosity especially in the limits of zero and infinite shear rates. Here, instead of using power law, Carreau model (bubbles, drops, and particles in non-Newtonian fluids. Taylor & Francis Group, New York, 2007) is used to determine the effective viscosity as a function of the shear strain rate. Carreau model can predict accurately the variation in the viscosity at all shear rates and provide more accurate solution for the flow physics in a single pore. Using the results for a single pore, normalized Fanning friction coefficient has been calculated and plotted as a function of the newly defined Reynolds number based on pressure gradient. For laminar flow, the variation in the friction coefficient with Reynolds number has been plotted and scaled. It is observed that generalized Newtonian fluid flows show Newtonian nature up to a certain Reynolds number. At high Reynolds number, deviation from the Newtonian behavior is observed. The main contribution of this paper is to present a closed-form solution for the flow in a single pore using Carreau model, which allows for fast evaluation of the relationship between flux and pressure gradient in an arbitrary pore diameter. In this way, we believe that our development will open the perspectives for using Carreau models in pore-network simulations at low computational costs to obtain more accurate prediction for generalized Newtonian fluid flows in porous media.

  11. On Laminar Flow of Non-Newtonian Fluids in Porous Media

    KAUST Repository

    Fayed, Hassan E.; Sheikh, Nadeem A.; Iliev, Oleg

    2015-01-01

    Flow of generalized Newtonian fluids in porous media can be modeled as a bundle of capillary tubes or a pore-scale network. In general, both approaches rely on the solution of Hagen–Poiseuille equation using power law to estimate the variations in the fluid viscosity due to the applied shear rate. Despite the effectiveness and simplicity, power law tends to provide unrealistic values for the effective viscosity especially in the limits of zero and infinite shear rates. Here, instead of using power law, Carreau model (bubbles, drops, and particles in non-Newtonian fluids. Taylor & Francis Group, New York, 2007) is used to determine the effective viscosity as a function of the shear strain rate. Carreau model can predict accurately the variation in the viscosity at all shear rates and provide more accurate solution for the flow physics in a single pore. Using the results for a single pore, normalized Fanning friction coefficient has been calculated and plotted as a function of the newly defined Reynolds number based on pressure gradient. For laminar flow, the variation in the friction coefficient with Reynolds number has been plotted and scaled. It is observed that generalized Newtonian fluid flows show Newtonian nature up to a certain Reynolds number. At high Reynolds number, deviation from the Newtonian behavior is observed. The main contribution of this paper is to present a closed-form solution for the flow in a single pore using Carreau model, which allows for fast evaluation of the relationship between flux and pressure gradient in an arbitrary pore diameter. In this way, we believe that our development will open the perspectives for using Carreau models in pore-network simulations at low computational costs to obtain more accurate prediction for generalized Newtonian fluid flows in porous media.

  12. Front‐tracking simulations of bubbles rising in non‐Newtonian fluids

    OpenAIRE

    Battistella, Alessandro; Van Schijndel, J.G.; Baltussen, Maike W.

    2017-01-01

    In the wide and complex field of multiphase flows, bubbly flows with non-Newtonian liquids are encountered in several important applications, such as in polymer solutions or fermentation broths. Despite the widespread application of non-Newtonian liquids, most of the models and closures used in industry are valid for Newtonian fluids only, if not even restricted to air-water systems. However, it is well known that the non-Newtonian rheology significantly influences the liquid and bubble behav...

  13. Boundary layer for non-newtonian fluids on curved surfaces

    International Nuclear Information System (INIS)

    Stenger, N.

    1981-04-01

    By using the basic equation of fluid motion (conservation of mass and momentum) the boundary layer parameters for a Non-Newtonian, incompressible and laminar fluid flow, has been evaluated. As a test, the flat plate boundary layer is first analized and afterwards, a case with pressure gradient, allowing separation, is studied. In the case of curved surfaces, the problem is first developed in general and afterwards particularized to a circular cylinder. Finally suction and slip in the flow interface are examined. The power law model is used to represent the stress strain relationship in Non-Newtonian flow. By varying the fluid exponent one can then, have an idea of how the Non-Newtonian behavior of the flow influences the parameters of the boundary layer. Two equations, in an appropriate coordinate system have been obtained after an order of magnitude analysis of the terms in the equations of motion is performed. (Author) [pt

  14. Non-Newtonian fluid structure interaction in flexible biomimetic microchannels

    Science.gov (United States)

    Kiran, M.; Dasgupta, Sunando; Chakraborty, Suman

    2017-11-01

    To investigate the complex fluid structure interactions in a physiologically relevant microchannel with deformable wall and non-Newtonian fluid that flows within it, we fabricated cylindrical microchannels of various softness out of PDMS. Experiments to measure the transient pressure drop across the channel were carried out with high sampling frequencies to capture the intricate flow physics. In particular, we showed that the waveforms varies greatly for each of the non-Newtonian and Newtonian cases for both non-deformable and deformable microchannels in terms of the peak amplitude, r.m.s amplitude and the crest factor. In addition, we carried out frequency sweep experiments to evaluate the frequency response of the system. We believe that these results will aid in the design of polymer based microfluidic phantoms for arterial FSI studies, and in particular for studying blood analog fluids in cylindrical microchannels as well as developing frequency specific Lab-on-chip systems for medical diagnostics.

  15. Calculation of the Pitot tube correction factor for Newtonian and non-Newtonian fluids.

    Science.gov (United States)

    Etemad, S Gh; Thibault, J; Hashemabadi, S H

    2003-10-01

    This paper presents the numerical investigation performed to calculate the correction factor for Pitot tubes. The purely viscous non-Newtonian fluids with the power-law model constitutive equation were considered. It was shown that the power-law index, the Reynolds number, and the distance between the impact and static tubes have a major influence on the Pitot tube correction factor. The problem was solved for a wide range of these parameters. It was shown that employing Bernoulli's equation could lead to large errors, which depend on the magnitude of the kinetic energy and energy friction loss terms. A neural network model was used to correlate the correction factor of a Pitot tube as a function of these three parameters. This correlation is valid for most Newtonian, pseudoplastic, and dilatant fluids at low Reynolds number.

  16. Conceptual Models of the Climate 2003 Program of Study: Non-Newtonian Geophysical Fluid Dynamics

    National Research Council Canada - National Science Library

    Balmforth, NeiI

    2004-01-01

    Non-Newtonian fluids occur commonly in our world. These fluids, such as toothpaste, saliva, oils, mud and lava, exhibit a number of behaviors that are different from Newtonian fluids and have a number of additional material properties...

  17. Newtonian heating effects in three-dimensional flow of viscoelastic fluid

    International Nuclear Information System (INIS)

    Qayyum, A.; Hayat, T.; Alhuthali, M. S.; Malaikah, H. M.

    2014-01-01

    A mathematical model is constructed to investigate the three-dimensional flow of a non-Newtonian fluid. An incompressible viscoelastic fluid is used in mathematical formulation. The conjugate convective process (in which heat the transfer rate from the bounding surface with a finite capacity is proportional to the local surface temperature) in three-dimensional flow of a differential type of non-Newtonian fluid is analyzed for the first time. Series solutions for the nonlinear differential system are computed. Plots are presented for the description of emerging parameters entering into the problem. It is observed that the conjugate heating phenomenon causes an appreciable increase in the temperature at the stretching wall. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

  18. On approximation of non-Newtonian fluid flow by the finite element method

    Science.gov (United States)

    Svácek, Petr

    2008-08-01

    In this paper the problem of numerical approximation of non-Newtonian fluid flow with free surface is considered. Namely, the flow of fresh concrete is addressed. Industrial mixtures often behaves like non-Newtonian fluids exhibiting a yield stress that needs to be overcome for the flow to take place, cf. [R.B. Bird, R.C. Armstrong, O. Hassager, Dynamics of Polymeric Liquids, vol. 1, Fluid Mechanics, Wiley, New York, 1987; R.P. Chhabra, J.F. Richardson, Non-Newtonian Flow in the Process Industries, Butterworth-Heinemann, London, 1999]. The main interest is paid to the mathematical formulation of the problem and to discretization with the aid of finite element method. The described numerical procedure is applied onto the solution of several problems.

  19. Borehole guided waves in a non-Newtonian (Maxwell) fluid-saturated porous medium

    International Nuclear Information System (INIS)

    Zhi-Wen, Cui; Jin-Xia, Liu; Ke-Xie, Wang; Gui-Jin, Yao

    2010-01-01

    The property of acoustic guided waves generated in a fluid-filled borehole surrounded by a non-Newtonian (Maxwell) fluid-saturated porous formation with a permeable wall is investigated. The influence of non-Newtonian effects on acoustic guided waves such as Stoneley waves, pseudo-Rayleigh waves, flexural waves, and screw waves propagations in a fluid-filled borehole is demonstrated based on the generalized Biot–Tsiklauri model by calculating their velocity dispersion and attenuation coefficients. The corresponding acoustic waveforms illustrate their properties in time domain. The results are also compared with those based on generalized Biot's theory. The results show that the influence of non-Newtonian effect on acoustic guided wave, especially on the attenuation coefficient of guided wave propagation in borehole is noticeable. (classical areas of phenomenology)

  20. Pseudo-Newtonian Equations for Evolution of Particles and Fluids in Stationary Space-times

    Energy Technology Data Exchange (ETDEWEB)

    Witzany, Vojtěch; Lämmerzahl, Claus, E-mail: vojtech.witzany@zarm.uni-bremen.de, E-mail: claus.laemmerzahl@zarm.uni-bremen.de [ZARM, Universität Bremen, Am Fallturm, D-28359 Bremen (Germany)

    2017-06-01

    Pseudo-Newtonian potentials are a tool often used in theoretical astrophysics to capture some key features of a black hole space-time in a Newtonian framework. As a result, one can use Newtonian numerical codes, and Newtonian formalism, in general, in an effective description of important astrophysical processes such as accretion onto black holes. In this paper, we develop a general pseudo-Newtonian formalism, which pertains to the motion of particles, light, and fluids in stationary space-times. In return, we are able to assess the applicability of the pseudo-Newtonian scheme. The simplest and most elegant formulas are obtained in space-times without gravitomagnetic effects, such as the Schwarzschild rather than the Kerr space-time; the quantitative errors are smallest for motion with low binding energy. Included is a ready-to-use set of fluid equations in Schwarzschild space-time in Cartesian and radial coordinates.

  1. Effect of non-Newtonian viscosity on the fluid-dynamic characteristics in stenotic vessels

    Science.gov (United States)

    Huh, Hyung Kyu; Ha, Hojin; Lee, Sang Joon

    2015-08-01

    Although blood is known to have shear-thinning and viscoelastic properties, the effects of such properties on the hemodynamic characteristics in various vascular environments are not fully understood yet. For a quantitative hemodynamic analysis, the refractive index of a transparent blood analogue needs to be matched with that of the flowing conduit in order to minimize the errors according to the distortion of the light. In this study, three refractive index-matched blood analogue fluids with different viscosities are prepared—one Newtonian and two non-Newtonian analogues—which correspond to healthy blood with 45 % hematocrit (i.e., normal non-Newtonian) and obese blood with higher viscosity (i.e., abnormal non-Newtonian). The effects of the non-Newtonian rheological properties of the blood analogues on the hemodynamic characteristics in the post-stenosis region of an axisymmetric stenosis model are experimentally investigated using particle image velocimetry velocity field measurement technique and pathline flow visualization. As a result, the centerline jet flow from the stenosis apex is suppressed by the shear-thinning feature of the blood analogues when the Reynolds number is smaller than 500. The lengths of the recirculation zone for abnormal and normal non-Newtonian blood analogues are 3.67 and 1.72 times shorter than that for the Newtonian analogue at Reynolds numbers smaller than 200. The Reynolds number of the transition from laminar to turbulent flow for all blood analogues increases as the shear-thinning feature increases, and the maximum wall shear stresses in non-Newtonian fluids are five times greater than those in Newtonian fluids. However, the shear-thinning effect on the hemodynamic characteristics is not significant at Reynolds numbers higher than 1000. The findings of this study on refractive index-matched non-Newtonian blood analogues can be utilized in other in vitro experiments, where non-Newtonian features dominantly affect the flow

  2. A Symmetry Particle Method towards Implicit Non‐Newtonian Fluids

    Directory of Open Access Journals (Sweden)

    Yalan Zhang

    2017-02-01

    Full Text Available In this paper, a symmetry particle method, the smoothed particle hydrodynamics (SPH method, is extended to deal with non‐Newtonian fluids. First, the viscous liquid is modeled by a non‐Newtonian fluid flow and the variable viscosity under shear stress is determined by the Carreau‐Yasuda model. Then a pressure correction method is proposed, by correcting density error with individual stiffness parameters for each particle, to ensure the incompressibility of fluid. Finally, an implicit method is used to improve efficiency and stability. It is found that the nonNewtonian behavior can be well displayed in all cases, and the proposed SPH algorithm is stable and efficient.

  3. Attractors of equations of non-Newtonian fluid dynamics

    International Nuclear Information System (INIS)

    Zvyagin, V G; Kondrat'ev, S K

    2014-01-01

    This survey describes a version of the trajectory-attractor method, which is applied to study the limit asymptotic behaviour of solutions of equations of non-Newtonian fluid dynamics. The trajectory-attractor method emerged in papers of the Russian mathematicians Vishik and Chepyzhov and the American mathematician Sell under the condition that the corresponding trajectory spaces be invariant under the translation semigroup. The need for such an approach was caused by the fact that for many equations of mathematical physics for which the Cauchy initial-value problem has a global (weak) solution with respect to the time, the uniqueness of such a solution has either not been established or does not hold. In particular, this is the case for equations of fluid dynamics. At the same time, trajectory spaces invariant under the translation semigroup could not be constructed for many equations of non-Newtonian fluid dynamics. In this connection, a different approach to the construction of trajectory attractors for dissipative systems was proposed in papers of Zvyagin and Vorotnikov without using invariance of trajectory spaces under the translation semigroup and is based on the topological lemma of Shura-Bura. This paper presents examples of equations of non-Newtonian fluid dynamics (the Jeffreys system describing movement of the Earth's crust, the model of motion of weak aqueous solutions of polymers, a system with memory) for which the aforementioned construction is used to prove the existence of attractors in both the autonomous and the non-autonomous cases. At the beginning of the paper there is also a brief exposition of the results of Ladyzhenskaya on the existence of attractors of the two-dimensional Navier-Stokes system and the result of Vishik and Chepyzhov for the case of attractors of the three-dimensional Navier-Stokes system. Bibliography: 34 titles

  4. Downhole Temperature Modeling for Non-Newtonian Fluids in ERD Wells

    Directory of Open Access Journals (Sweden)

    Dan Sui

    2018-04-01

    Full Text Available Having precise information of fluids' temperatures is a critical process during planning of drilling operations, especially for extended reach drilling (ERD. The objective of this paper is to develop an accurate temperature model that can precisely calculate wellbore temperature distributions. An established semi-transient temperature model for vertical wellbores is extended and improved to include deviated wellbores and more realistic scenarios using non-Newtonian fluids. The temperature model is derived based on an energy balance between the formation and the wellbore. Heat transfer is considered steady-state in the wellbore and transient in the formation through the utilization of a formation cooling effect. In this paper, the energy balance is enhanced by implementing heat generation from the drill bit friction and contact friction force caused by drillpipe rotation. A non-linear geothermal gradient as a function of wellbore inclination, is also introduced to extend the model to deviated wellbores. Additionally, the model is improved by considering temperature dependent drilling fluid transport and thermal properties. Transport properties such as viscosity and density are obtained by lab measurements, which allows for investigation of the effect of non-Newtonian fluid behavior on the heat transfer. Furthermore, applying a non-Newtonian pressure loss model enables an opportunity to evaluate the impact of viscous forces on fluid properties and thus the overall heat transfer. Results from sensitivity analysis of both drilling fluid properties and other relevant parameters will be presented. The main application area of this model is related to optimization of drilling fluid, hydraulics, and wellbore design parameters, ultimately leading to safe and cost efficient operations.

  5. Dynamics of magnetic nano-flake vortices in Newtonian fluids

    Energy Technology Data Exchange (ETDEWEB)

    Bazazzadeh, Nasim, E-mail: n.bazazzadeh@gmail.com [Department of Physics, Shahid Beheshti University, G.C., Evin, Tehran 19839 (Iran, Islamic Republic of); Mohseni, Seyed Majid, E-mail: m-mohseni@sbu.ac.ir [Department of Physics, Shahid Beheshti University, G.C., Evin, Tehran 19839 (Iran, Islamic Republic of); Khavasi, Amin, E-mail: khavasi@sharif.edu [Department of Electrical Engineering, Sharif University of Technology, Tehran 11555-4363 (Iran, Islamic Republic of); Zibaii, Mohammad Ismail, E-mail: mizibaye@gmail.com [Laser and Plasma Research Institute, Shahid Beheshti University, G.C., Evin, Tehran 19839 (Iran, Islamic Republic of); Movahed, S.M.S., E-mail: m_movahed@sbu.ac.ir [Department of Physics, Shahid Beheshti University, G.C., Evin, Tehran 19839 (Iran, Islamic Republic of); Jafari, G.R., E-mail: gjafari@gmail.com [Department of Physics, Shahid Beheshti University, G.C., Evin, Tehran 19839 (Iran, Islamic Republic of)

    2016-12-01

    We study the rotational motion of nano-flake ferromagnetic disks suspended in a Newtonian fluid, as a potential material owing the vortex-like magnetic configuration. Using analytical expressions for hydrodynamic, magnetic and Brownian torques, the stochastic angular momentum equation is determined in the dilute limit conditions under applied magnetic field. Results are compared against experimental ones and excellent agreement is observed. We also estimate the uncertainty in the orientation of the disks due to the Brownian torque when an external magnetic field aligns them. Interestingly, this uncertainty is roughly proportional to the ratio of thermal energy of fluid to the magnetic energy stored in the disks. Our approach can be implemented in many practical applications including biotechnology and multi-functional fluidics. - Highlights: • The rotational motion of magnetic-vortex microdiscs in a Newtonian fluid is studied. • Results are compared against experimental ones and excellent agreement is observed. • The uncertainty in the orientation of the microdiscs is analytically derived.

  6. Secondary flow in a curved artery model with Newtonian and non-Newtonian blood-analog fluids

    Science.gov (United States)

    Najjari, Mohammad Reza; Plesniak, Michael W.

    2016-11-01

    Steady and pulsatile flows of Newtonian and non-Newtonian fluids through a 180°-curved pipe were investigated using particle image velocimetry (PIV). The experiment was inspired by physiological pulsatile flow through large curved arteries, with a carotid artery flow rate imposed. Sodium iodide (NaI) and sodium thiocyanate (NaSCN) were added to the working fluids to match the refractive index (RI) of the test section to eliminate optical distortion. Rheological measurements revealed that adding NaI or NaSCN changes the viscoelastic properties of non-Newtonian solutions and reduces their shear-thinning property. Measured centerline velocity profiles in the upstream straight pipe agreed well with an analytical solution. In the pulsatile case, secondary flow structures, i.e. deformed-Dean, Dean, Wall and Lyne vortices, were observed in various cross sections along the curved pipe. Vortical structures at each cross section were detected using the d2 vortex identification method. Circulation analysis was performed on each vortex separately during the systolic deceleration phase, and showed that vortices split and rejoin. Secondary flow structures in steady flows were found to be morphologically similar to those in pulsatile flows for sufficiently high Dean number. supported by the George Washington University Center for Biomimetics and Bioinspired Engineering.

  7. External gear pumps operating with non-Newtonian fluids: Modelling and experimental validation

    Science.gov (United States)

    Rituraj, Fnu; Vacca, Andrea

    2018-06-01

    External Gear Pumps are used in various industries to pump non-Newtonian viscoelastic fluids like plastics, paints, inks, etc. For both design and analysis purposes, it is often a matter of interest to understand the features of the displacing action realized by meshing of the gears and the description of the behavior of the leakages for this kind of pumps. However, very limited work can be found in literature about methodologies suitable to model such phenomena. This article describes the technique of modelling external gear pumps that operate with non-Newtonian fluids. In particular, it explains how the displacing action of the unit can be modelled using a lumped parameter approach which involves dividing fluid domain into several control volumes and internal flow connections. This work is built upon the HYGESim simulation tool, conceived by the authors' research team in the last decade, which is for the first time extended for the simulation of non-Newtonian fluids. The article also describes several comparisons between simulation results and experimental data obtained from numerous experiments performed for validation of the presented methodology. Finally, operation of external gear pump with fluids having different viscosity characteristics is discussed.

  8. A new 3D immersed boundary method for non-Newtonian fluid-structure-interaction with application

    Science.gov (United States)

    Zhu, Luoding

    2017-11-01

    Motivated by fluid-structure-interaction (FSI) phenomena in life sciences (e.g., motions of sperm and cytoskeleton in complex fluids), we introduce a new immersed boundary method for FSI problems involving non-Newtonian fluids in three dimensions. The non-Newtonian fluids are modelled by the FENE-P model (including the Oldroyd-B model as an especial case) and numerically solved by a lattice Boltzmann scheme (the D3Q7 model). The fluid flow is modelled by the lattice Boltzmann equations and numerically solved by the D3Q19 model. The deformable structure and the fluid-structure-interaction are handled by the immersed boundary method. As an application, we study a FSI toy problem - interaction of an elastic plate (flapped at its leading edge and restricted nowhere else) with a non-Newtonian fluid in a 3D flow. Thanks to the support of NSF-DMS support under research Grant 1522554.

  9. Electro-osmosis of non-Newtonian fluids in porous media using lattice Poisson-Boltzmann method.

    Science.gov (United States)

    Chen, Simeng; He, Xinting; Bertola, Volfango; Wang, Moran

    2014-12-15

    Electro-osmosis in porous media has many important applications in various areas such as oil and gas exploitation and biomedical detection. Very often, fluids relevant to these applications are non-Newtonian because of the shear-rate dependent viscosity. The purpose of this study was to investigate the behaviors and physical mechanism of electro-osmosis of non-Newtonian fluids in porous media. Model porous microstructures (granular, fibrous, and network) were created by a random generation-growth method. The nonlinear governing equations of electro-kinetic transport for a power-law fluid were solved by the lattice Poisson-Boltzmann method (LPBM). The model results indicate that: (i) the electro-osmosis of non-Newtonian fluids exhibits distinct nonlinear behaviors compared to that of Newtonian fluids; (ii) when the bulk ion concentration or zeta potential is high enough, shear-thinning fluids exhibit higher electro-osmotic permeability, while shear-thickening fluids lead to the higher electro-osmotic permeability for very low bulk ion concentration or zeta potential; (iii) the effect of the porous medium structure depends significantly on the constitutive parameters: for fluids with large constitutive coefficients strongly dependent on the power-law index, the network structure shows the highest electro-osmotic permeability while the granular structure exhibits the lowest permeability on the entire range of power law indices considered; when the dependence of the constitutive coefficient on the power law index is weaker, different behaviors can be observed especially in case of strong shear thinning. Copyright © 2014 Elsevier Inc. All rights reserved.

  10. Post-Newtonian reference ellipsoid for relativistic geodesy

    Science.gov (United States)

    Kopeikin, Sergei; Han, Wenbiao; Mazurova, Elena

    2016-02-01

    We apply general relativity to construct the post-Newtonian background manifold that serves as a reference spacetime in relativistic geodesy for conducting a relativistic calculation of the geoid's undulation and the deflection of the plumb line from the vertical. We chose an axisymmetric ellipsoidal body made up of a perfect homogeneous fluid uniformly rotating around a fixed axis, as a source generating the reference geometry of the background manifold through Einstein's equations. We then reformulate and extend hydrodynamic calculations of rotating fluids done by a number of previous researchers for astrophysical applications to the realm of relativistic geodesy to set up algebraic equations defining the shape of the post-Newtonian reference ellipsoid. To complete this task, we explicitly perform all integrals characterizing gravitational field potentials inside the fluid body and represent them in terms of the elementary functions depending on the eccentricity of the ellipsoid. We fully explore the coordinate (gauge) freedom of the equations describing the post-Newtonian ellipsoid and demonstrate that the fractional deviation of the post-Newtonian level surface from the Maclaurin ellipsoid can be made much smaller than the previously anticipated estimate based on the astrophysical application of the coordinate gauge advocated by Bardeen and Chandrasekhar. We also derive the gauge-invariant relations of the post-Newtonian mass and the constant angular velocity of the rotating fluid with the parameters characterizing the shape of the post-Newtonian ellipsoid including its eccentricity, a semiminor axis, and a semimajor axis. We formulate the post-Newtonian theorems of Pizzetti and Clairaut that are used in geodesy to connect the geometric parameters of the reference ellipsoid to the physically measurable force of gravity at the pole and equator of the ellipsoid. Finally, we expand the post-Newtonian geodetic equations describing the post-Newtonian ellipsoid to

  11. Non-Newtonian fluid flow in annular pipes and entropy generation ...

    Indian Academy of Sciences (India)

    analytical solution for the flow of third-grade non-Newtonian fluid in a pipe .... where c1,c2,d1,d2,t0,1,2...7,h1,h2,k1,2... ,12,m1 and m2 are defined as ..... Yurusoy M 2004 Flow of a third grade fluid between concentric circular cylinders. Math.

  12. Investigation of the fluid flow dynamic parameters for Newtonian and non-Newtonian materials: an approach to understanding the fluid flow-like structures within fault zones

    Science.gov (United States)

    Tanaka, H.; Shiomi, Y.; Ma, K.-F.

    2017-11-01

    To understand the fault zone fluid flow-like structure, namely the ductile deformation structure, often observed in the geological field (e.g., Ramsay and Huber The techniques of modern structure geology, vol. 1: strain analysis, Academia Press, London, 1983; Hobbs and Ord Structure geology: the mechanics of deforming metamorphic rocks, Vol. I: principles, Elsevier, Amsterdam, 2015), we applied a theoretical approach to estimate the rate of deformation, the shear stress and the time to form a streak-line pattern in the boundary layer of viscous fluids. We model the dynamics of streak lines in laminar boundary layers for Newtonian and pseudoplastic fluids and compare the results to those obtained via laboratory experiments. The structure of deformed streak lines obtained using our model is consistent with experimental observations, indicating that our model is appropriate for understanding the shear rate, flow time and shear stress based on the profile of deformed streak lines in the boundary layer in Newtonian and pseudoplastic viscous materials. This study improves our understanding of the transportation processes in fluids and of the transformation processes in fluid-like materials. Further application of this model could facilitate understanding the shear stress and time history of the fluid flow-like structure of fault zones observed in the field.[Figure not available: see fulltext.

  13. Gass-Assisted Displacement of Non-Newtonian Fluids

    DEFF Research Database (Denmark)

    Rasmussen, Henrik Koblitz; Eriksson, Torbjörn Gerhard

    2003-01-01

    in a circular cylinder. This is a simple model system used to investigate the gas-fluid displacement, as the problem is reduced to an axis-symmetric flow problem. The understanding of this process is relevant for the geometrically much more complex polymer processing operation Gas-assisted injection moulding...... (GAIM). This is a process, where a mould is filled partly with a polymer melt followed by the injection of inert gas into the core of the polymer melt. The numerical analysis of the fluid flow concerning the experimental observations data in these publications is all based on Newtonian or general...... equation of Boger fluids is the Oldroyd-B model. This model has, with success, been able to describe the complex flow behaviours of Boger fluid. Though, refinements in the flow analysis can be obtained using more complex constitutive models. To keep the flow analysis as simple as possible the Oldroyd...

  14. The quantification of hemodynamic parameters downstream of a Gianturco Zenith stent wire using newtonian and non-newtonian analog fluids in a pulsatile flow environment.

    Science.gov (United States)

    Walker, Andrew M; Johnston, Clifton R; Rival, David E

    2012-11-01

    Although deployed in the vasculature to expand vessel diameter and improve blood flow, protruding stent struts can create complex flow environments associated with flow separation and oscillating shear gradients. Given the association between magnitude and direction of wall shear stress (WSS) and endothelial phenotype expression, accurate representation of stent-induced flow patterns is critical if we are to predict sites susceptible to intimal hyperplasia. Despite the number of stents approved for clinical use, quantification on the alteration of hemodynamic flow parameters associated with the Gianturco Z-stent is limited in the literature. In using experimental and computational models to quantify strut-induced flow, the majority of past work has assumed blood or representative analogs to behave as Newtonian fluids. However, recent studies have challenged the validity of this assumption. We present here the experimental quantification of flow through a Gianturco Z-stent wire in representative Newtonian and non-Newtonian blood analog environments using particle image velocimetry (PIV). Fluid analogs were circulated through a closed flow loop at physiologically appropriate flow rates whereupon PIV snapshots were acquired downstream of the wire housed in an acrylic tube with a diameter characteristic of the carotid artery. Hemodynamic parameters including WSS, oscillatory shear index (OSI), and Reynolds shear stresses (RSS) were measured. Our findings show that the introduction of the stent wire altered downstream hemodynamic parameters through a reduction in WSS and increases in OSI and RSS from nonstented flow. The Newtonian analog solution of glycerol and water underestimated WSS while increasing the spatial coverage of flow reversal and oscillatory shear compared to a non-Newtonian fluid of glycerol, water, and xanthan gum. Peak RSS were increased with the Newtonian fluid, although peak values were similar upon a doubling of flow rate. The introduction of the

  15. Flocking particles in a non-Newtonian shear thickening fluid

    Science.gov (United States)

    Mucha, Piotr B.; Peszek, Jan; Pokorný, Milan

    2018-06-01

    We prove the existence of strong solutions to the Cucker–Smale flocking model coupled with an incompressible viscous non-Newtonian fluid with the stress tensor of a power–law structure for . The fluid part of the system admits strong solutions while the solutions to the CS part are weak. The coupling is performed through a drag force on a periodic spatial domain . Additionally, we construct a Lyapunov functional determining the large time behavior of solutions to the system.

  16. Introducing Non-Newtonian Fluid Mechanics Computations with Mathematica in the Undergraduate Curriculum

    Science.gov (United States)

    Binous, Housam

    2007-01-01

    We study four non-Newtonian fluid mechanics problems using Mathematica[R]. Constitutive equations describing the behavior of power-law, Bingham and Carreau models are recalled. The velocity profile is obtained for the horizontal flow of power-law fluids in pipes and annuli. For the vertical laminar film flow of a Bingham fluid we determine the…

  17. CFD-PBM Coupled Simulation of an Airlift Reactor with Non-Newtonian Fluid

    Directory of Open Access Journals (Sweden)

    Han Mei

    2017-09-01

    Full Text Available Hydrodynamics of an AirLift Reactor (ALR with tap water and non-Newtonian fluid was studied experimentally and by numerical simulations. The Population Balance Model (PBM with multiple breakup and coalescence mechanisms was used to describe bubble size characteristics in the ALR. The interphase forces for closing the two-fluid model were formulated by considering the effect of Bubble Size Distribution (BSD. The BSD in the ALR obtained from the coupled Computational Fluid Dynamics (CFD-PBM model was validated against results from digital imaging measurements. The simulated velocity fields of both the gas and liquid phases were compared to measured fields obtained with Particle Image Velocimetry (PIV. The simulated results show different velocity field profile features at the top of the ALR between tap water and non-Newtonian fluid, which are in agreement with experiments. In addition, good agreement between simulations and experiments was obtained in terms of overall gas holdup and bubble Sauter mean diameter.

  18. Conditions of equilibrium of a rotating ideal fluid in the parametrized post-Newtonian formalism

    International Nuclear Information System (INIS)

    Bondarenko, N.P.

    1986-01-01

    Conditions of equilibrium of a rotating ideal fluid in parametrized post-Newtonian hydrodynamics are obtained by the variational method. They generalize the analogous equilibrium conditions in the post-Newtonian approximation of the general theory of relativity. A conservation law for the total energy is obtained by integrating the equations of motion

  19. Numerical study on the heat transfer performance of non-Newtonian fluid flow in a manifold microchannel heat sink

    International Nuclear Information System (INIS)

    Li, Si-Ning; Zhang, Hong-Na; Li, Xiao-Bin; Li, Qian; Li, Feng-Chen; Qian, Shizhi; Joo, Sang Woo

    2017-01-01

    Highlights: • Heat transfer performance of non-Newtonian fluid flow in a MHS is studied. • Pseudo-plastic fluid flow can clearly promote the heat transfer efficiency in MMC. • Heat transfer enhancement is attributed to the emergence of secondary flow. • The heat transfer uniformity can also be improved by pseudo-plastic fluid flow. - Abstract: As the miniaturization and integration become the leading trend of the micro-electro-mechanical systems, it is of great significance to improve the microscaled heat transfer performance. This paper presents a three-dimensional (3D) numerical simulation on the flow characteristics and heat transfer performance of non-Newtonian fluid flow in a manifold microchannel (MMC) heat sink and traditional microchannel (TMC) heat sink. The non-Newtonian fluid was described by the power-law model. The analyses concentrated on the non-Newtonian fluid effect on the heat transfer performance, including the heat transfer efficiency and uniformity of temperature distribution, as well as the influence of inlet/outlet configurations on fluid flow and heat transfer. Comparing with Newtonian fluid flow, pseudo-plastic fluid could reduce the drag resistance in both MMC and TMC, while the dilatant fluid brought in quite larger drag resistance. For the heat transfer performance, the introduction of pseudo-plastic fluid flow greatly improved the heat transfer efficiency owing to the generation of secondary flow due to the shear-thinning property. Besides, the temperature distribution in MMC was more uniform by using pseudo-plastic fluid. Moreover, the inlet/outlet configuration was also important for the design and arrangement of microchannel heat sinks, since the present work showed that the maximum temperature was prone to locating in the corners near the inlet and outlet. This work provides guidance for optimal design of small-scale heat transfer devices in many cooling applications, such as biomedical chips, electronic systems, and

  20. Lie group analysis of flow and heat transfer of non-Newtonian

    Indian Academy of Sciences (India)

    law nanofluid over a stretching surface under convective boundary conditions and temperature-dependent fluid viscosity has been numerically investigated. The power-law rheology is adopted to describe non-Newtonian characteristics of the ...

  1. Displacement of one Newtonian fluid by another: density effects in axial annular flow

    DEFF Research Database (Denmark)

    Szabo, Peter; Hassager, Ole

    1997-01-01

    The arbitrary Lagrange-Euler (ALE) finite elementtechnique is used to simulate 3D displacement oftwo immiscible Newtonian fluids in vertical annular wells. For equally viscous fluids the effect of distinct fluid densities is investigated in the region of low to intermediate Reynolds numbers......, the efficiency of the displacement is analysed for various flow situations....

  2. Characterization of the transition of regimes in a non-newtonian fluids in ducts

    International Nuclear Information System (INIS)

    Santana, C.C.; Ataide, C.H.; Massarani, G.

    1983-01-01

    By using own experimental data and also those obtained from the literature, the velocities at which transition from laminar to turbulent flows occurs are analysed in time-independent non-newtonian fluids, through the relationship between generalized Reynolds numbers and the rheological fluid parameters. (Author) [pt

  3. Hydrodynamically Coupled Brownian Dynamics simulations for flow on non-Newtonian fluids

    NARCIS (Netherlands)

    Ahuja, Vishal Raju

    2018-01-01

    This thesis deals with model development for particle-based flow simulations of non-Newtonian fluids such as polymer solutions. A novel computational technique called Hydrodynamically Coupled Brownian Dynamics (HCBD) is presented in this thesis. This technique essentially couples the Brownian motion

  4. On the existence of weak solution to the coupled fluid-structure interaction problem for non-Newtonian shear-dependent fluid

    Czech Academy of Sciences Publication Activity Database

    Hundertmark-Zaušková, A.; Lukáčová-Medviďová, M.; Nečasová, Šárka

    2016-01-01

    Roč. 68, č. 1 (2016), s. 193-243 ISSN 0025-5645 R&D Projects: GA ČR(CZ) GAP201/11/1304 Institutional support: RVO:67985840 Keywords : non-Newtonian fluids * fluid-structure interaction * shear-thinning fluids Subject RIV: BA - General Mathematics Impact factor: 0.592, year: 2016 http://projecteuclid.org/euclid.jmsj/1453731541

  5. Asymmetric bubble collapse and jetting in generalized Newtonian fluids

    Science.gov (United States)

    Shukla, Ratnesh K.; Freund, Jonathan B.

    2017-11-01

    The jetting dynamics of a gas bubble near a rigid wall in a non-Newtonian fluid are investigated using an axisymmetric simulation model. The bubble gas is assumed to be homogeneous, with density and pressure related through a polytropic equation of state. An Eulerian numerical description, based on a sharp interface capturing method for the shear-free bubble-liquid interface and an incompressible Navier-Stokes flow solver for generalized fluids, is developed specifically for this problem. Detailed simulations for a range of rheological parameters in the Carreau model show both the stabilizing and destabilizing non-Newtonian effects on the jet formation and impact. In general, for fixed driving pressure ratio, stand-off distance and reference zero-shear-rate viscosity, shear-thinning and shear-thickening promote and suppress jet formation and impact, respectively. For a sufficiently large high-shear-rate limit viscosity, the jet impact is completely suppressed. Thresholds are also determined for the Carreau power-index and material time constant. The dependence of these threshold rheological parameters on the non-dimensional driving pressure ratio and wall stand-off distance is similarly established. Implications for tissue injury in therapeutic ultrasound will be discussed.

  6. Steady flow of non-Newtonian fluids - monotonicity methods in generalized orlicz spaces

    Czech Academy of Sciences Publication Activity Database

    Wróblewska, Aneta

    2010-01-01

    Roč. 72, č. 11 (2010), s. 4136-4147 ISSN 0362-546X Institutional research plan: CEZ:AV0Z10190503 Keywords : non-Newtonian fluid * Orlicz spaces * modular convergence of symmetric gradients * generalized Minty method * smart fluids Subject RIV: BA - General Mathematics Impact factor: 1.279, year: 2010 http://www.sciencedirect.com/science/article/pii/S0362546X10000568

  7. A Numerical Study of Mesh Adaptivity in Multiphase Flows with Non-Newtonian Fluids

    Science.gov (United States)

    Percival, James; Pavlidis, Dimitrios; Xie, Zhihua; Alberini, Federico; Simmons, Mark; Pain, Christopher; Matar, Omar

    2014-11-01

    We present an investigation into the computational efficiency benefits of dynamic mesh adaptivity in the numerical simulation of transient multiphase fluid flow problems involving Non-Newtonian fluids. Such fluids appear in a range of industrial applications, from printing inks to toothpastes and introduce new challenges for mesh adaptivity due to the additional ``memory'' of viscoelastic fluids. Nevertheless, the multiscale nature of these flows implies huge potential benefits for a successful implementation. The study is performed using the open source package Fluidity, which couples an unstructured mesh control volume finite element solver for the multiphase Navier-Stokes equations to a dynamic anisotropic mesh adaptivity algorithm, based on estimated solution interpolation error criteria, and conservative mesh-to-mesh interpolation routine. The code is applied to problems involving rheologies ranging from simple Newtonian to shear-thinning to viscoelastic materials and verified against experimental data for various industrial and microfluidic flows. This work was undertaken as part of the EPSRC MEMPHIS programme grant EP/K003976/1.

  8. Steady flow of non-Newtonian fluids - monotonicity methods in generalized orlicz spaces

    Czech Academy of Sciences Publication Activity Database

    Wróblewska, Aneta

    2010-01-01

    Roč. 72, č. 11 (2010), s. 4136-4147 ISSN 0362-546X Institutional research plan: CEZ:AV0Z10190503 Keywords : non-Newtonian fluid * Orlicz spaces * modular convergence of symmetric gradients * general ized Minty method * smart fluids Subject RIV: BA - General Mathematics Impact factor: 1.279, year: 2010 http://www.sciencedirect.com/science/article/pii/S0362546X10000568

  9. Open mathematical problems regarding non-Newtonian fluids

    International Nuclear Information System (INIS)

    Wilson, Helen J

    2012-01-01

    We present three open problems in the mathematical modelling of the flow of non-Newtonian fluids. The first problem is rather long standing: a discontinuity in the dependence of the rise velocity of a gas bubble on its volume. This is very well characterized experimentally but not, so far, fully reproduced either numerically or analytically. The other two are both instabilities. The first is observed experimentally but never predicted analytically or numerically. In the second instability, numerical studies reproduce the experimental observations but there is as yet no analytical or semi-analytical prediction of the linear instability which must be present. (invited article)

  10. Transverse thermopherotic MHD Oldroyd-B fluid with Newtonian heating

    Science.gov (United States)

    Mehmood, R.; Rana, S.; Nadeem, S.

    2018-03-01

    Hydromagnetic transverse flow of an Oldroyd-B type fluid with suspension of nanoparticles and Newtonian heating effects is conferred in this article. Relaxation and Retardation time effects are taken into consideration. Using suitable transformations physical problem is converted into non-linear ordinary differential equations which are tackled numerically via Runge-Kutta Fehlberg integration scheme. Illustration of embedded constraints on flow characteristics are extracted through graphs. The physical response of velocity, temperature and concentration are investigated computationally. Momentum boundary layer thickness decreases but local heat and mass flux rises for Deborah number and Hartman number. The results provide interesting insights into certain applicable transport phenomena involving hydromagnetic rheological fluids.

  11. Free surface flow of a suspension of rigid particles in a non-Newtonian fluid

    DEFF Research Database (Denmark)

    Svec, Oldrich; Skocek, Jan; Stang, Henrik

    2012-01-01

    A numerical framework capable of predicting the free surface flow of a suspension of rigid particles in a non-Newtonian fluid is described. The framework is a combination of the lattice Boltzmann method for fluid flow, the mass tracking algorithm for free surface representation, the immersed...

  12. Acoustic waveform of continuous bubbling in a non-Newtonian fluid.

    Science.gov (United States)

    Vidal, Valérie; Ichihara, Mie; Ripepe, Maurizio; Kurita, Kei

    2009-12-01

    We study experimentally the acoustic signal associated with a continuous bubble bursting at the free surface of a non-Newtonian fluid. Due to the fluid rheological properties, the bubble shape is elongated, and, when bursting at the free surface, acts as a resonator. For a given fluid concentration, at constant flow rate, repetitive bubble bursting occurs at the surface. We report a modulation pattern of the acoustic waveform through time. Moreover, we point out the existence of a precursor acoustic signal, recorded on the microphone array, previous to each bursting. The time delay between this precursor and the bursting signal is well correlated with the bursting signal frequency content. Their joint modulation through time is driven by the fluid rheology, which strongly depends on the presence of small satellite bubbles trapped in the fluid due to the yield stress.

  13. Comparative PIV and LDA studies of Newtonian and non-Newtonian flows in an agitated tank.

    Science.gov (United States)

    Story, Anna; Jaworski, Zdzisław; Simmons, Mark J; Nowak, Emilia

    2018-01-01

    The paper presents results of an experimental study of the fluid velocity field in a stirred tank equipped with a Prochem Maxflo T (PMT) type impeller which was rotating at a constant frequency of N  = 4.1 or 8.2 s -1 inducing transitional ( Re  = 499 or 1307) or turbulent ( Re  = 2.43 × 10 4 ) flow of the fluid. The experiments were performed for a Newtonian fluid (water) and a non-Newtonian fluid (0.2 wt% aqueous solution of carboxymethyl cellulose, CMC) exhibiting mild viscoelastic properties. Measurements were carried out using laser light scattering on tracer particles which follow the flow (2-D PIV). For both the water and the CMC solution one primary and two secondary circulation loops were observed within the fluid volume; however, the secondary loops were characterized by much lower intensity. The applied PMT-type impeller produced in the Newtonian fluid an axial primary flow, whilst in the non-Newtonian fluid the flow was more radial. The results obtained in the form of the local mean velocity components were in satisfactory agreement with the literature data from LDA. Distribution of the shear rate in the studied system was also analyzed. For the non-Newtonian fluid an area was computed where the elastic force dominates over the viscous one. The area was nearly matching the region occupied by the primary circulation loop.

  14. Analysis of HD Journal Bearings Considering Elastic Deformation and Non-Newtonian Rabinowitsch Fluid Model

    Directory of Open Access Journals (Sweden)

    J. Javorova

    2016-06-01

    Full Text Available The purpose of this paper is to study the performance of a finite length journal bearing, taking into account effects of non-Newtonian Rabinowitsch flow rheology and elastic deformations of the bearing liner. According to the Rabinowitsch fluid model, the cubic-stress constitutive equation is used to account for the non-Newtonian effects of pseudoplastic and dilatant lubricants. Integrating the continuity equation across the film, the nonlinear non-Newtonian Reynolds-type equation is derived. The elasticity part of the problem is solved on the base of Vlassov model of an elastic foundation. The numerical solution of the modified Reynolds equation is carried out by using FDM with over-relaxation technique. The results for steady state bearing performance characteristics have been calculated for various values of nonlinear factor and elasticity parameters. It was concluded that in comparison with the Newtonian lubricants, higher values of film pressure and load carrying capacity have been obtained for dilatant lubricants, while the case was reversed for pseudoplastic lubricants.

  15. Multivariable Real-Time Control of Viscosity Curve for a Continuous Production Process of a Non-Newtonian Fluid

    Directory of Open Access Journals (Sweden)

    Roberto Mei

    2018-01-01

    Full Text Available The application of a multivariable predictive controller to the mixing process for the production of a non-Newtonian fluid is discussed in this work. A data-driven model has been developed to describe the dynamic behaviour of the rheological properties of the fluid as a function of the operating conditions using experimental data collected in a pilot plant. The developed model provides a realistic process representation and it is used to test and verify the multivariable controller, which has been designed to maintain viscosity curves of the non-Newtonian fluid within a given region of the viscosity-vs-shear rate plane in presence of process disturbances occurring in the mixing process.

  16. Direct measurement of the ballistic motion of a freely floating colloid in Newtonian and viscoelastic fluids.

    Science.gov (United States)

    Hammond, Andrew P; Corwin, Eric I

    2017-10-01

    A thermal colloid suspended in a liquid will transition from a short-time ballistic motion to a long-time diffusive motion. However, the transition between ballistic and diffusive motion is highly dependent on the properties and structure of the particular liquid. We directly observe a free floating tracer particle's ballistic motion and its transition to the long-time regime in both a Newtonian fluid and a viscoelastic Maxwell fluid. We examine the motion of the free particle in a Newtonian fluid and demonstrate a high degree of agreement with the accepted Clercx-Schram model for motion in a dense fluid. Measurements of the functional form of the ballistic-to-diffusive transition provide direct measurements of the temperature, viscosity, and tracer radius. We likewise measure the motion in a viscoelastic Maxwell fluid and find a significant disagreement between the theoretical asymptotic behavior and our measured values of the microscopic properties of the fluid. We observe a greatly increased effective mass for a freely moving particle and a decreased plateau modulus.

  17. Experimental model for non-Newtonian fluid viscosity estimation: Fit to mathematical expressions

    Directory of Open Access Journals (Sweden)

    Guillem Masoliver i Marcos

    2017-01-01

    Full Text Available The  construction  process  of  a  viscometer,  developed  in  collaboration  with  a  final  project  student,  is  here  presented.  It  is  intended  to  be  used  by   first  year's  students  to  know  the  viscosity  as  a  fluid  property, for  both  Newtonian  and  non-Newtonian  flows.  Viscosity  determination  is  crucial  for  the  fluids  behaviour knowledge  related  to  their  reologic  and  physical  properties.  These  have  great  implications  in  engineering aspects  such  as  friction  or  lubrication.  With  the  present  experimental  model  device  three  different fluids are  analyzed  (water,  kétchup  and  a  mixture  with  cornstarch  and  water.  Tangential stress is measured versus velocity in order to characterize all the fluids in different thermal conditions. A mathematical fit process is proposed to be done in order to adjust the results to expected analytical expressions, obtaining good results for these fittings, with R2 greater than 0.88 in any case.

  18. CFD simulation of gas and non-Newtonian fluid two-phase flow in anaerobic digesters.

    Science.gov (United States)

    Wu, Binxin

    2010-07-01

    This paper presents an Eulerian multiphase flow model that characterizes gas mixing in anaerobic digesters. In the model development, liquid manure is assumed to be water or a non-Newtonian fluid that is dependent on total solids (TS) concentration. To establish the appropriate models for different TS levels, twelve turbulence models are evaluated by comparing the frictional pressure drops of gas and non-Newtonian fluid two-phase flow in a horizontal pipe obtained from computational fluid dynamics (CFD) with those from a correlation analysis. The commercial CFD software, Fluent12.0, is employed to simulate the multiphase flow in the digesters. The simulation results in a small-sized digester are validated against the experimental data from literature. Comparison of two gas mixing designs in a medium-sized digester demonstrates that mixing intensity is insensitive to the TS in confined gas mixing, whereas there are significant decreases with increases of TS in unconfined gas mixing. Moreover, comparison of three mixing methods indicates that gas mixing is more efficient than mixing by pumped circulation while it is less efficient than mechanical mixing.

  19. Unsteady boundary layer flow and heat transfer of a Casson fluid past an oscillating vertical plate with Newtonian heating.

    Science.gov (United States)

    Hussanan, Abid; Zuki Salleh, Mohd; Tahar, Razman Mat; Khan, Ilyas

    2014-01-01

    In this paper, the heat transfer effect on the unsteady boundary layer flow of a Casson fluid past an infinite oscillating vertical plate with Newtonian heating is investigated. The governing equations are transformed to a systems of linear partial differential equations using appropriate non-dimensional variables. The resulting equations are solved analytically by using the Laplace transform method and the expressions for velocity and temperature are obtained. They satisfy all imposed initial and boundary conditions and reduce to some well-known solutions for Newtonian fluids. Numerical results for velocity, temperature, skin friction and Nusselt number are shown in various graphs and discussed for embedded flow parameters. It is found that velocity decreases as Casson parameters increases and thermal boundary layer thickness increases with increasing Newtonian heating parameter.

  20. Numerical analysis of non-Newtonian rheology effect on hydrocyclone flow field

    Directory of Open Access Journals (Sweden)

    Lin Yang

    2015-03-01

    Full Text Available In view of the limitations of the existing Newton fluid effects on the vortex flow mechanism study, numerical analysis of non Newton fluid effects was presented. Using Reynolds stress turbulence model (RSM and mixed multiphase flow model (Mixture of FLUENT (fluid calculation software and combined with the constitutive equation of apparent viscosity of non-Newtonian fluid, the typical non-Newtonian fluid (drilling fluid, polymer flooding sewage and crude oil as medium and Newton flow field (water as medium were compared by quantitative analysis. Based on the research results of water, the effects of non-Newtonian rheology on the key parameters including the combined vortex motion index n and tangential velocity were analyzed. The study shows that: non-Newtonian rheology has a great effect on tangential velocity and n value, and tangential velocity decreases with non-Newtonian increasing. The three kinds of n values (constant segment are: 0.564(water, 0.769(polymer flooding sewage, 0.708(drilling fluid and their variation amplitudes are larger than Newtonian fluid. The same time, non-Newtonian rheology will lead to the phenomenon of turbulent drag reduction in the vortex flow field. Compared with the existing formula calculation results shown, the calculation result of non-Newtonian rheology is most consistent with the simulation result, and the original theory has large deviations. The study provides reference for theory research of non-Newtonian cyclone separation flow field.

  1. Unsteady boundary layer flow and heat transfer of a Casson fluid past an oscillating vertical plate with Newtonian heating.

    Directory of Open Access Journals (Sweden)

    Abid Hussanan

    Full Text Available In this paper, the heat transfer effect on the unsteady boundary layer flow of a Casson fluid past an infinite oscillating vertical plate with Newtonian heating is investigated. The governing equations are transformed to a systems of linear partial differential equations using appropriate non-dimensional variables. The resulting equations are solved analytically by using the Laplace transform method and the expressions for velocity and temperature are obtained. They satisfy all imposed initial and boundary conditions and reduce to some well-known solutions for Newtonian fluids. Numerical results for velocity, temperature, skin friction and Nusselt number are shown in various graphs and discussed for embedded flow parameters. It is found that velocity decreases as Casson parameters increases and thermal boundary layer thickness increases with increasing Newtonian heating parameter.

  2. On a criterion of incipient motion and entrainment into suspension of a particle from cuttings bed in shear flow of non-Newtonian fluid

    Science.gov (United States)

    Ignatenko, Yaroslav; Bocharov, Oleg; May, Roland

    2017-10-01

    Solids transport is a major issue in high angle wells. Bed-load forms by sediment while transport and accompanied by intermittent contact with stream-bed by rolling, sliding and bouncing. The study presents the results of a numerical simulation of a laminar steady-state flow around a particle at rest and in free motion in a shear flow of Herschel-Bulkley fluid. The simulation was performed using the OpenFOAM open-source CFD package. A criterion for particle incipient motion and entrainment into suspension from cuttings bed (Shields criteria) based on forces and torques balance is discussed. Deflection of the fluid parameters from the ones of Newtonian fluid leads to decreasing of the drag and lift forces and the hydrodynamic moment. Thus, the critical shear stress (Shields parameter) for the considered non-Newtonian fluid must be greater than the one for a Newtonian fluid.

  3. Unsteady free convection flow of a micropolar fluid with Newtonian heating: Closed form solution

    Directory of Open Access Journals (Sweden)

    Hussanan Abid

    2017-01-01

    Full Text Available This article investigates the unsteady free convection flow of a micropolar fluid over a vertical plate oscillating in its own plane with Newtonian heating condition. The problem is modelled in terms of partial differential equations with some physical conditions. Closed form solutions in terms of exponential and complementary error functions of Gauss are obtained by using the Laplace transform technique. They satisfy the governing equations and impose boundary and initial conditions. The present solution in the absence of microrotation reduces to well-known solutions of Newtonian fluid. Graphs are plotted to study the effects of various physical parameters on velocity and microrotation. Numerical results for skin friction and wall couple stress is computed in tables. Apart from the engineering point of view, the present article has strong advantage over the published literature as the exact solutions obtained here can be used as a benchmark for comparison with numerical/ approximate solutions and experimental data.

  4. Nonisothermal flow of a non-Newtonian fluid with viscous heating between two parallel plates

    International Nuclear Information System (INIS)

    Imal, M.; Pinarbasi, A.

    2004-01-01

    In this study the pressure gradient-flow rate relationship for steady-state nonisothermal pressure-driven flow of a non-Newtonian fluid in a channel is investigated including the effect of viscous heating is taken into account. The viscosity of the fluid depends on both temperature and shear-rate. Exponential dependence of viscosity on temperature is modelled through Arrhenius law. Non-Newtonian behaviour of the fluid is modelled according to the Carreau rheological equation, which reflects the characteristics of most polymers adequately with an exponential temperature dependence of viscosity. Flow governing motion and energy balance equations are coupled and solution of this non-linear boundary value problem is found iteratively using a pseudo spectral method based on Chebyshev polynomials. The effect of activation energy parameter and Brinkman number, as well as the power-law index and material time constant on the flow is studied. It is found that while the pressure gradient-flow rate graph is monotonic for certain ranges of flow controlling parameters, there is a large jump in the graph under certain values of these parameters.(1 table and 5 figures are included.)

  5. Modeling of flow of particles in a non-Newtonian fluid using lattice Boltzmann method

    DEFF Research Database (Denmark)

    Skocek, Jan; Svec, Oldrich; Spangenberg, Jon

    2011-01-01

    is necessary. In this contribution, the model at the scale of aggregates is introduced. The conventional lattice Boltzmann method for fluid flow is enriched with the immersed boundary method with direct forcing to simulate the flow of rigid particles in a non- Newtonian liquid. Basic ingredients of the model...

  6. The Effect of Heat Transfer and Polymer Concentration on Non-Newtonian Fluid from Pore-Scale Simulation of Rock X-ray Micro-CT

    Directory of Open Access Journals (Sweden)

    Moussa Tembely

    2017-10-01

    Full Text Available Most of the pore-scale imaging and simulations of non-Newtonian fluid are based on the simplifying geometry of network modeling and overlook the fluid rheology and heat transfer. In the present paper, we developed a non-isothermal and non-Newtonian numerical model of the flow properties at pore-scale by simulation of the 3D micro-CT images using a Finite Volume Method (FVM. The numerical model is based on the resolution of the momentum and energy conservation equations. Owing to an adaptive mesh generation technique and appropriate boundary conditions, rock permeability and mobility are accurately computed. A temperature and concentration-dependent power-law viscosity model in line with the experimental measurement of the fluid rheology is adopted. The model is first applied at isothermal condition to 2 benchmark samples, namely Fontainebleau sandstone and Grosmont carbonate, and is found to be in good agreement with the Lattice Boltzmann method (LBM. Finally, at non-isothermal conditions, an effective mobility is introduced that enables to perform a numerical sensitivity study to fluid rheology, heat transfer, and operating conditions. While the mobility seems to evolve linearly with polymer concentration in agreement with a derived theoretical model, the effect of the temperature seems negligible by comparison. However, a sharp contrast is found between carbonate and sandstone under the effect of a constant temperature gradient. Besides concerning the flow index and consistency factor, a master curve is derived when normalizing the mobility for both the carbonate and the sandstone.

  7. EXPERIMENTAL BUBBLE FORMATION IN A LARGE SCALE SYSTEM FOR NEWTONIAN AND NONNEWTONIAN FLUIDS

    Energy Technology Data Exchange (ETDEWEB)

    Leishear, R; Michael Restivo, M

    2008-06-26

    The complexities of bubble formation in liquids increase as the system size increases, and a photographic study is presented here to provide some insight into the dynamics of bubble formation for large systems. Air was injected at the bottom of a 28 feet tall by 30 inch diameter column. Different fluids were subjected to different air flow rates at different fluid depths. The fluids were water and non-Newtonian, Bingham plastic fluids, which have yield stresses requiring an applied force to initiate movement, or shearing, of the fluid. Tests showed that bubble formation was significantly different in the two types of fluids. In water, a field of bubbles was formed, which consisted of numerous, distributed, 1/4 to 3/8 inch diameter bubbles. In the Bingham fluid, large bubbles of 6 to 12 inches in diameter were formed, which depended on the air flow rate. This paper provides comprehensive photographic results related to bubble formation in these fluids.

  8. Bubble coalescence in a Newtonian fluid

    Science.gov (United States)

    Garg, Vishrut; Basaran, Osman

    2017-11-01

    Bubble coalescence plays a central role in the hydrodynamics of gas-liquid systems such as bubble column reactors, spargers, and foams. Two bubbles approaching each other at velocity V coalesce when the thin film between them ruptures, which is often the rate-limiting step. Experimental studies of this system are difficult, and recent works provide conflicting results on the effect of V on coalescence times. We simulate the head-on approach of two bubbles of equal radii R in an incompressible Newtonian fluid (density ρ, viscosity μ, and surface tension σ) by solving numerically the free boundary problem comprised of the Navier Stokes and continuity equations. Simulations are made challenging by the existence of highly disparate lengthscales, i.e. film thickness and drop radii, which are resolved by using the method of elliptic mesh generation. For a given liquid, the bubbles are shown to coalesce for all velocities below a critical value. The effects of Ohnesorge number Oh = μ /√{ ρσR } on coalescence time and critical velocity are also investigated.

  9. Flow of a non-Newtonian fluid through channels with permeable wall

    Energy Technology Data Exchange (ETDEWEB)

    Martins-Costa, Maria Laura [Universidade Federal Fluminense, Niteroi, RJ (Brazil). Dept. de Engenharia Mecanica. Lab. de Matematica Teorica e Aplicada]. E-mail: laura@mec.uff.br; Gama, Rogerio M. Saldanha da [Laboratorio Nacional de Computacao Cientifica (LNCC), Petropolis, RJ (Brazil)]. E-mail: rsgama@domain.com.br; Frey, Sergio [Rio Grande do Sul Univ., Porto Alegre, RS (Brazil). Dept. de Engenharia Mecanica. Grupo de Estudos Termicos e Energeticos

    2000-07-01

    In the present work the momentum transport in two adjacent flow regions is described by means of a continuum theory of mixtures, specially developed to model multiphase phenomena. A generalized Newtonian fluid flows through the permeable wall channel, originating a pure fluid region and a mixture region - where the fluid saturates the porous matrix. The fluid and the porous matrix are treated as continuous constituents of a binary mixture coexisting superposed, each of them occupying simultaneously the whole volume of the mixture. An Ostwald-de Waele behavior is assumed for both the fluid constituent (in the mixture region) and the fluid (in the so-called pure fluid region), while the porous matrix, represented by the solid constituent, is assumed rigid, homogeneous, isotropic and at rest. Compatibility conditions at the interface (pure fluid-mixture) for momentum transfer are proposed and discussed. Assuming no flow across the interface, the velocity should be zero on the solid parts of the boundary and should match the fluid diffusing velocity on the fluid parts of the boundary. Also the shear stress at the pure fluid region is to be balanced by a multiple of the partial shear stress at the mixture region. A minimum principle for the above-described problem, assuming fully developed flow in both regions, is presented, providing an easy and reliable way for carrying out numerical simulations. (author)

  10. Variational methods for problems from plasticity theory and for generalized Newtonian fluids

    CERN Document Server

    Fuchs, Martin

    2000-01-01

    Variational methods are applied to prove the existence of weak solutions for boundary value problems from the deformation theory of plasticity as well as for the slow, steady state flow of generalized Newtonian fluids including the Bingham and Prandtl-Eyring model. For perfect plasticity the role of the stress tensor is emphasized by studying the dual variational problem in appropriate function spaces. The main results describe the analytic properties of weak solutions, e.g. differentiability of velocity fields and continuity of stresses. The monograph addresses researchers and graduate students interested in applications of variational and PDE methods in the mechanics of solids and fluids.

  11. Newtonian heating effect on unsteady hydromagnetic Casson fluid flow past a flat plate with heat and mass transfer

    Directory of Open Access Journals (Sweden)

    M. Das

    2015-12-01

    Full Text Available The influence of Newtonian heating on heat and mass transfer in unsteady hydromagnetic flow of a Casson fluid past a vertical plate in the presence of thermal radiation and chemical reaction is studied. The Casson fluid model is used to distinguish the non-Newtonian fluid behavior. The fluid flow is induced due to periodic oscillations of the plate along its length and a uniform transverse magnetic field is applied in a direction which is normal to the direction of fluid flow. The partial differential equations governing the flow, heat, and mass transfer are transformed to non-dimensional form using suitable non-dimensional variables which are then solved analytically by using Laplace transform technique. The numerical values of the fluid velocity, fluid temperature, and species concentration are depicted graphically whereas the values of skin-friction, Nusselt number, and Sherwood number are presented in tabular form. It is noticed that the fluid velocity and temperature decrease with increasing values of Casson parameter while concentration decreases with increasing values of chemical reaction parameter and Schmidt number. Such a fluid flow model has several industrial and medical applications such as in glass manufacturing, paper production, purification of crude oil and study of blood flow in the cardiovascular system.

  12. Two parameters Lie group analysis and numerical solution of unsteady free convective flow of non-Newtonian fluid

    Directory of Open Access Journals (Sweden)

    M.J. Uddin

    2016-09-01

    Full Text Available The two-dimensional unsteady laminar free convective heat and mass transfer fluid flow of a non-Newtonian fluid adjacent to a vertical plate has been analyzed numerically. The two parameters Lie group transformation method that transforms the three independent variables into a single variable is used to transform the continuity, the momentum, the energy and the concentration equations into a set of coupled similarity equations. The transformed equations have been solved by the Runge–Kutta–Fehlberg fourth-fifth order numerical method with shooting technique. Numerical calculations were carried out for the various parameters entering into the problem. The dimensionless velocity, temperature and concentration profiles were shown graphically and the skin friction, heat and mass transfer rates were given in tables. It is found that friction factor and heat transfer (mass transfer rate for methanol are higher (lower than those of hydrogen and water vapor. Friction factor decreases while heat and mass transfer rate increase as the Prandtl number increases. Friction (heat and mass transfer rate factor of Newtonian fluid is higher (lower than the dilatant fluid.

  13. Laboratory Investigation of Rheology and Infiltration Process of Non-Newtonian Fluids through Porous Media in a Non-Isothermal Flow Regime for Effective Remediation of Contaminants

    Science.gov (United States)

    Naseer, F.

    2017-12-01

    Contamination of soil and groundwater by adsorbent (persistent) contaminants have been a major concern. Mine tailings, Acid mine drainage, waste disposal areas, active or abandoned surface and underground mines are some major causes of soil and water contamination. It is need of the hour to develop cost effective and efficient remediation techniques for clean-up of soil and aquifers. The objective of this research is to study a methodology of using non-Newtonian fluids for effective remediation of adsorbent contaminants in porous media under non-isothermal flow regimes. The research comprises of three components. Since, non-Newtonian fluid rheology has not been well studied in cold temperatures, the first component of the objective is to expose a non-Newtonian fluid (Guar gum solution) to different temperatures ranging from 30 °C through -5 °C to understand the change in viscosity, shear strength and contact angle of the fluid. Study of the flow characteristic of non-Newtonian fluids in complex porous media has been limited. Hence, the second component of this study will focus on a comparison of flow characteristics of a Newtonian fluid, non-Newtonian fluid and a combination of both fluids in a glass-tube-bundle setup that will act as a synthetic porous media. The study of flow characteristics will also be done for different thermal regimes ranging from -5 °C to 30 °C. The third component of the research will be to compare the effectiveness Guar gum to remediate a surrogate adsorbed contaminant at a certain temperature from the synthetic porous media. Guar gum is biodegradable and hence it is benign to the environment. Through these experiments, the mobility and behavior of Guar gum under varying temperature ranges will be characterized and its effectiveness in removing contaminants from soils will be understood. The impact of temperature change on the fluid and flow stability in the porous medium will be examined in this research. Guar gum is good suspension

  14. Non-Newtonian fluid flow in an axisymmetric channel with porous wall

    Directory of Open Access Journals (Sweden)

    M. Hosseini

    2013-12-01

    Full Text Available In the present article Optimal Homotopy Asymptotic Method (OHAM is used to obtain the solutions of momentum and heat transfer equations of non-Newtonian fluid flow in an axisymmetric channel with porous wall for turbine cooling applications. Numerical method is used for validity of this analytical method and excellent agreement is observed between the solutions obtained from OHAM and numerical results. Trusting to this validity, effects of some other parameters are discussed. The results show that Nusselt number increases with increase of Reynolds number, Prandtl number and power law index.

  15. Two-phase flow modeling for low concentration spherical particle motion through a Newtonian fluid

    CSIR Research Space (South Africa)

    Smit GJF

    2010-11-01

    Full Text Available the necessity to model the discrete nature of sep- cite this article in press as: G.J.F. Smit et al., Two-phase flow modeling for low concentration spherical particle motion through a ian fluid, Appl. Math. Comput. (2010), doi:10.1016/j.amc.2010.07.055 2... and Ribberin large-scale and long term morphologica Please cite this article in press as: G.J.F. Smit Newtonian fluid, Appl. Math. Comput. (2010), � 2010 Elsevier Inc. All rights reserved. modeling of multiphase flow has increasingly become the subject...

  16. Experimental investigation of non-Newtonian droplet collisions : the role of extensional viscosity

    NARCIS (Netherlands)

    Finotello, Giulia; De, Shauvik; Vrouwenvelder, Jeroen C.R.; Padding, J.T.; Buist, Kay A.; Jongsma, Alfred; Innings, Fredrik; Kuipers, J.

    2018-01-01

    We investigate the collision behaviour of a shear thinning non-Newtonian fluid xanthan, by binary droplet collision experiments. Droplet collisions of non-Newtonian fluids are more complex than their Newtonian counterpart as the viscosity no longer remains constant during the collision process.

  17. Physically based model for extracting dual permeability parameters using non-Newtonian fluids

    Science.gov (United States)

    Abou Najm, M. R.; Basset, C.; Stewart, R. D.; Hauswirth, S.

    2017-12-01

    Dual permeability models are effective for the assessment of flow and transport in structured soils with two dominant structures. The major challenge to those models remains in the ability to determine appropriate and unique parameters through affordable, simple, and non-destructive methods. This study investigates the use of water and a non-Newtonian fluid in saturated flow experiments to derive physically-based parameters required for improved flow predictions using dual permeability models. We assess the ability of these two fluids to accurately estimate the representative pore sizes in dual-domain soils, by determining the effective pore sizes of macropores and micropores. We developed two sub-models that solve for the effective macropore size assuming either cylindrical (e.g., biological pores) or planar (e.g., shrinkage cracks and fissures) pore geometries, with the micropores assumed to be represented by a single effective radius. Furthermore, the model solves for the percent contribution to flow (wi) corresponding to the representative macro and micro pores. A user-friendly solver was developed to numerically solve the system of equations, given that relevant non-Newtonian viscosity models lack forms conducive to analytical integration. The proposed dual-permeability model is a unique attempt to derive physically based parameters capable of measuring dual hydraulic conductivities, and therefore may be useful in reducing parameter uncertainty and improving hydrologic model predictions.

  18. Negative wake behind bubbles in non-newtonian liquids

    DEFF Research Database (Denmark)

    Hassager, Ole

    1979-01-01

    Gas bubbles rising by gravity in non-Newtonian elastic liquids are different to gas bubbles in viscous Newtonian fluids in at least two ways. First, the bubbles in the non-Newtonian liquids often have a peculiar tip at the rear pole, and second, the terminal rise velocity versus volume curve ofte...

  19. Diffusion in Poiseuille and Couette flows of binary mixtures of incompressible newtonian fluids

    International Nuclear Information System (INIS)

    Caetano Filho, E.; Qassim, R.Y.

    1981-07-01

    Using the continuum theory of binary mixtures of incompressible Newtonian fluids, Poiseuille and Couette flows are studied with a view to determining whether diffusion occurs in such flows. It is shown that diffusion is absent in the Couette case. However, in Poiseuille flow there are significant differences between the velocities of the species comprising the mixture. This result is in broad agreement with that of Mills for similar mixtures of nonuniform composition. (Author) [pt

  20. On Numerical Methods in Non-Newtonian Flows

    International Nuclear Information System (INIS)

    Fileas, G.

    1982-12-01

    The constitutive equations for non-Newtonian flows are presented and the various flow models derived from continuum mechanics and molecular theories are considered and evaluated. Detailed account is given of numerical simulation employing differential and integral models of different kinds of non-Newtonian flows using finite-difference and finite-element techniques. Appreciating the fact that no book or concentrated material on Numerical Non-Newtonian Fluid Flow exists at the present, procedures for computer set-ups are described and references are given for finite-difference, finite-element and molecular-theory based programmes for several kinds of flow. Achievements and unreached goals in the field of numerical simulation of non-Newtonian flows are discussed and the lack of numerical work in the fields of suspension flows and heat transfer is pointed out. Finally, FFOCUS is presented as a newly built computer program which can simulate freezing flows on Newtonian fluids through various geometries and is aimed to be further developed to handle non-Newtonian freezing flows and certain types of suspension phenomena involved in corium flow after a hypothetical core melt-down accident in a PWR. (author)

  1. Natural convection heat transfer in shallow horizontal rectangular enclosures uniformly heated from the side and filled with non-Newtonian power law fluids

    International Nuclear Information System (INIS)

    Lamsaadi, M.; Naimi, M.; Hasnaoui, M.

    2006-01-01

    A combined analytical and numerical study is conducted for two dimensional, steady state, buoyancy driven flows of non-Newtonian power law fluids confined in a shallow rectangular cavity submitted to uniform fluxes of heat along both its short vertical sides, while its long horizontal walls are considered adiabatic. The effect of the non-Newtonian behavior on the fluid flow and heat transfer characteristics is examined. An approximate theoretical solution is developed on the basis of the parallel flow assumption and validated numerically by solving the full governing equations

  2. Non-Newtonian particulate flow simulation: A direct-forcing immersed boundary-lattice Boltzmann approach

    Science.gov (United States)

    Amiri Delouei, A.; Nazari, M.; Kayhani, M. H.; Kang, S. K.; Succi, S.

    2016-04-01

    In the current study, a direct-forcing immersed boundary-non-Newtonian lattice Boltzmann method (IB-NLBM) is developed to investigate the sedimentation and interaction of particles in shear-thinning and shear-thickening fluids. In the proposed IB-NLBM, the non-linear mechanics of non-Newtonian particulate flows is detected by combination of the most desirable features of immersed boundary and lattice Boltzmann methods. The noticeable roles of non-Newtonian behavior on particle motion, settling velocity and generalized Reynolds number are investigated by simulating benchmark problem of one-particle sedimentation under the same generalized Archimedes number. The effects of extra force due to added accelerated mass are analyzed on the particle motion which have a significant impact on shear-thinning fluids. For the first time, the phenomena of interaction among the particles, such as Drafting, Kissing, and Tumbling in non-Newtonian fluids are investigated by simulation of two-particle sedimentation and twelve-particle sedimentation. The results show that increasing the shear-thickening behavior of fluid leads to a significant increase in the kissing time. Moreover, the transverse position of particles for shear-thinning fluids during the tumbling interval is different from Newtonian and the shear-thickening fluids. The present non-Newtonian particulate study can be applied in several industrial and scientific applications, like the non-Newtonian sedimentation behavior of particles in food industrial and biological fluids.

  3. Saffman-Taylor Instability for a non-Newtonian fluid

    Science.gov (United States)

    Daripa, Prabir

    2013-11-01

    Motivated by applications, we study classical Saffman-Taylor instability involving displacement of an Oldroyd-B fluid displaced by air in a Hele-Shaw cell. The lubrication approximation is used by neglecting the vertical component of the velocity. We obtain an explicit expression of one of the components of the extra-stress perturbations tensor in terms of the horizontal velocity perturbations. The main result is an explicit formula for the growth constant (in time) of perturbations, given by a ratio in which a term depending on the relaxation and retardation (time) constants appears in the denominator of the ratio. This exact result compares extremely well with known numerical results. It is found that flow is more unstable than the corresponding Newtonian case. This is a joint work with Gelu Pasa. The research has been made possible by an NPRP Grant # 08-777-1-141 from the Qatar National Research Fund (a member of the Qatar Foundation).

  4. Flows of Newtonian and Power-Law Fluids in Symmetrically Corrugated Cappilary Fissures and Tubes

    Science.gov (United States)

    Walicka, A.

    2018-02-01

    In this paper, an analytical method for deriving the relationships between the pressure drop and the volumetric flow rate in laminar flow regimes of Newtonian and power-law fluids through symmetrically corrugated capillary fissures and tubes is presented. This method, which is general with regard to fluid and capillary shape, can also be used as a foundation for different fluids, fissures and tubes. It can also be a good base for numerical integration when analytical expressions are hard to obtain due to mathematical complexities. Five converging-diverging or diverging-converging geometrics, viz. wedge and cone, parabolic, hyperbolic, hyperbolic cosine and cosine curve, are used as examples to illustrate the application of this method. For the wedge and cone geometry the present results for the power-law fluid were compared with the results obtained by another method; this comparison indicates a good compatibility between both the results.

  5. Flows of Newtonian and Power-Law Fluids in Symmetrically Corrugated Cappilary Fissures and Tubes

    Directory of Open Access Journals (Sweden)

    Walicka A.

    2018-02-01

    Full Text Available In this paper, an analytical method for deriving the relationships between the pressure drop and the volumetric flow rate in laminar flow regimes of Newtonian and power-law fluids through symmetrically corrugated capillary fissures and tubes is presented. This method, which is general with regard to fluid and capillary shape, can also be used as a foundation for different fluids, fissures and tubes. It can also be a good base for numerical integration when analytical expressions are hard to obtain due to mathematical complexities. Five converging-diverging or diverging-converging geometrics, viz. wedge and cone, parabolic, hyperbolic, hyperbolic cosine and cosine curve, are used as examples to illustrate the application of this method. For the wedge and cone geometry the present results for the power-law fluid were compared with the results obtained by another method; this comparison indicates a good compatibility between both the results.

  6. Structural Optimization of Non-Newtonian Rectifiers

    DEFF Research Database (Denmark)

    Jensen, Kristian Ejlebjærg; Okkels, Fridolin

    When the size of fluidic devices is scaled down, inertial effects start to vanish such that the governing equation becomes linear. Some microfluidic devices rely on the non-linear term related to the inertia of the fluid, and one example is fluid rectifiers (diodes) e.g. related to some micropumps....... These rectifiers rely on the device geometry for their working mechanism, but on further downscaling the inertial effect vanishes and the governing equation starts to show symmetry properties. These symmetry properties reduce the geometry influence to the point where fluid rectifiers cease to function....... In this context it is natural to look for other sources of non-linearity and one possibility is to introduce a non-Newtonian working fluid. Non-Newtonian properties are due to stretching of large particles/molecules in the fluid and this is commonly seen for biological samples in “lab-on-a-chip” systems...

  7. Simulating single-phase and two-phase non-Newtonian fluid flow of a digital rock scanned at high resolution

    Science.gov (United States)

    Tembely, Moussa; Alsumaiti, Ali M.; Jouini, Mohamed S.; Rahimov, Khurshed; Dolatabadi, Ali

    2017-11-01

    Most of the digital rock physics (DRP) simulations focus on Newtonian fluids and overlook the detailed description of rock-fluid interaction. A better understanding of multiphase non-Newtonian fluid flow at pore-scale is crucial for optimizing enhanced oil recovery (EOR). The Darcy scale properties of reservoir rocks such as the capillary pressure curves and the relative permeability are controlled by the pore-scale behavior of the multiphase flow. In the present work, a volume of fluid (VOF) method coupled with an adaptive meshing technique is used to perform the pore-scale simulation on a 3D X-ray micro-tomography (CT) images of rock samples. The numerical model is based on the resolution of the Navier-Stokes equations along with a phase fraction equation incorporating the dynamics contact model. The simulations of a single phase flow for the absolute permeability showed a good agreement with the literature benchmark. Subsequently, the code is used to simulate a two-phase flow consisting of a polymer solution, displaying a shear-thinning power law viscosity. The simulations enable to access the impact of the consistency factor (K), the behavior index (n), along with the two contact angles (advancing and receding) on the relative permeability.

  8. ANALYSIS OF MARANGONI CONVECTION OF NON-NEWTONIAN POWER LAW FLUIDS WITH LINEAR TEMPERATURE DISTRIBUTION

    Directory of Open Access Journals (Sweden)

    Yan Zhang

    2011-01-01

    Full Text Available The problem of steady, laminar, thermal Marangoni convection flow of non-Newtonian power law fluid along a horizontal surface with variable surface temperature is studied. The partial differential equations are transformed into ordinary differential equations by using a suitable similarity transformation and analytical approximate solutions are obtained by an efficient transformation, asymptotic expansion and Padé approximants technique. The effects of power law index and Marangoni number on velocity and temperature profiles are examined and discussed.

  9. On multiple solutions of non-Newtonian Carreau fluid flow over an inclined shrinking sheet

    Science.gov (United States)

    Khan, Masood; Sardar, Humara; Gulzar, M. Mudassar; Alshomrani, Ali Saleh

    2018-03-01

    This paper presents the multiple solutions of a non-Newtonian Carreau fluid flow over a nonlinear inclined shrinking surface in presence of infinite shear rate viscosity. The governing boundary layer equations are derived for the Carreau fluid with infinite shear rate viscosity. The suitable transformations are employed to alter the leading partial differential equations to a set of ordinary differential equations. The consequential non-linear ODEs are solved numerically by an active numerical approach namely Runge-Kutta Fehlberg fourth-fifth order method accompanied by shooting technique. Multiple solutions are presented graphically and results are shown for various physical parameters. It is important to state that the velocity and momentum boundary layer thickness reduce with increasing viscosity ratio parameter in shear thickening fluid while opposite trend is observed for shear thinning fluid. Another important observation is that the wall shear stress is significantly decreased by the viscosity ratio parameter β∗ for the first solution and opposite trend is observed for the second solution.

  10. Simulation of forced convection in non-Newtonian fluid through sandstones

    Science.gov (United States)

    Gokhale, M. Y.; Fernandes, Ignatius

    2017-11-01

    Numerical simulation is carried out to study forced convection in non-Newtonian fluids flowing through sandstones. Simulation is carried out using lattice Boltzmann method (LBM) for both shear-thinning and shear-thickening, by varying the power law index from 0.5 to 1.5 in Carreau-Yasuda model. Parameters involved in LBM and Carreau model are identified to achieve numerical convergence. Permeability and porosity are varied in the range of 10-10-10-6 and 0.1-0.7, respectively, to match actual geometrical properties of sandstone. Numerical technology is validated by establishing Darcy's law by plotting the graph between velocity and pressure gradient. Consequently, investigation is carried out to study the influence of material properties of porous media on flow properties such as velocity profiles, temperature profiles, and Nusselt number.

  11. Coupled Effects of non-Newtonian Rheology and Aperture Variability on Flow in a Single Fracture

    Science.gov (United States)

    Di Federico, V.; Felisa, G.; Lauriola, I.; Longo, S.

    2017-12-01

    Modeling of non-Newtonian flow in fractured media is essential in hydraulic fracturing and drilling operations, EOR, environmental remediation, and to understand magma intrusions. An important step in the modeling effort is a detailed understanding of flow in a single fracture, as the fracture aperture is spatially variable. A large bibliography exists on Newtonian and non-Newtonian flow in variable aperture fractures. Ultimately, stochastic or deterministic modeling leads to the flowrate under a given pressure gradient as a function of the parameters describing the aperture variability and the fluid rheology. Typically, analytical or numerical studies are performed adopting a power-law (Oswald-de Waele) model. Yet the power-law model, routinely used e.g. for hydro-fracturing modeling, does not characterize real fluids at low and high shear rates. A more appropriate rheological model is provided by e.g. the four-parameter Carreau constitutive equation, which is in turn approximated by the more tractable truncated power-law model. Moreover, fluids of interest may exhibit yield stress, which requires the Bingham or Herschel-Bulkely model. This study employs different rheological models in the context of flow in variable aperture fractures, with the aim of understanding the coupled effect of rheology and aperture spatial variability with a simplified model. The aperture variation, modeled within a stochastic or deterministic framework, is taken to be one-dimensional and i) perpendicular; ii) parallel to the flow direction; for stochastic modeling, the influence of different distribution functions is examined. Results for the different rheological models are compared with those obtained for the pure power-law. The adoption of the latter model leads to overestimation of the flowrate, more so for large aperture variability. The presence of yield stress also induces significant changes in the resulting flowrate for assigned external pressure gradient.

  12. The influence of pH on gas-liquid mass transfer in non-Newtonian fluids

    OpenAIRE

    Li Shaobai; Fan Jungeng; Xu Shuang; Li Rundong; Luan Jingde

    2017-01-01

    In this study, the effect of pH on the mass transfer of oxygen bubble swarms in non-Newtonian fluids was experimentally studied. The volumetric liquid side mass transfer coefficient (kLa), liquid side mass transfer coefficient (kL), and specific interfacial area (a) were investigated. The pH was regulated by the addition of hydrochloric acid and sodium hydroxide (NaOH). It was found that the kLa increased with the gas flow rate increasing and decreased with the apparent viscosity of the liqui...

  13. Motion of charged suspended particle in a non-Newtonian fluid between two long parallel plates

    Energy Technology Data Exchange (ETDEWEB)

    Abd Elkhalek, M M [Nuclear Research Center-Atomic Energy Authority, Cairo (Egypt)

    1997-12-31

    The motion of charged suspended particle in a non-Newtonian fluid between two long parallel plates is discussed. The equation of motion of a suspended particle was suggested by Closkin. The equations of motion are reduced to ordinary differential equations by similarity transformation and solved numerically by using Runge-Kutta method. The trajectories of particles are calculated by integrating the equation of motion of a single particle. The present simulation requires some empirical parameters concerning the collision of the particles with the wall. The effect of solid particles on flow properties are discussed. Some typical results for both fluid and particle phases and density distributions of the particles are presented graphically. 4 figs.

  14. Motion of Charged Suspended Particle in a Non-Newtonian Fluid between Two Long Parallel Plated

    International Nuclear Information System (INIS)

    Abd-El Khalek, M.M.

    1998-01-01

    The motion of charged suspended particle in a non-Newtonian fluid between two long parallel plates is discussed. The equation of motion of a suspended particle was suggested by Closkin. The equations of motion are reduced to ordinary differential equations by similarity transformations and solved numerically by using the Runge-Kutta method. The trajectories of particles are calculated by integrating the equation of motion of a single particle. The present simulation requires some empirical parameters concerning the collision of the particles with the wall. The effects of solid particles on flow properties are discussed. Some typical results for both fluid and particle phases and density distributions of the particles are presented graphically

  15. Slip-flow and heat transfer of a non-newtonian nanofluid in a microtube.

    Science.gov (United States)

    Niu, Jun; Fu, Ceji; Tan, Wenchang

    2012-01-01

    The slip-flow and heat transfer of a non-Newtonian nanofluid in a microtube is theoretically studied. The power-law rheology is adopted to describe the non-Newtonian characteristics of the flow, in which the fluid consistency coefficient and the flow behavior index depend on the nanoparticle volume fraction. The velocity profile, volumetric flow rate and local Nusselt number are calculated for different values of nanoparticle volume fraction and slip length. The results show that the influence of nanoparticle volume fraction on the flow of the nanofluid depends on the pressure gradient, which is quite different from that of the Newtonian nanofluid. Increase of the nanoparticle volume fraction has the effect to impede the flow at a small pressure gradient, but it changes to facilitate the flow when the pressure gradient is large enough. This remarkable phenomenon is observed when the tube radius shrinks to micrometer scale. On the other hand, we find that increase of the slip length always results in larger flow rate of the nanofluid. Furthermore, the heat transfer rate of the nanofluid in the microtube can be enhanced due to the non-Newtonian rheology and slip boundary effects. The thermally fully developed heat transfer rate under constant wall temperature and constant heat flux boundary conditions is also compared.

  16. Development of a new continuous process for mixing of complex non-Newtonian fluids

    Science.gov (United States)

    Migliozzi, Simona; Mazzei, Luca; Sochon, Bob; Angeli, Panagiota; Thames Multiphase Team; Coral Project Collaboration

    2017-11-01

    Design of new continuous mixing operations poses many challenges, especially when dealing with highly viscous non-Newtonian fluids. Knowledge of complex rheological behaviour of the working mixture is crucial for development of an efficient process. In this work, we investigate the mixing performance of two different static mixers and the effects of the mixture rheology on the manufacturing of novel non-aqueous-based oral care products using experimental and computational fluid dynamic methods. The two liquid phases employed, i.e. a carbomer suspension in polyethylene glycol and glycerol, start to form a gel when they mix. We studied the structure evolution of the liquid mixture using time-resolved rheometry and we obtained viscosity rheograms at different phase ratios from pressure drop measurements in a customized mini-channel. The numerical results and rheological model were validated with experimental measurements carried out in a specifically designed setup. EPSRS-CORAL.

  17. A boundary integral method for two-dimensional (non)-Newtonian drops in slow viscous flow

    NARCIS (Netherlands)

    Toose, E.M.; Geurts, B.J.; Kuerten, J.G.M.

    1995-01-01

    A boundary integral method for the simulation of the time-dependent deformation of Newtonian or non-Newtonian drops suspended in a Newtonian fluid is developed. The boundary integral formulation for Stokes flow is used and the non-Newtonian stress is treated as a source term which yields an extra

  18. A model to analyse the flow of an incompressible Newtonian fluid through a rigid, homogeneous, isotropic and infinite porous medium

    International Nuclear Information System (INIS)

    Gama, R.M.S. da; Sampaio, R.

    1985-01-01

    The flow of an incompressible Newtonian fluid through a rigid, homogeneous, isotropic and infinite porous medium which has a given inicial distribuition of the mentioned fluid, is analyzed. It is proposed a model that assumes that the motion is caused by concentration gradient, but it does not consider the friction between the porous medium and the fluid. We solve an onedimensional case where the mathematical problem is reduced to the solution of a non-linear hyperbolic system of differential equations, subjected to an inicial condition given by a step function, called 'Riemann Problem'. (Author) [pt

  19. On a numerical strategy to compute gravity currents of non-Newtonian fluids

    International Nuclear Information System (INIS)

    Vola, D.; Babik, F.; Latche, J.-C.

    2004-01-01

    This paper is devoted to the presentation of a numerical scheme for the simulation of gravity currents of non-Newtonian fluids. The two dimensional computational grid is fixed and the free-surface is described as a polygonal interface independent from the grid and advanced in time by a Lagrangian technique. Navier-Stokes equations are semi-discretized in time by the Characteristic-Galerkin method, which finally leads to solve a generalized Stokes problem posed on a physical domain limited by the free surface to only a part of the computational grid. To this purpose, we implement a Galerkin technique with a particular approximation space, defined as the restriction to the fluid domain of functions of a finite element space. The decomposition-coordination method allows to deal without any regularization with a variety of non-linear and possibly non-differentiable constitutive laws. Beside more analytical tests, we revisit with this numerical method some simulations of gravity currents of the literature, up to now investigated within the simplified thin-flow approximation framework

  20. Boundary layer flow of MHD generalized Maxwell fluid over an exponentially accelerated infinite vertical surface with slip and Newtonian heating at the boundary

    Directory of Open Access Journals (Sweden)

    M.A. Imran

    2018-03-01

    Full Text Available The aim of this article is to investigate the unsteady natural convection flow of Maxwell fluid with fractional derivative over an exponentially accelerated infinite vertical plate. Moreover, slip condition, radiation, MHD and Newtonian heating effects are also considered. A modern definition of fractional derivative operator recently introduced by Caputo and Fabrizio has been used to formulate the fractional model. Semi analytical solutions of the dimensionless problem are obtained by employing Stehfest’s and Tzou’s algorithms in order to find the inverse Laplace transforms for temperature and velocity fields. Temperature and rate of heat transfer for non-integer and integer order derivatives are computed and reduced to some known solutions from the literature. Finally, in order to get insight of the physical significance of the considered problem regarding velocity and Nusselt number, some graphical illustrations are made using Mathcad software. As a result, in comparison between Maxwell and viscous fluid (fractional and ordinary we found that viscous (fractional and ordinary fluids are swiftest than Maxwell (fractional and ordinary fluids. Keywords: Free convection, Slip, Maxwell fluid, Newtonian heating, Exponentially accelerated plate, Caputo-Fabrizio fractional derivatives, Stehfest’s and Tzou’s algorithms

  1. Numerical solution of pipe flow problems for generalized Newtonian fluids

    International Nuclear Information System (INIS)

    Samuelsson, K.

    1993-01-01

    In this work we study the stationary laminar flow of incompressible generalized Newtonian fluids in a pipe with constant arbitrary cross-section. The resulting nonlinear boundary value problems can be written in a variational formulation and solved using finite elements and the augmented Lagrangian method. The solution of the boundary value problem is obtained by finding a saddle point of the augmented Lagrangian. In the algorithm the nonlinear part of the equations is treated locally and the solution is obtained by iteration between this nonlinear problem and a global linear problem. For the solution of the linear problem we use the SSOR preconditioned conjugate gradient method. The approximating problem is solved on a sequence of adaptively refined grids. A scheme for adjusting the value of the crucial penalization parameter of the augmented Lagrangian is proposed. Applications to pipe flow and a problem from the theory of capacities are given. (author) (34 refs.)

  2. Newtonian and pseudo-Newtonian Hill problem

    International Nuclear Information System (INIS)

    Steklain, A.F.; Letelier, P.S.

    2006-01-01

    A pseudo-Newtonian Hill problem based on the Paczynski-Wiita pseudo-Newtonian potential that reproduces general relativistic effects is presented and compared with the usual Newtonian Hill problem. Poincare maps, Lyapunov exponents and fractal escape techniques are employed to study bounded and unbounded orbits. In particular we consider the systems composed by Sun, Earth and Moon and composed by the Milky Way, the M2 cluster and a star. We find that some pseudo-Newtonian systems-including the M2 system-are more stable than their Newtonian equivalent

  3. Increasing heat transfer of non-Newtonian nanofluid in rectangular microchannel with triangular ribs

    Science.gov (United States)

    Shamsi, Mohammad Reza; Akbari, Omid Ali; Marzban, Ali; Toghraie, Davood; Mashayekhi, Ramin

    2017-09-01

    In this study, computational fluid dynamics and the laminar flow of the non-Newtonian fluid have been numerically studied. The cooling fluid includes water and 0.5 wt% Carboxy methyl cellulose (CMC) making the non-Newtonian fluid. In order to make the best of non-Newtonian nanofluid in this simulation, solid nanoparticles of Aluminum Oxide have been added to the non-Newtonian fluid in volume fractions of 0-2% with diameters of 25, 45 and 100 nm. The supposed microchannel is rectangular and two-dimensional in Cartesian coordination. The power law has been used to speculate the dynamic viscosity of the cooling nanofluid. The field of numerical solution is simulated in the Reynolds number range of 5 nanoparticles as well as the use for nanoparticles with smaller diameters lead to greater heat transfer. Among all the studied forms, the triangular rib from with an angle of attack 30° has the biggest Nusselt number and the smallest pressure drop along the microchannel. Also, an increase in the angle of attack and as a result of a sudden contact between the fluid and the ribs and also a reduction in the coflowing length (length of the rib) cause a cut in heat transfer by the fluid in farther parts from the solid wall (tip of the rib).

  4. Non-Newtonian ink transfer in gravure-offset printing

    International Nuclear Information System (INIS)

    Ghadiri, Fatemeh; Ahmed, Dewan Hasan; Sung, Hyung Jin; Shirani, Ebrahim

    2011-01-01

    The inks used in gravure-offset printing are non-Newtonian fluids with higher viscosities and lower surface tensions than Newtonian fluids. This paper examines the transfer of a non-Newtonian ink between a flat plate and a groove when the plate is moved upward with a constant velocity while the groove is held fixed. Numerical simulations were carried out with the Carreau model to explore the behavior of this non-Newtonian ink in gravure-offset printing. The volume of fluid (VOF) method was implemented to capture the interface during the ink transfer process. The effects of varying the contact angle of the ink on the flat plate and groove walls and geometrical parameters such as the groove angle and the groove depth on the breakup time of the liquid filament that forms between the plate and the groove and the ink transfer ratio were determined. Our results indicate that increasing the groove contact angle and decreasing the flat plate contact angle enhance the ink transfer ratio and the breakup time. However, increasing the groove depth and the groove angle decreases the transfer ratio and the breakup time. By optimizing these parameters, it is possible to achieve an ink transfer from the groove to the flat plate of approximately 92%. Moreover, the initial width and the vertical velocity of the neck of the ink filament have significant influences on the ink transfer ratio and the breakup time.

  5. Influence of Thermal Radiation on Unsteady Free Convection MHD Flow of Brinkman Type Fluid in a Porous Medium with Newtonian Heating

    Directory of Open Access Journals (Sweden)

    Farhad Ali

    2013-01-01

    Full Text Available The focus of this paper is to analyze the influence of thermal radiation on some unsteady magnetohydrodynamic (MHD free convection flows of an incompressible Brinkman type fluid past a vertical flat plate embedded in a porous medium with the Newtonian heating boundary condition. The fluid is considered as a gray absorbing-emitting but nonscattering medium and the Rosseland approximation in the energy equations is used to describe the radiative heat flux for optically thick fluid. For a detailed analysis of the problem, four important situations of flow due to (i impulsive motion of the plate (ii uniform acceleration of the plate (iii nonuniform acceleration of the plate, and (iv highly nonuniform acceleration of the plate are considered. The governing equations are first transformed into a system of dimensionless equations and then solved analytically using the Laplace transform technique. Numerical results for temperature and velocity are shown graphically, while skin friction and Nusselt number are computed in tables. The results show that temperature and velocity increase on increasing radiation and Newtonian heating parameters. However, the results of magnetic and porosity parameters on velocity are found quite opposite.

  6. Generation of Oil Droplets in a Non-Newtonian Liquid Using a Microfluidic T-Junction

    Directory of Open Access Journals (Sweden)

    Enrico Chiarello

    2015-11-01

    Full Text Available We have compared the formation of oil drops in Newtonian and non-Newtonian fluids in a T-junction microfluidic device. As Newtonian fluids, we used aqueous solutions of glycerol, while as non-Newtonian fluids we prepared aqueous solutions of xanthan, a stiff rod-like polysaccharide, which exhibit strong shear-thinning effects. In the squeezing regime, the formation of oil droplets in glycerol solutions is found to scale with the ratio of the dispersed flow rate to the continuous one and with the capillary number associated to the continuous phase. Switching to xanthan solutions does not seem to significantly alter the droplet formation process. Any quantitative difference with respect to the Newtonian liquid can be accounted for by a suitable choice of the capillary number, corresponding to an effective xanthan viscosity that depends on the flow rates. We have deduced ample variations in the viscosity, on the order of 10 and more, during normal operation conditions of the T-junction. This allowed estimating the actual shear rates experienced by the xanthan solutions, which go from tens to hundreds of s−1.

  7. Non-Newtonian Flow-Induced Deformation From Pressurized Cavities in Absorbing Porous Tissues

    Science.gov (United States)

    Ahmed, Aftab; Siddique, Javed

    2017-11-01

    We investigate the behavior of a spherical cavity in a soft biological tissue modeled as a deformable porous material during an injection of non-Newtonian fluid that follows a power law model. Fluid flows into the neighboring tissue due to high cavity pressure where it is absorbed by capillaries and lymphatics at a rate proportional to the local pressure. Power law fluid pressure and displacement of solid in the tissue are computed as function of radial distance and time. Numerical solutions indicate that shear thickening fluids exhibit less fluid pressure and induce small solid deformation as compared to shear thinning fluids. The absorption in the biological tissue increases as a consequence of flow induced deformation for power law fluids. In most cases non-Newtonian results are compared with viscous fluid case to magnify the differences.

  8. Magnetohydrodynamic peristaltic motion of a Newtonian fluid through porous walls through suction and injection

    Science.gov (United States)

    Sivaiah, R.; Hemadri Reddy, R.

    2017-11-01

    In this paper, we investigate the peristaltic transport of a conducting Newtonian fluid bounded by permeable walls with suction and injection moving with constant velocity of the wave in the wave frame of reference under the consideration of long wavelength and low Reynolds number. The analytical solution for the velocity field, pressure gradient and the frictional force are obtained. The effect of suction/injection parameter, amplitude ratio and the permeability parameter including slip on the flow quantities are discussed graphically. It is found that the greater the suction/injection parameter, the smaller the pressure rise against the pump works. Further, the pressure rise increases with increasing Magnetic parameter.

  9. Analytical solution of settling behavior of a particle in incompressible Newtonian fluid by using Parameterized Perturbation Method

    Directory of Open Access Journals (Sweden)

    Reza Mohammadyari

    2015-08-01

    Full Text Available The problem of solid particle settling is a well known problem in mechanic of fluids. The parametrized Perturbation Method is applied to analytically solve the unsteady motion of a spherical particle falling in a Newtonian fluid using the drag of the form given by Oseen/Ferreira, for a range of Reynolds numbers. Particle equation of motion involved added mass term and ignored the Basset term. By using this new kind of perturbation method called parameterized perturbation method (PPM, analytical expressions for the instantaneous velocity, acceleration and position of the particle were derived. The presented results show the effectiveness of PPM and high rate of convergency of the method to achieve acceptable answers.

  10. A study on the unsteady flow of two immiscible micropolar and Newtonian fluids through a horizontal channel: A numerical approach

    Science.gov (United States)

    Devakar, M.; Raje, Ankush

    2018-05-01

    The unsteady flow of two immiscible micropolar and Newtonian fluids through a horizontal channel is considered. In addition to the classical no-slip and hyper-stick conditions at the boundary, it is assumed that the fluid velocities and shear stresses are continuous across the fluid-fluid interface. Three cases for the applied pressure gradient are considered to study the problem: one with constant pressure gradient and the other two cases with time-dependent pressure gradients, viz. periodic and decaying pressure gradient. The Crank-Nicolson approach has been used to obtain numerical solutions for fluid velocity and microrotation for diverse sets of fluid parameters. The nature of fluid velocities and microrotation with various values of pressure gradient, Reynolds number, ratio of viscosities, micropolarity parameter and time is illustrated through graphs. It has been observed that micropolarity parameter and ratio of viscosities reduce the fluid velocities.

  11. PREDICTION OF GAS HOLD-UP IN A COMBINED LOOP AIR LIFT FLUIDIZED BED REACTOR USING NEWTONIAN AND NON-NEWTONIAN LIQUIDS

    Directory of Open Access Journals (Sweden)

    Sivakumar Venkatachalam

    2011-09-01

    Full Text Available Many experiments have been conducted to study the hydrodynamic characteristics of column reactors and loop reactors. In this present work, a novel combined loop airlift fluidized bed reactor was developed to study the effect of superficial gas and liquid velocities, particle diameter, fluid properties on gas holdup by using Newtonian and non-Newtonian liquids. Compressed air was used as gas phase. Water, 5% n-butanol, various concentrations of glycerol (60 and 80% were used as Newtonian liquids, and different concentrations of carboxy methyl cellulose aqueous solutions (0.25, 0.6 and 1.0% were used as non-Newtonian liquids. Different sizes of spheres, Bearl saddles and Raschig rings were used as solid phases. From the experimental results, it was found that the increase in superficial gas velocity increases the gas holdup, but it decreases with increase in superficial liquid velocity and viscosity of liquids. Based on the experimental results a correlation was developed to predict the gas hold-up for Newtonian and non-Newtonian liquids for a wide range of operating conditions at a homogeneous flow regime where the superficial gas velocity is approximately less than 5 cm/s

  12. Spreading dynamics of power-law fluid droplets

    International Nuclear Information System (INIS)

    Liang Zhanpeng; Peng Xiaofeng; Wang Xiaodong; Lee, D-J; Su Ay

    2009-01-01

    This paper aims at providing a summary of the theoretical models available for non-Newtonian fluid spreading dynamics. Experimental findings and model predictions for a Newtonian fluid spreading test are briefly reviewed. Then how the complete wetting and partial wetting power-law fluids spread over a solid substrate is examined. The possible extension of Newtonian fluid models to power-law fluids is also discussed.

  13. Time Independent Fluids

    Science.gov (United States)

    Collyer, A. A.

    1973-01-01

    Discusses theories underlying Newtonian and non-Newtonian fluids by explaining flow curves exhibited by plastic, shear-thining, and shear-thickening fluids and Bingham plastic materials. Indicates that the exact mechanism governing shear-thickening behaviors is a problem of further study. (CC)

  14. Physics of non-Newtonian fluids and interdisciplinary relations (biology and criminology)

    Science.gov (United States)

    Holubova, R.

    2018-03-01

    The aim of the paper is the presentation of an interdisciplinary topic that allows applying content knowledge in physics, mathematics and biology in real life environment. Students use to play games and view crime scenes but in common they have little knowledge about the science used during crime scene investigation. In this paper the science background of blood spatter analysis is presented—the physics of non-Newtonian fluids, the biology of blood and mathematics—the measurement and calculation of the angle of inpact, the relationship between height and spatter diameter. This topic was choosen according to the analysis of interviews with secondary and high school learners realized at four schools in Moravia, Czech Republic. The topic can be taught at secondary schools so as at a higher level at high schools. Hands-on activities are included. The teaching strategy supports group work. The appropriateness and reasonableness of the topic was checked in the real teaching process and the activities have had a positive feedback.

  15. Numerical study of shear thickening fluid with discrete particles embedded in a base fluid

    Directory of Open Access Journals (Sweden)

    W Zhu

    2016-09-01

    Full Text Available The Shear Thickening Fluid (STF is a dilatant material, which displays non-Newtonian characteristics in its unique ability to transit from a low viscosity fluid to a high viscosity fluid. The research performed investigates the STF behavior by modeling and simulation of the interaction between the base flow and embedded rigid particles when subjected to shear stress. The model considered the Lagrangian description of the rigid particles and the Eulerian description of fluid flow. The numerical analysis investigated key parameters such as applied flow acceleration, particle distribution and arrangement, volume concentration of particles, particle size, shape and their behavior in a Newtonian and non-Newtonian fluid base. The fluid-particle interaction model showed that the arrangement, size, shape and volume concentration of the particles had a significant effect on the behavior of the STF. Although non-conclusive, the addition of particles in non-Newtonian fluids showed a promising trend of improved shear thickening effects at high shear strain rates.

  16. Flow characteristics of Newtonian and non-Newtonian fluids in a vessel stirred by a 60° pitched blade impeller

    Directory of Open Access Journals (Sweden)

    Jamshid M. Nouri

    2008-03-01

    Full Text Available Mean and rms velocity characteristics of two Newtonian flows at Reynolds numbers of 12,800 (glycerin solution and 48,000 (water and of a non-Newtonian flow (0.2% CMC solution, at a power number similar to the Newtonian glycerin flow in a mixing vessel stirred by a 60° pitched blade impeller have been measured by laser Doppler velocimetry (LDV. The velocity measurements, resolved over 360° and 1.08° of impeller rotation, showed that the mean flow of the two power number matched glycerin and CMC flows were similar to within 3% of the impeller tip velocity and the turbulence intensities generally lower in the CMC flow by up to 5% of the tip velocity. The calculated mean flow quantities showed similar discharge coefficient and pumping efficiency in all three flows and similar strain rate between the two power number matched glycerin and CMC flows; the strain rate of the higher Reynolds number Newtonian flow was found to be slightly higher. The energy balance around the impeller indicated that the CMC flow dissipated up to 9% more of the total input power and converted 7% less into the turbulence compared to the glycerin flow with the same power input which could lead to less effective mixing processes where the micro-mixing is important.

  17. The influence of pH on gas-liquid mass transfer in non-Newtonian fluids

    Directory of Open Access Journals (Sweden)

    Li Shaobai

    2017-01-01

    Full Text Available In this study, the effect of pH on the mass transfer of oxygen bubble swarms in non-Newtonian fluids was experimentally studied. The volumetric liquid side mass transfer coefficient (kLa, liquid side mass transfer coefficient (kL, and specific interfacial area (a were investigated. The pH was regulated by the addition of hydrochloric acid and sodium hydroxide (NaOH. It was found that the kLa increased with the gas flow rate increasing and decreased with the apparent viscosity of the liquid increasing. In the case of pH 7 was attributed to the decomposition of the Xanthan molecular structure by the hydroxyl of NaOH.

  18. A Wall Boundary Condition for the Simulation of a Turbulent Non-Newtonian Domestic Slurry in Pipes

    Directory of Open Access Journals (Sweden)

    Dhruv Mehta

    2018-01-01

    Full Text Available The concentration (using a lesser amount of water of domestic slurry promotes resource recovery (nutrients and biomass while saving water. This article is aimed at developing numerical methods to support engineering processes such as the design and implementation of sewerage for concentrated domestic slurry. The current industrial standard for computational fluid dynamics-based analyses of turbulent flows is Reynolds-averaged Navier–Stokes (RANS modelling. This is assisted by the wall function approach proposed by Launder and Spalding, which permits the use of under-refined grids near wall boundaries while simulating a wall-bounded flow. Most RANS models combined with wall functions have been successfully validated for turbulent flows of Newtonian fluids. However, our experiments suggest that concentrated domestic slurry shows a Herschel–Bulkley-type non-Newtonian behaviour. Attempts have been made to derive wall functions and turbulence closures for non-Newtonian fluids; however, the resulting laws or equations are either inconsistent across experiments or lack relevant experimental support. Pertinent to this study, laws or equations reported in literature are restricted to a class of non-Newtonian fluids called power law fluids, which, as compared to Herschel–Bulkley fluids, yield at any amount of applied stress. An equivalent law for Herschel–Bulkley fluids that require a minimum-yield stress to flow is yet to be reported in literature. This article presents a theoretically derived (with necessary approximations law of the wall for Herschel–Bulkley fluids and implements it in a RANS solver using a specified shear approach. This results in a more accurate prediction of the wall shear stress experienced by a circular pipe with a turbulent Herschel–Bulkley fluid flowing through it. The numerical results are compared against data from our experiments and those reported in literature for a range of Reynolds numbers and rheological

  19. The Effect of Surface Tension on the Gravity-driven Thin Film Flow of Newtonian and Power-law Fluids

    Science.gov (United States)

    Hu, Bin; Kieweg, Sarah L.

    2012-01-01

    Gravity-driven thin film flow is of importance in many fields, as well as for the design of polymeric drug delivery vehicles, such as anti-HIV topical microbicides. There have been many prior works on gravity-driven thin films. However, the incorporation of surface tension effect has not been well studied for non-Newtonian fluids. After surface tension effect was incorporated into our 2D (i.e. 1D spreading) power-law model, we found that surface tension effect not only impacted the spreading speed of the microbicide gel, but also had an influence on the shape of the 2D spreading profile. We observed a capillary ridge at the front of the fluid bolus. Previous literature shows that the emergence of a capillary ridge is strongly related to the contact line fingering instability. Fingering instabilities during epithelial coating may change the microbicide gel distribution and therefore impact how well it can protect the epithelium. In this study, we focused on the capillary ridge in 2D flow and performed a series of simulations and showed how the capillary ridge height varies with other parameters, such as surface tension coefficient, inclination angle, initial thickness, and power-law parameters. As shown in our results, we found that capillary ridge height increased with higher surface tension, steeper inclination angle, bigger initial thickness, and more Newtonian fluids. This study provides the initial insights of how to optimize the flow and prevent the appearance of a capillary ridge and fingering instability. PMID:23687391

  20. Similarity solution of axisymmetric non-Newtonian wall jets with swirl

    Czech Academy of Sciences Publication Activity Database

    Kolář, Václav

    2011-01-01

    Roč. 12, č. 6 (2011), s. 3413-3420 ISSN 1468-1218 R&D Projects: GA AV ČR IAA200600801 Institutional research plan: CEZ:AV0Z20600510 Keywords : similarity solution * wall jets * non-Newtonian fluids * power-law fluids * swirl Subject RIV: BK - Fluid Dynamics Impact factor: 2.043, year: 2011

  1. Hyperdiffusive Dynamics in Newtonian Nanoparticle Fluids

    KAUST Repository

    Srivastava, Samanvaya

    2015-10-20

    © 2015 American Chemical Society. Hyperdiffusive relaxations in soft glassy materials are typically associated with out-of-equilibrium states, and nonequilibrium physics and aging are often invoked in explaining their origins. Here, we report on hyperdiffusive motion in model soft materials comprised of single-component polymer-tethered nanoparticles, which exhibit a readily accessible Newtonian flow regime. In these materials, polymer-mediated interactions lead to strong nanoparticle correlations, hyperdiffusive relaxations, and unusual variations of properties with temperature. We propose that hyperdiffusive relaxations in such materials can arise naturally from nonequilibrium or non-Brownian volume fluctuations forced by equilibrium thermal rearrangements of the particle pair orientations corresponding to equilibrated shear modes.

  2. Hyperdiffusive Dynamics in Newtonian Nanoparticle Fluids

    KAUST Repository

    Srivastava, Samanvaya; Agarwal, Praveen; Mangal, Rahul; Koch, Donald L.; Narayanan, Suresh; Archer, Lynden A.

    2015-01-01

    © 2015 American Chemical Society. Hyperdiffusive relaxations in soft glassy materials are typically associated with out-of-equilibrium states, and nonequilibrium physics and aging are often invoked in explaining their origins. Here, we report on hyperdiffusive motion in model soft materials comprised of single-component polymer-tethered nanoparticles, which exhibit a readily accessible Newtonian flow regime. In these materials, polymer-mediated interactions lead to strong nanoparticle correlations, hyperdiffusive relaxations, and unusual variations of properties with temperature. We propose that hyperdiffusive relaxations in such materials can arise naturally from nonequilibrium or non-Brownian volume fluctuations forced by equilibrium thermal rearrangements of the particle pair orientations corresponding to equilibrated shear modes.

  3. Compressible generalized Newtonian fluids

    Czech Academy of Sciences Publication Activity Database

    Málek, Josef; Rajagopal, K.R.

    2010-01-01

    Roč. 61, č. 6 (2010), s. 1097-1110 ISSN 0044-2275 Institutional research plan: CEZ:AV0Z20760514 Keywords : power law fluid * uniform temperature * compressible fluid Subject RIV: BJ - Thermodynamics Impact factor: 1.290, year: 2010

  4. Structural Optimization of non-Newtonian Microfluidics

    DEFF Research Database (Denmark)

    Jensen, Kristian Ejlebjærg

    2013-01-01

    Many of the biological fluids analyzed in Lab-on-a-Chip systems contain elastic components, which gives the fluids elastic character. Such fluids are said to be non-Newtonian or, more precisely, viscoelastic. They can give rise to exotic effects on the macroscale, which are never seen for fluids...... with components relying on viscoelastic effects, but the non-intuitive nature of these fluids complicates the design process. This thesis combines the method of topology optimization with differential constitutive equations, which govern the flow of viscoelastic fluids. The optimization method iteratively...... finite element package. The code is capable of calculating the viscoelastic flow in a benchmark geometry, and we hope that it will help newcomers as well as experienced researchers in the field of differential constitutive equations. v...

  5. A Finite Difference Scheme for Double-Diffusive Unsteady Free Convection from a Curved Surface to a Saturated Porous Medium with a Non-Newtonian Fluid

    KAUST Repository

    El-Amin, Mohamed

    2011-05-14

    In this paper, a finite difference scheme is developed to solve the unsteady problem of combined heat and mass transfer from an isothermal curved surface to a porous medium saturated by a non-Newtonian fluid. The curved surface is kept at constant temperature and the power-law model is used to model the non-Newtonian fluid. The explicit finite difference method is used to solve simultaneously the equations of momentum, energy and concentration. The consistency of the explicit scheme is examined and the stability conditions are determined for each equation. Boundary layer and Boussinesq approximations have been incorporated. Numerical calculations are carried out for the various parameters entering into the problem. Velocity, temperature and concentration profiles are shown graphically. It is found that as time approaches infinity, the values of wall shear, heat transfer coefficient and concentration gradient at the wall, which are entered in tables, approach the steady state values.

  6. Studying mixing in Non-Newtonian blue maize flour suspensions using color analysis.

    Directory of Open Access Journals (Sweden)

    Grissel Trujillo-de Santiago

    Full Text Available BACKGROUND: Non-Newtonian fluids occur in many relevant flow and mixing scenarios at the lab and industrial scale. The addition of acid or basic solutions to a non-Newtonian fluid is not an infrequent operation, particularly in Biotechnology applications where the pH of Non-Newtonian culture broths is usually regulated using this strategy. METHODOLOGY AND FINDINGS: We conducted mixing experiments in agitated vessels using Non-Newtonian blue maize flour suspensions. Acid or basic pulses were injected to reveal mixing patterns and flow structures and to follow their time evolution. No foreign pH indicator was used as blue maize flours naturally contain anthocyanins that act as a native, wide spectrum, pH indicator. We describe a novel method to quantitate mixedness and mixing evolution through Dynamic Color Analysis (DCA in this system. Color readings corresponding to different times and locations within the mixing vessel were taken with a digital camera (or a colorimeter and translated to the CIELab scale of colors. We use distances in the Lab space, a 3D color space, between a particular mixing state and the final mixing point to characterize segregation/mixing in the system. CONCLUSION AND RELEVANCE: Blue maize suspensions represent an adequate and flexible model to study mixing (and fluid mechanics in general in Non-Newtonian suspensions using acid/base tracer injections. Simple strategies based on the evaluation of color distances in the CIELab space (or other scales such as HSB can be adapted to characterize mixedness and mixing evolution in experiments using blue maize suspensions.

  7. Empirical resistive-force theory for slender biological filaments in shear-thinning fluids

    Science.gov (United States)

    Riley, Emily E.; Lauga, Eric

    2017-06-01

    Many cells exploit the bending or rotation of flagellar filaments in order to self-propel in viscous fluids. While appropriate theoretical modeling is available to capture flagella locomotion in simple, Newtonian fluids, formidable computations are required to address theoretically their locomotion in complex, nonlinear fluids, e.g., mucus. Based on experimental measurements for the motion of rigid rods in non-Newtonian fluids and on the classical Carreau fluid model, we propose empirical extensions of the classical Newtonian resistive-force theory to model the waving of slender filaments in non-Newtonian fluids. By assuming the flow near the flagellum to be locally Newtonian, we propose a self-consistent way to estimate the typical shear rate in the fluid, which we then use to construct correction factors to the Newtonian local drag coefficients. The resulting non-Newtonian resistive-force theory, while empirical, is consistent with the Newtonian limit, and with the experiments. We then use our models to address waving locomotion in non-Newtonian fluids and show that the resulting swimming speeds are systematically lowered, a result which we are able to capture asymptotically and to interpret physically. An application of the models to recent experimental results on the locomotion of Caenorhabditis elegans in polymeric solutions shows reasonable agreement and thus captures the main physics of swimming in shear-thinning fluids.

  8. Variational formulation for the Newtonian cosmology

    Energy Technology Data Exchange (ETDEWEB)

    De Ritis, R [Naples Univ. (Italy). Ist. di Fisica Teorica; Istituto Nazionale di Fisica Nucleare, Naples (Italy)); Pisello, D [Istituto Nazionale di Fisica Nucleare, Naples (Italy); Platania, G [Naples Univ. (Italy). Ist. di Fisica Sperimentale; C.N.R. Gruppo Nazionale di Astronomia, U.d.R., Napoli (Italy)); Scudellaro, P [Naples Univ. (Italy). Scuola di Perfezionamento in Fisica Teorica e Nucleare

    1979-12-11

    Using the ''generalized Clebsch representation'' for the velocity field of a fluid in the Eulerian description, an action principle for the equation of the Newtonian cosmology has been found. The invariance group of the equation results a generalization of the Heckmann-Schuking group; in this case, the action and the conserved currents are studied.

  9. Technical Report on NETL's Non Newtonian Multiphase Slurry Workshop: A path forward to understanding non-Newtonian multiphase slurry flows

    Energy Technology Data Exchange (ETDEWEB)

    Guenther, Chris [National Energy Technology Lab. (NETL), Morgantown, WV (United States); Garg, Rahul [National Energy Technology Lab. (NETL), Morgantown, WV (United States)

    2013-08-19

    The Department of Energy’s (DOE) National Energy Technology Laboratory (NETL) sponsored a workshop on non-Newtonian multiphase slurry at NETL’s Morgantown campus August 19 and 20, 2013. The objective of this special two-day meeting of 20-30 invited experts from industry, National Labs and academia was to identify and address technical issues associated with handling non-Newtonian multiphase slurries across various facilities managed by DOE. Particular emphasis during this workshop was placed on applications managed by the Office of Environmental Management (EM). The workshop was preceded by two webinars wherein personnel from ORP and NETL provided background information on the Hanford WTP project and discussed the critical design challenges facing this project. In non-Newtonian fluids, viscosity is not constant and exhibits a complex dependence on applied shear stress or deformation. Many applications under EM’s tank farm mission involve non-Newtonian slurries that are multiphase in nature; tank farm storage and handling, slurry transport, and mixing all involve multiphase flow dynamics, which require an improved understanding of the mechanisms responsible for rheological changes in non-Newtonian multiphase slurries (NNMS). To discuss the issues in predicting the behavior of NNMS, the workshop focused on two topic areas: (1) State-of-the-art in non-Newtonian Multiphase Slurry Flow, and (2) Scaling up with Confidence and Ensuring Safe and Reliable Long-Term Operation.

  10. An analytical investigation on unsteady motion of vertically falling spherical particles in non-Newtonian fluid by Collocation Method

    Directory of Open Access Journals (Sweden)

    M. Rahimi-Gorji

    2015-06-01

    Full Text Available An analytical investigation is applied for unsteady motion of a rigid spherical particle in a quiescent shear-thinning power-law fluid. The results were compared with those obtained from Collocation Method (CM and the established Numerical Method (Fourth order Runge–Kutta scheme. It was shown that CM gave accurate results. Collocation Method (CM and Numerical Method are used to solve the present problem. We obtained that the CM which was used to solve such nonlinear differential equation with fractional power is simpler and more accurate than series method such as HPM which was used in some previous works by others but the new method named Akbari-Ganji’s Method (AGM is an accurate and simple method which is slower than CM for solving such problems. The terminal settling velocity—that is the velocity at which the net forces on a falling particle eliminate—for three different spherical particles (made of plastic, glass and steel and three flow behavior index n, in three sets of power-law non-Newtonian fluids was investigated, based on polynomial solution (CM. Analytical results obtained indicated that the time of reaching the terminal velocity in a falling procedure is significantly increased with growing of the particle size that validated with Numerical Method. Further, with approaching flow behavior to Newtonian behavior from shear-thinning properties of flow (n → 1, the transient time to achieving the terminal settling velocity is decreased.

  11. Pore scale simulations for the extension of the Darcy-Forchheimer law to shear thinning fluids

    Science.gov (United States)

    Tosco, Tiziana; Marchisio, Daniele; Lince, Federica; Boccardo, Gianluca; Sethi, Rajandrea

    2014-05-01

    results of flow simulations show the superposition of two contributions to pressure drops: one, strictly related to the non-Newtonian properties of the fluid, dominates at low Reynolds numbers, while a quadratic one, arising at higher Reynolds numbers, is dependent only on the porous medium properties. The results suggest that, for Newtonian flow, the porous medium can be fully described by two macroscopic parameters, namely permeability K and inertial coefficient β. Conversely, for non-Newtonian flow, an additional parameter is required, represented by the shift factor α, which depends on the properties of both porous medium and fluid, which is not easy to be determined in laboratory tests, but can be in turn calculated from 2D or 3D pore-scale flow simulations, following the approach which was adopted in this work. References 1. Sorbie, K.S. Polymer-improved oil recovery; Blackie ; CRC Press: Glasgow, Boca Raton, Fla., 1991. 2. Xue, D.; Sethi, R. Viscoelastic gels of guar and xanthan gum mixtures provide long-term stabilization of iron micro- and nanoparticles. J Nanopart Res 2012, 14(11). 3. Bird, R.B.; Armstrong, R.C.; Hassager, O. Dynamics of polymeric liquids. Volume 1. Fluid mechanics; John Wiley and Sons Inc.: New York - NY, 1977. 4. Tosco, T.; Marchisio, D.L.; Lince, F.; Sethi, R. Extension of the Darcy-Forchheimer Law for Shear-Thinning Fluids and Validation via Pore-Scale Flow Simulations. Transport in Porous Media 2013, 96(1), 1-20.

  12. Empirical Correlations and CFD Simulations of Vertical Two-Phase Gas-Liquid (Newtonian and Non-Newtonian) Slug Flow Compared Against Experimental Data of Void Fraction

    DEFF Research Database (Denmark)

    Ratkovich, Nicolas Rios; Majumder, S.K.; Bentzen, Thomas Ruby

    2013-01-01

    Gas-Newtonian liquid two-phase flows (TPFs) are presented in several industrial processes (e.g. oil-gas industry). In spite of the common occurrence of these TPFs, the understanding of them is limited compared to single-phase flows. Various studies on TPF focus on developing empirical correlations...... based on large sets of experimental data for void fraction, which have proven accurate for specific conditions for which they were developed limiting their applicability. On the other hand, few studies focus on gas-non-Newtonian liquids TPFs, which are very common in chemical processes. The main reason...... is due to the characterization of the viscosity, which determines the hydraulic regime and flow behaviours of the system. The focus of this study is the analysis of the TPF (slug flow) for Newtonian and non-Newtonian liquids in a vertical pipe in terms of void fraction using computational fluid dynamics...

  13. Entropy Generation Analysis of Power-Law Non-Newtonian Fluid Flow Caused by Micropatterned Moving Surface

    Directory of Open Access Journals (Sweden)

    M. H. Yazdi

    2014-01-01

    Full Text Available In the present study, the first and second law analyses of power-law non-Newtonian flow over embedded open parallel microchannels within micropatterned permeable continuous moving surface are examined at prescribed surface temperature. A similarity transformation is used to reduce the governing equations to a set of nonlinear ordinary differential equations. The dimensionless entropy generation number is formulated by an integral of the local rate of entropy generation along the width of the surface based on an equal number of microchannels and no-slip gaps interspersed between those microchannels. The velocity, the temperature, the velocity gradient, and the temperature gradient adjacent to the wall are substituted into this equation resulting from the momentum and energy equations obtained numerically by Dormand-Prince pair and shooting method. Finally, the entropy generation numbers, as well as the Bejan number, are evaluated. It is noted that the presence of the shear thinning (pseudoplastic fluids creates entropy along the surface, with an opposite effect resulting from shear thickening (dilatant fluids.

  14. Effect of thermal radiation and chemical reaction on non-Newtonian fluid through a vertically stretching porous plate with uniform suction

    Directory of Open Access Journals (Sweden)

    Zeeshan Khan

    2018-06-01

    Full Text Available In this work, we discuss the unsteady flow of non-Newtonian fluid with the properties of heat source/sink in the presence of thermal radiation moving through a binary mixture embedded in a porous medium. The basic equations of motion including continuity, momentum, energy and concentration are simplified and solved analytically by using Homotopy Analysis Method (HAM. The energy and concentration fields are coupled with Dankohler and Schmidt numbers. By applying suitable transformation, the coupled nonlinear partial differential equations are converted to couple ordinary differential equations. The effect of physical parameters involved in the solutions of velocity, temperature and concentration profiles are discussed by assign numerical values and results obtained shows that the velocity, temperature and concentration profiles are influenced appreciably by the radiation parameter, Prandtl number, suction/injection parameter, reaction order index, solutal Grashof number and the thermal Grashof. It is observed that the non-Newtonian parameter H leads to an increase in the boundary layer thickness. It was established that the Prandtl number decreases thee thermal boundary layer thickness which helps in maintaining system temperature of the fluid flow. It is observed that the temperature profiles higher for heat source parameter and lower for heat sink parameter throughout the boundary layer. Fromm this simulation it is analyzed that an increase in the Schmidt number decreases the concentration boundary layer thickness. Additionally, for the sake of comparison numerical method (ND-Solve and Adomian Decomposition Method are also applied and good agreement is found. Keywords: Unsteady flow, Viscous fluid, Thermal radiation, Porous plate, Arrhenius kinetics, HAM and numerical method

  15. A DNS Investigation of Non-Newtonian Turbulent Open Channel Flow

    Science.gov (United States)

    Guang, Raymond; Rudman, Murray; Chryss, Andrew; Slatter, Paul; Bhattacharya, Sati

    2010-06-01

    The flow of non-Newtonian fluids in open channels has great significance in many industrial settings from water treatment to mine waste disposal. The turbulent behaviour during transportation of these materials is of interest for many reasons, one of which is keeping settleable particles in suspension. The mechanism governing particle transport in turbulent flow has been studied in the past, but is not well understood. A better understanding of the mechanism operating in the turbulent flow of non-Newtonian suspensions in open channel would lead to improved design of many of the systems used in the mining and mineral processing industries. The objective of this paper is to introduce our work on the Direct Numerical Simulation of turbulent flow of non-Newtonian fluids in an open channel. The numerical method is based on spectral element/Fourier formulation. The flow simulation of a Herschel-Bulkley fluid agrees qualitatively with experimental results. The simulation results over-predict the flow velocity by approximately 15% for the cases considered, although the source of the discrepancy is difficult to ascertain. The effect of variation in yield stress and assumed flow depth are investigated and used to assess the sensitivity of the flow to these physical parameters. This methodology is seen to be useful in designing and optimising the transport of slurries in open channels.

  16. Impinging jet spray formation using non-Newtonian liquids

    Science.gov (United States)

    Rodrigues, Neil S.

    Over the past two decades there has been a heightened interest in implementing gelled propellants for rocket propulsion, especially for hypergolic bi-propellants such as monomethylhydrazine (MMH) and nitrogen tetroxide oxidizer (NTO). Due to the very high level of toxicity of hypergolic liquid rocket propellants, increasing safety is an important area of need for continued space exploration and defense operations. Gelled propellants provide an attractive solution to meeting the requirements for safety, while also potentially improving performance. A gelling agent can be added to liquid propellants exhibiting Newtonian behavior to transform the liquid into a non-Newtonian fluid with some solid-like behavior, i.e. a gel. Non-Newtonian jet impingement is very different from its Newtonian counterpart in terms of fluid flow, atomization, and combustion. This is due to the added agents changing physical properties such as the bulk rheology (viscosity) and interfacial rheology (surface tension). Spray characterization of jet impingement with Newtonian liquids has been studied extensively in existing literature. However, there is a scarcity in literature of studies that consider the spray characterization of jet impingement with gelled propellants. This is a rather critical void since a major tradeoff of utilizing gelled propellants is the difficulty with atomization due to the increased effective viscosity. However, this difficulty can be overcome by using gels that exhibit shear-thinning behavior---viscosity decreases with increasing strain rate. Shear-thinning fluids are ideal because they have the distinct advantage of only flowing easily upon pressure. Thereby, greatly reducing the amount of propellant that could be accidentally leaked during both critical functions such as liftoff or engagement in the battlefield and regular tasks like refilling propellant tanks. This experimental work seeks to help resolve the scarcity in existing literature by providing drop size

  17. Structural Optimization of non-Newtonian Microfluidics

    DEFF Research Database (Denmark)

    Jensen, Kristian Ejlebjærg; Okkels, Fridolin

    2011-01-01

    We present results for topology optimization of a non-Newtonian rectifier described with a differential constitutive model. The results are novel in the sense that a differential constitutive model has not been combined with topology optimization previously. We find that it is necessary to apply...... optimization of fluids. We test the method on a microfluidic rectifier and find solutions topologically different from experimentally realized designs....

  18. Numerical exploration of a non-Newtonian Carreau fluid flow driven by catalytic surface reactions on an upper horizontal surface of a paraboloid of revolution, buoyancy and stretching at the free stream

    Directory of Open Access Journals (Sweden)

    I.L. Animasaun

    2017-12-01

    Full Text Available Geometrically, the upper pointed surface of an aircraft and bonnet of a car are examples of upper horizontal surfaces of a paraboloid of revolution (uhspr. The motion of these objects strongly depends on the boundary layer that is formed within the immediate space on it. However, each of these surfaces is neither a horizontal/vertical nor cone/wedge and neither a cone nor a wedge. This article presents the motion of 2-dimensional Blasius flow of Carreau fluid on the surface of such object. The case in which the reaction between the Carreau fluid and catalyst at the surface produces significant temperature differences which consequently set up buoyancy-driven flows within the boundary layer is investigated. Single first-order Arrhenius kinetics is adopted to model the reaction on the surface of the catalyst situated on uhspr which initiates the free convection. Suitable similarity variables are applied to non-dimensionalized, parameterized and reduce the governing partial differential equations to a coupled ordinary differential equations (BVP. The BVP is solved numerically using the shooting technique. Temperature distribution in the flow of viscoelastic Carreau fluid is greater than that of a Newtonian fluid. Local heat transfer rate decreases faster when the Carreau fluid is characterized as shear-thinning. Maximum concentration is guaranteed at a small value of power-law index n and large value of thickness parameter. Keywords: Viscoelastic-Carreau fluid, Catalitic surface, Paraboloid of revolution, Numerical method, Uhspr, Boundary layer analysis

  19. Steady laminar flow of fractal fluids

    Energy Technology Data Exchange (ETDEWEB)

    Balankin, Alexander S., E-mail: abalankin@ipn.mx [Grupo Mecánica Fractal, ESIME, Instituto Politécnico Nacional, México D.F., 07738 (Mexico); Mena, Baltasar [Laboratorio de Ingeniería y Procesos Costeros, Instituto de Ingeniería, Universidad Nacional Autónoma de México, Sisal, Yucatán, 97355 (Mexico); Susarrey, Orlando; Samayoa, Didier [Grupo Mecánica Fractal, ESIME, Instituto Politécnico Nacional, México D.F., 07738 (Mexico)

    2017-02-12

    We study laminar flow of a fractal fluid in a cylindrical tube. A flow of the fractal fluid is mapped into a homogeneous flow in a fractional dimensional space with metric induced by the fractal topology. The equations of motion for an incompressible Stokes flow of the Newtonian fractal fluid are derived. It is found that the radial distribution for the velocity in a steady Poiseuille flow of a fractal fluid is governed by the fractal metric of the flow, whereas the pressure distribution along the flow direction depends on the fractal topology of flow, as well as on the fractal metric. The radial distribution of the fractal fluid velocity in a steady Couette flow between two concentric cylinders is also derived. - Highlights: • Equations of Stokes flow of Newtonian fractal fluid are derived. • Pressure distribution in the Newtonian fractal fluid is derived. • Velocity distribution in Poiseuille flow of fractal fluid is found. • Velocity distribution in a steady Couette flow is established.

  20. Non-Newtonian fluids: Frictional pressure loss prediction for fully-developed flow in straight pipes

    Science.gov (United States)

    1991-10-01

    ESDU 91025 discusses models used to describe the rheology of time independent pseudohomogeneous non-Newtonian fluids (power-law, Bingham, Herschel-Bulkley and a generalized model due to Metzner and Reed); they are used to calculate the laminar flow pressure drop (which is independent of pipe roughness in this regime). Values of a generalized Reynolds number are suggested to define transitional and turbulent flow. For turbulent flow in smooth pipes, pressure loss is estimated on the basis of an experimentally determined rheogram using either the Dodge-Metzner or Bowen approach depending on the available measurements. Bowen requires results for at least two pipe diameters. The choice of Dodge-Metzner when data are limited is discussed; seven possible methods are assessed against five sets of experimental results drawn from the literature. No method is given for transitional flow, which it is suggested should be avoided, but the turbulent correlation is recommended because it will yield an overestimate. Suggestions are made for the treatment of roughness effects. Several worked examples illustrate the use of the methods and a flowchart guides the user through the process from experimentally characterizing the behavior of the fluid to determining the pressure drop. A computer program, ESDUpac A9125, is also provided.

  1. Entropy analysis of convective MHD flow of third grade non-Newtonian fluid over a stretching sheet

    Directory of Open Access Journals (Sweden)

    M.M. Rashidi

    2017-03-01

    Full Text Available The purpose of this article is to study and analyze the convective flow of a third grade non-Newtonian fluid due to a linearly stretching sheet subject to a magnetic field. The dimensionless entropy generation equation is obtained by solving the reduced momentum and energy equations. The momentum and energy equations are reduced to a system of ordinary differential equations by a similarity method. The optimal homotopy analysis method (OHAM is used to solve the resulting system of ordinary differential equations. The effects of the magnetic field, Biot number and Prandtl number on the velocity component and temperature are studied. The results show that the thermal boundary-layer thickness gets decreased with increasing the Prandtl number. In addition, Brownian motion plays an important role to improve thermal conductivity of the fluid. The main purpose of the paper is to study the effects of Reynolds number, dimensionless temperature difference, Brinkman number, Hartmann number and other physical parameters on the entropy generation. These results are analyzed and discussed.

  2. Simulating non-Newtonian flows with the moving particle semi-implicit method with an SPH kernel

    International Nuclear Information System (INIS)

    Xiang, Hao; Chen, Bin

    2015-01-01

    The moving particle semi-implicit (MPS) method and smoothed particle hydrodynamics (SPH) are commonly used mesh-free particle methods for free surface flows. The MPS method has superiority in incompressible flow simulation and simple programing. However, the crude kernel function is not accurate enough for the discretization of the divergence of the shear stress tensor by the particle inconsistency when the MPS method is extended to non-Newtonian flows. This paper presents an improved MPS method with an SPH kernel to simulate non-Newtonian flows. To improve the consistency of the partial derivative, the SPH cubic spline kernel and the Taylor series expansion are combined with the MPS method. This approach is suitable for all non-Newtonian fluids that can be described with τ  = μ(|γ|) Δ (where τ is the shear stress tensor, μ is the viscosity, |γ| is the shear rate, and Δ is the strain tensor), e.g., the Casson and Cross fluids. Two examples are simulated including the Newtonian Poiseuille flow and container filling process of the Cross fluid. The results of Poiseuille flow are more accurate than the traditional MPS method, and different filling processes are obtained with good agreement with previous results, which verified the validation of the new algorithm. For the Cross fluid, the jet fracture length can be correlated with We 0.28 Fr 0.78 (We is the Weber number, Fr is the Froude number). (paper)

  3. Effect of thermal radiation and chemical reaction on non-Newtonian fluid through a vertically stretching porous plate with uniform suction

    Science.gov (United States)

    Khan, Zeeshan; Khan, Ilyas; Ullah, Murad; Tlili, I.

    2018-06-01

    In this work, we discuss the unsteady flow of non-Newtonian fluid with the properties of heat source/sink in the presence of thermal radiation moving through a binary mixture embedded in a porous medium. The basic equations of motion including continuity, momentum, energy and concentration are simplified and solved analytically by using Homotopy Analysis Method (HAM). The energy and concentration fields are coupled with Dankohler and Schmidt numbers. By applying suitable transformation, the coupled nonlinear partial differential equations are converted to couple ordinary differential equations. The effect of physical parameters involved in the solutions of velocity, temperature and concentration profiles are discussed by assign numerical values and results obtained shows that the velocity, temperature and concentration profiles are influenced appreciably by the radiation parameter, Prandtl number, suction/injection parameter, reaction order index, solutal Grashof number and the thermal Grashof. It is observed that the non-Newtonian parameter H leads to an increase in the boundary layer thickness. It was established that the Prandtl number decreases thee thermal boundary layer thickness which helps in maintaining system temperature of the fluid flow. It is observed that the temperature profiles higher for heat source parameter and lower for heat sink parameter throughout the boundary layer. Fromm this simulation it is analyzed that an increase in the Schmidt number decreases the concentration boundary layer thickness. Additionally, for the sake of comparison numerical method (ND-Solve) and Adomian Decomposition Method are also applied and good agreement is found.

  4. Newtonian and post-Newtonian approximations are asymptotic to general relativity

    International Nuclear Information System (INIS)

    Futamase, T.; Schutz, B.F.

    1983-01-01

    A precise definition of the Newtonian and post-Newtonian hierarchy of approximations to general relativity is given by studying a C/sup infinity/ sequence of solutions to Einstein's equations that is defined by initial data having the Newtonian scaling property: v/sup i/approx.epsilon, rhoapprox.epsilon 2 , papprox.epsilon 4 , where epsilon is the parameter along the sequence. We map one solution in the sequence to another by identifying them at constant spatial position x/sup i/ and Newtonian dynamical time tau = epsilont. This mapping defines a congruence parametrized by epsilon, and the various post-Newtonian approximations emerge as derivatives of the relativistic solutions along this congruence. We thereby show for the first time that the approximations are genuine asymptotic approximations to general relativity. The proof is given in detail up to first post-Newtonian order, but is easily extended. The results will be applied in the following paper to radiation reaction in binary star systems, to give a proof of the validity of the ''quadrupole formula'' free from any divergences

  5. Swimming efficiency in a shear-thinning fluid

    Science.gov (United States)

    Nganguia, Herve; Pietrzyk, Kyle; Pak, On Shun

    2017-12-01

    Micro-organisms expend energy moving through complex media. While propulsion speed is an important property of locomotion, efficiency is another factor that may determine the swimming gait adopted by a micro-organism in order to locomote in an energetically favorable manner. The efficiency of swimming in a Newtonian fluid is well characterized for different biological and artificial swimmers. However, these swimmers often encounter biological fluids displaying shear-thinning viscosities. Little is known about how this nonlinear rheology influences the efficiency of locomotion. Does the shear-thinning rheology render swimming more efficient or less? How does the swimming efficiency depend on the propulsion mechanism of a swimmer and rheological properties of the surrounding shear-thinning fluid? In this work, we address these fundamental questions on the efficiency of locomotion in a shear-thinning fluid by considering the squirmer model as a general locomotion model to represent different types of swimmers. Our analysis reveals how the choice of surface velocity distribution on a squirmer may reduce or enhance the swimming efficiency. We determine optimal shear rates at which the swimming efficiency can be substantially enhanced compared with the Newtonian case. The nontrivial variations of swimming efficiency prompt questions on how micro-organisms may tune their swimming gaits to exploit the shear-thinning rheology. The findings also provide insights into how artificial swimmers should be designed to move through complex media efficiently.

  6. Diagnosis at a glance of biological non-Newtonian fluids with Film Interference Flow Imaging (FIFI)

    Science.gov (United States)

    Hidema, R.; Yamada, N.; Furukawa, H.

    2012-04-01

    In the human body, full of biological non-Newtonian fluids exist. For example, synovial fluids exist in our joints, which contain full of biopolymers, such as hyaluronan and mucin. It is thought that these polymers play critical roles on the smooth motion of the joint. Indeed, luck of biopolymers in synovial fluid cause joint pain. Here we study the effects of polymer in thin liquid layer by using an original experimental method called Film Interference Flow Imaging (FIFI). A vertically flowing soap film containing polymers is made as two-dimensional flow to observe turbulence. The thickness of water layer is about 4 μm sandwiched between surfactant mono-layers. The interference pattern of the soap film is linearly related to the flow velocity in the water layer through the change in the thickness of the film. Thus the flow velocity is possibly analyzed by the single image analysis of the interference pattern, that is, FIFI. The grid turbulence was made in the flowing soap films containing the long flexible polymer polyethyleneoxide (PEO, Mw=3.5x106), and rigid polymer hydroxypropyl cellulose (HPC, Mw > 1.0 x106). The decaying process of the turbulence is affected by PEO and HPC at several concentrations. The effects of PEO are sharply seen even at low concentrations, while the effects of HPC are gradually occurred at much higher concentration compared to the PEO. It is assumed that such a difference between PEO and HPC is due to the polymer stretching or polymer orientation under turbulence, which is observed and analyzed by FIFI. We believe the FIFI will be applied in the future to examine biological fluids such as synovial fluids quickly and quantitatively.

  7. The rheology of non-suspended sediment transport mediated by a Newtonian fluid

    Science.gov (United States)

    Pähtz, Thomas; Durán, Orencio

    2017-04-01

    Using a coupled DEM/RANS numerical model of non-suspended sediment transport in a Newtonian fluid (Durán et al., POF 103306, 2012), we find that the gas-like part of the granular transport flow can be described by a universal condition that constrains the average geometry of interparticle collisions. We show that this condition corresponds to a constant sliding friction coefficient μ at an appropriately defined bed surface, thus explaining the success of Bagnold's old idea to describe the sediment transport in analogy to sliding friction. We are currently exploring whether this rheology applies to gas-like granular flows in general. We further find a transition of the gas-like flow to either a solid-like flow (solid-to-gas transition), which is typical for aeolian sediment transport ('saltation'), or a liquid-like flow (liquid-to-gas transition), which is typical for subaqueous sediment transport ('bedload'). The transition occurs at about the location of maximal particle collision frequency. If there is a liquid-like flow below the transition, we find that it can be described by a μ(I) rheology, where I is the visco-intertial number, an appropriately defined average of the viscous and intertial number.

  8. Numerical Analyses of the Non-Newtonian Flow Performance and Thermal Effect on a Bearing Coated with a High Tin Content

    Directory of Open Access Journals (Sweden)

    K. Mehala

    2016-12-01

    Full Text Available The hydrodynamic bearings are stressed by severe workings conditions, such as speed, load, and the oil will be increasingly solicit by pressure and shear. The Newtonian behavior is far from being awarded in this case, the most loaded bearings operating at very high speeds; the shear rate of the oil is of higher order. A numerical analysis of the behavior of non-Newtonian fluid for plain cylindrical journal bearing finite dimension coated with antifriction material with a high tin content, for to facilitate the accommodation of the surfaces and save the silk of the shaft in the case of a contact. this analyses is implemented using the code-ANSYS CFX, by solving the energy equation with the finite difference method, considering that laminar regime and the fluid is non Newtonian by using the power law Ostwald model, the coefficient n is equal to 1.25 and for different model such as Bingham, cross and Hereshek-Bulkley model. This study aims to better predict the non-Newtonian behavior of the oil film in bearings operating under more severe conditions. The purpose conducted during this study is to predict the effect of non-Newtonian behavior of the film; the journal bearing operating under severe conditions, the speed of rotation varies from 1000 to 9000 rpm and the bearing working under radial load 2 to 10 kN. Temperature and the pressure within the fluid film assumed non-Newtonian are high, with a coefficient n greater than 1 that is to say for viscoelastic fluids.

  9. Analysis of pressure falloff tests of non-Newtonian power-law fluids in naturally-fractured bounded reservoirs

    Directory of Open Access Journals (Sweden)

    Omotayo Omosebi

    2015-12-01

    This article presents an analytic technique for interpreting pressure falloff tests of non-Newtonian Power-law fluids in wells that are located near boundaries in dual-porosity reservoirs. First, dimensionless pressure solutions are obtained and Stehfest inversion algorithm is used to develop new type curves. Subsequently, long-time analytic solutions are presented and interpretation procedure is proposed using direct synthesis. Two examples, including real field data from a heavy oil reservoir in Colombian eastern plains basin, are used to validate and demonstrate application of this technique. Results agree with conventional type-curve matching procedure. The approach proposed in this study avoids the use of type curves, which is prone to human errors. It provides a better alternative for direct estimation of formation and flow properties from falloff data.

  10. MASS TRANSFER COEFFICIENTS FOR A NON-NEWTONIAN FLUID AND WATER WITH AND WITHOUT ANTI-FOAM AGENTS

    Energy Technology Data Exchange (ETDEWEB)

    Leishear, R.

    2009-09-09

    Mass transfer rates were measured in a large scale system, which consisted of an 8.4 meter tall by 0.76 meter diameter column containing one of three fluids: water with an anti-foam agent, water without an anti-foam agent, and AZ101 simulant, which simulated a non-Newtonian nuclear waste. The testing contributed to the evaluation of large scale mass transfer of hydrogen in nuclear waste tanks. Due to its radioactivity, the waste was chemically simulated, and due to flammability concerns oxygen was used in lieu of hydrogen. Different liquids were used to better understand the mass transfer processes, where each of the fluids was saturated with oxygen, and the oxygen was then removed from solution as air bubbled up, or sparged, through the solution from the bottom of the column. Air sparging was supplied by a single tube which was co-axial to the column, the decrease in oxygen concentration was recorded, and oxygen measurements were then used to determine the mass transfer coefficients to describe the rate of oxygen transfer from solution. Superficial, average, sparging velocities of 2, 5, and 10 mm/second were applied to each of the liquids at three different column fill levels, and mass transfer coefficient test results are presented here for combinations of superficial velocities and fluid levels.

  11. MASS TRANSFER COEFFICIENTS FOR A NON-NEWTONIAN FLUID AND WATER WITH AND WITHOUT ANTI-FOAM AGENTS

    International Nuclear Information System (INIS)

    Leishear, R.

    2009-01-01

    Mass transfer rates were measured in a large scale system, which consisted of an 8.4 meter tall by 0.76 meter diameter column containing one of three fluids: water with an anti-foam agent, water without an anti-foam agent, and AZ101 simulant, which simulated a non-Newtonian nuclear waste. The testing contributed to the evaluation of large scale mass transfer of hydrogen in nuclear waste tanks. Due to its radioactivity, the waste was chemically simulated, and due to flammability concerns oxygen was used in lieu of hydrogen. Different liquids were used to better understand the mass transfer processes, where each of the fluids was saturated with oxygen, and the oxygen was then removed from solution as air bubbled up, or sparged, through the solution from the bottom of the column. Air sparging was supplied by a single tube which was co-axial to the column, the decrease in oxygen concentration was recorded, and oxygen measurements were then used to determine the mass transfer coefficients to describe the rate of oxygen transfer from solution. Superficial, average, sparging velocities of 2, 5, and 10 mm/second were applied to each of the liquids at three different column fill levels, and mass transfer coefficient test results are presented here for combinations of superficial velocities and fluid levels

  12. Determination of the diffusion coefficient of salts in non-Newtonian liquids by the Taylor dispersion method

    Energy Technology Data Exchange (ETDEWEB)

    Mey, Paula; Varges, Priscilla R.; Mendes, Paulo R. de Souza [Dept. of Mechanical Engineering. Pontificia Universidade Catolica do RJ (PUC-Rio), RJ (Brazil)], e-mails: prvarges@puc-rio.br, pmendes@puc-rio.br

    2010-07-01

    This research looked for a method to determine the binary diffusion coefficient D of salts in liquids (especially in drilling fluids) not only accurately, but in a reasonable time. We chose to use the Taylor Dispersion Method. This technique has been used for measuring binary diffusion coefficients in gaseous, liquid and supercritical fluids, due to its simplicity and accuracy. In the method, the diffusion coefficient is determined by the analysis of the dispersion of a pulse of soluble material in a solvent flowing laminarly through a tube. This work describes the theoretical basis and the experimental requirements for the application of the Taylor Dispersion Method, emphasizing the description of our experiment. A mathematical formulation for both Newtonian and non-Newtonian fluids is presented. The relevant sources of errors are discussed. The experimental procedure and associated analysis are validated by applying the method in well known systems, such as NaCl in water.D of salts in liquids (especially in drilling fluids) not only accurately, but in a reasonable time. We chose to use the Taylor Dispersion Method. This technique has been used for measuring binary diffusion coefficients in gaseous, liquid and supercritical fluids, due to its simplicity and accuracy. In the method, the diffusion coefficient is determined by the analysis of the dispersion of a pulse of soluble material in a solvent flowing laminarly through a tube. This work describes the theoretical basis and the experimental requirements for the application of the Taylor Dispersion Method, emphasizing the description of our experiment. A mathematical formulation for both Newtonian and non-Newtonian fluids is presented. The relevant sources of errors are discussed. The experimental procedure and associated analysis are validated by applying the method in well known systems, such as NaCl in water. (author)

  13. The role of the rheological properties of non-newtonian fluids in controlling dispersive mixing in a batch electrophoretic cell with Joule heating

    Directory of Open Access Journals (Sweden)

    M.A. Bosse

    2001-03-01

    Full Text Available The problem of the effect of Joule heating generation on the hydrodynamic profile and the solute transport found in electrophoretic devices is addressed in this article. The research is focused on the following two problems: The first one is centered around the effect of Joule heating on the hydrodynamic velocity profile and it is referred to as "the carrier fluid problem." The other one is related to the effect of Joule heating on the solute transport inside electrophoretic cells and it is referred to as "the solute problem". The hydrodynamic aspects were studied first to yield the velocity profiles required for analysis of the solute transport problem. The velocity profile obtained in this study is analytical and the results are valid for non-Newtonian fluids carriers. To this end, the power-law model was used to study the effect of the rheology of the material in conjunction with the effect of Joule heating generation inside batch electrophoretic devices. This aspect of the research was then effectively used to study the effect of Joule heating generation on the motion of solutes (such as macromolecules under the influence of non-Newtonian carriers. This aspect of the study was performed using an area-averaging approach that yielded analytical results for the effective diffusivity of the device.

  14. Boundary layer flow of MHD generalized Maxwell fluid over an exponentially accelerated infinite vertical surface with slip and Newtonian heating at the boundary

    Science.gov (United States)

    Imran, M. A.; Riaz, M. B.; Shah, N. A.; Zafar, A. A.

    2018-03-01

    The aim of this article is to investigate the unsteady natural convection flow of Maxwell fluid with fractional derivative over an exponentially accelerated infinite vertical plate. Moreover, slip condition, radiation, MHD and Newtonian heating effects are also considered. A modern definition of fractional derivative operator recently introduced by Caputo and Fabrizio has been used to formulate the fractional model. Semi analytical solutions of the dimensionless problem are obtained by employing Stehfest's and Tzou's algorithms in order to find the inverse Laplace transforms for temperature and velocity fields. Temperature and rate of heat transfer for non-integer and integer order derivatives are computed and reduced to some known solutions from the literature. Finally, in order to get insight of the physical significance of the considered problem regarding velocity and Nusselt number, some graphical illustrations are made using Mathcad software. As a result, in comparison between Maxwell and viscous fluid (fractional and ordinary) we found that viscous (fractional and ordinary) fluids are swiftest than Maxwell (fractional and ordinary) fluids.

  15. Non-newtonian heat transfer on a plate heat exchanger with generalized configurations

    Energy Technology Data Exchange (ETDEWEB)

    Carezzato, A.; Tadini, C.C.; Gut, J.A.W. [Department of Chemical Engineering, Escola Politecnica, University of Sao Paulo, Sao Paulo (Brazil); Alcantara, M.R. [Department of Fundamental Chemistry, Institute of Chemistry, University of Sao Paulo, Sao Paulo (Brazil); Telis-Romero, J. [Department of Food Engineering and Technology, Universidade Estadual Paulista, Sao Jose do Rio Preto (Brazil)

    2007-01-15

    For the configuration optimization of plate heat exchangers (PHEs), the mathematical models for heat transfer and pressure drop must be valid for a wide range of operational conditions of all configurations of the exchanger or the design results may be compromised. In this investigation, the thermal model of a PHE is adjusted to fit experimental data obtained from non-Newtonian heat transfer for eight different configurations, using carboxymethylcellulose solutions (CMC) as test fluid. Although it is possible to successfully adjust the model parameters, Newtonian and non-Newtonian heat transfer cannot be represented by a single generalized correlation. In addition, the specific heat, thermal conductivity and power-law rheological parameters of CMC solutions were correlated with temperature, over a range compatible with a continuous pasteurization process. (Abstract Copyright [2007], Wiley Periodicals, Inc.)

  16. Failure and nonfailure of fluid filaments in extension

    DEFF Research Database (Denmark)

    Hassager, Ole; Kolte, Mette Irene; Renardy, Michael

    1998-01-01

    The phenomenon of ductile failure of Newtonian and viscoelastic fluid filaments without surface tension is studied by a 2D finite element method and by ID non-linear analysis. The viscoelastic fluids are described by single integral constitutive equations. The main conclusions are: (1) Newtonian...... fluid filaments do not exhibit ductile failure without surface tension; (2) some viscoelastic fluids form stable filaments while other fluids exhibit ductile failure as a result of an elastic instability; (3) for large Deborah numbers, the Considere condition may be used to predict the Hencky strain...

  17. Dynamics of polymeric liquids. Vol. 1, 2nd Ed.: Fluid mechanics

    International Nuclear Information System (INIS)

    Bird, R.B.; Armstrong, R.C.; Hassager, O.

    1987-01-01

    This book examines Newtonian liquids and polymer fluid mechanics. It begins with a review of the main ideas of fluid dynamics as well as key points of Newtonian fluids. Major revisions include extensive updating of all material and a greater emphasis on fluid dynamics problem solving. It presents summaries of experiments describing the difference between polymeric and simple fluids. In addition, it traces, roughly in historical order, various methods for solving polymer fluid dynamics problems

  18. MHD free convection flow of a non-Newtonian power-law fluid over ...

    African Journals Online (AJOL)

    ... flow have been presented for various parameters such as Prandtl number, flow behavior index (n), porous plate parameter and magnetic parameter. The local Nusselt number and skin friction coefficient is also presented graphically. Keywords: Magnetohydrodynamic flow; free convection flow; Non-Newtonian power-law

  19. Viscous Flow with Large Fluid-Fluid Interface Displacement

    DEFF Research Database (Denmark)

    Rasmussen, Henrik Koblitz; Hassager, Ole; Saasen, Arild

    1998-01-01

    The arbitrary Lagrange-Euler (ALE) kinematic description has been implemented in a 3D transient finite element program to simulate multiple fluid flows with fluid-fluid interface or surface displacements. The description of fluid interfaces includes variable interfacial tension, and the formulation...... is useful in the simulation of low and intermediate Reynolds number viscous flow. The displacement of two immiscible Newtonian fluids in a vertical (concentric and eccentric) annulus and a (vertical and inclined)tube is simulated....

  20. Flow and Displacement of Non-Newtonian Fluid(Power-Law Model) by Surface Tension and Gravity Force in Inclined Circular Tube

    International Nuclear Information System (INIS)

    Moh, Jeong Hah; Cho, Y. I.

    2014-01-01

    This paper presents the theoretical analysis of a flow driven by surface tension and gravity in an inclined circular tube. A governing equation is developed for describing the displacement of a non-Newtonian fluid(Power-law model) that continuously flows into a circular tube owing to surface tension, which represents a second-order, nonlinear, non-homogeneous, and ordinary differential form. It was found that quantitatively, the theoretical predictions of the governing equation were in excellent agreement with the solutions of the equation for horizontal tubes and the past experimental data. In addition, the predictions compared very well with the results of the force balance equation for steady

  1. Entropy generation in non-Newtonian fluid flow in a slider bearing

    Indian Academy of Sciences (India)

    In the present study, entropy production in flow fields due to slider bearings is formulated. The rate of entropy generation is computed for different fluid properties and geometric configurations of the slider bearing. In order to account for the non-Newtonian effect, a special type of third-grade fluid is considered. It is found that ...

  2. Numerical study of entropy generation and melting heat transfer on MHD generalised non-Newtonian fluid (GNF): Application to optimal energy

    Science.gov (United States)

    Iqbal, Z.; Mehmood, Zaffar; Ahmad, Bilal

    2018-05-01

    This paper concerns an application to optimal energy by incorporating thermal equilibrium on MHD-generalised non-Newtonian fluid model with melting heat effect. Highly nonlinear system of partial differential equations is simplified to a nonlinear system using boundary layer approach and similarity transformations. Numerical solutions of velocity and temperature profile are obtained by using shooting method. The contribution of entropy generation is appraised on thermal and fluid velocities. Physical features of relevant parameters have been discussed by plotting graphs and tables. Some noteworthy findings are: Prandtl number, power law index and Weissenberg number contribute in lowering mass boundary layer thickness and entropy effect and enlarging thermal boundary layer thickness. However, an increasing mass boundary layer effect is only due to melting heat parameter. Moreover, thermal boundary layers have same trend for all parameters, i.e., temperature enhances with increase in values of significant parameters. Similarly, Hartman and Weissenberg numbers enhance Bejan number.

  3. A Conditionally Stable Scheme for a Transient Flow of a Non-Newtonian Fluid Saturating a Porous Medium

    KAUST Repository

    El-Amin, Mohamed

    2012-06-02

    The problem of thermal dispersion effects on unsteady free convection from an isothermal horizontal circular cylinder to a non-Newtonian fluid saturating a porous medium is examined numerically. The Darcy-Brinkman-Forchheimer model is employed to describe the flow field. The thermal diffusivity coefficient has been assumed to be the sum of the molecular diffusivity and the dynamic diffusivity due to mechanical dispersion. The simultaneous development of the momentum and thermal boundary layers are obtained by using finite difference method. The stability conditions are determined for each difference equation. Using an explicit finite difference scheme, solutions at each time-step have been found and then stepped forward in time until reaching steady state solution. Velocity and temperature profiles are shown graphically. It is found that as time approaches infinity, the values of friction factor and heat transfer coefficient approach the steady state values.

  4. A Conditionally Stable Scheme for a Transient Flow of a Non-Newtonian Fluid Saturating a Porous Medium

    KAUST Repository

    El-Amin, Mohamed; Salama, Amgad; Sun, Shuyu

    2012-01-01

    The problem of thermal dispersion effects on unsteady free convection from an isothermal horizontal circular cylinder to a non-Newtonian fluid saturating a porous medium is examined numerically. The Darcy-Brinkman-Forchheimer model is employed to describe the flow field. The thermal diffusivity coefficient has been assumed to be the sum of the molecular diffusivity and the dynamic diffusivity due to mechanical dispersion. The simultaneous development of the momentum and thermal boundary layers are obtained by using finite difference method. The stability conditions are determined for each difference equation. Using an explicit finite difference scheme, solutions at each time-step have been found and then stepped forward in time until reaching steady state solution. Velocity and temperature profiles are shown graphically. It is found that as time approaches infinity, the values of friction factor and heat transfer coefficient approach the steady state values.

  5. Thermal convection of viscoelastic shear-thinning fluids

    International Nuclear Information System (INIS)

    Albaalbaki, Bashar; Khayat, Roger E; Ahmed, Zahir U

    2016-01-01

    The Rayleigh–Bénard convection for non-Newtonian fluids possessing both viscoelastic and shear-thinning behaviours is examined. The Phan-Thien–Tanner (PTT) constitutive equation is implemented to model the non-Newtonian character of the fluid. It is found that while the shear-thinning and viscoelastic effects could annihilate one another for the steady roll flow, presence of both behaviours restricts the roll stability limit significantly compared to the cases when the fluid is either inelastic shear-thinning or purely viscoelastic with constant viscosity. (paper)

  6. Numerical Modeling of Fluid-Structure Interaction with Rheologically Complex Fluids

    OpenAIRE

    Chen, Xingyuan

    2014-01-01

    In the present work the interaction between rheologically complex fluids and elastic solids is studied by means of numerical modeling. The investigated complex fluids are non-Newtonian viscoelastic fluids. The fluid-structure interaction (FSI) of this kind is frequently encountered in injection molding, food processing, pharmaceutical engineering and biomedicine. The investigation via experiments is costly, difficult or in some cases, even impossible. Therefore, research is increasingly aided...

  7. The fluid dynamics of the chocolate fountain

    Science.gov (United States)

    Townsend, Adam K.; Wilson, Helen J.

    2016-01-01

    We consider the fluid dynamics of the chocolate fountain. Molten chocolate is a mildly shear-thinning non-Newtonian fluid. Dividing the flow into three main domains—the pumped flow up the centre, the film flow over each dome, and the freely falling curtain flow between the domes—we generate a wide-ranging study of Newtonian and non-Newtonian fluid mechanics. The central pumped flow is a benchmark to elucidate the effects of shear-thinning. The dome flow can be modelled as a thin-film flow with the leading-order effects being a simple balance of gravity and viscosity. Finally, the curtain flow is analytically intractable but is related to the existing theory of water bells (both inviscid and viscous). In pipe flow, Newtonian fluids exhibit a parabolic velocity profile; shear-thinning makes the profile more blunted. In thin-film flow over the dome, gravitational and viscous effects balance and the dome shape is not important beyond the local slope. We find that the chocolate thins and slows down as it travels down the dome. Finally, in the curtain flow, we predict the shape of the falling sheet for an inviscid fluid, and compare this with the literature to predict the shape for a viscous fluid, having shown that viscous forces are too great to ignore. We also find that the primary effect driving the shape of the curtain (which falls inwards towards the axis of the fountain) is surface tension. We find that the three domains provide excellent introductions to non-Newtonian mechanics, the important mathematical technique of scaling, and how to manipulate existing data to make our own predictions. We also find that the topic generates interest among the public in our engagement work.

  8. The fluid dynamics of the chocolate fountain

    International Nuclear Information System (INIS)

    Townsend, Adam K; Wilson, Helen J

    2016-01-01

    We consider the fluid dynamics of the chocolate fountain. Molten chocolate is a mildly shear-thinning non-Newtonian fluid. Dividing the flow into three main domains—the pumped flow up the centre, the film flow over each dome, and the freely falling curtain flow between the domes—we generate a wide-ranging study of Newtonian and non-Newtonian fluid mechanics. The central pumped flow is a benchmark to elucidate the effects of shear-thinning. The dome flow can be modelled as a thin-film flow with the leading-order effects being a simple balance of gravity and viscosity. Finally, the curtain flow is analytically intractable but is related to the existing theory of water bells (both inviscid and viscous). In pipe flow, Newtonian fluids exhibit a parabolic velocity profile; shear-thinning makes the profile more blunted. In thin-film flow over the dome, gravitational and viscous effects balance and the dome shape is not important beyond the local slope. We find that the chocolate thins and slows down as it travels down the dome. Finally, in the curtain flow, we predict the shape of the falling sheet for an inviscid fluid, and compare this with the literature to predict the shape for a viscous fluid, having shown that viscous forces are too great to ignore. We also find that the primary effect driving the shape of the curtain (which falls inwards towards the axis of the fountain) is surface tension. We find that the three domains provide excellent introductions to non-Newtonian mechanics, the important mathematical technique of scaling, and how to manipulate existing data to make our own predictions. We also find that the topic generates interest among the public in our engagement work. (paper)

  9. Rate-Dependent Slip of Newtonian Liquid at Smooth Surfaces

    International Nuclear Information System (INIS)

    Zhu, Yingxi; Granick, Steve

    2001-01-01

    Newtonian fluids were placed between molecularly smooth surfaces whose spacing was vibrated at spacings where the fluid responded as a continuum. Hydrodynamic forces agreed with predictions from the no-slip boundary condition only provided that flow rate (peak velocity normalized by spacing) was low, but implied partial slip when it exceeded a critical level, different in different systems, correlated with contact angle (surface wettability). With increasing flow rate and partially wetted surfaces, hydrodynamic forces became up to 2--4 orders of magnitude less than expected by assuming the no-slip boundary condition that is commonly stated in textbooks

  10. Newtonian cosmology Newton would understand

    International Nuclear Information System (INIS)

    Lemons, D.S.

    1988-01-01

    Isaac Newton envisioned a static, infinite, and initially uniform, zero field universe that was gravitationally unstable to local condensations of matter. By postulating the existence of such a universe and using it as a boundary condition on Newtonian gravity, a new field equation for gravity is derived, which differs from the classical one by a time-dependent cosmological term proportional to the average mass density of the universe. The new field equation not only makes Jeans' analysis of the gravitational instability of a Newtonian universe consistent, but also gives rise to a family of Newtonian evolutionary cosmologies parametrized by a time-invariant expansion velocity. This Newtonian cosmology contrasts with both 19th-century ones and with post general relativity Newtonian cosmology

  11. Break-up of a non-Newtonian jet injected downwards in a ...

    Indian Academy of Sciences (India)

    atomization and spray coating, crop spraying, ink jet printing, printing of polymer transis- tors, and ... particular ones used in printing and coating, the liquids encountered are non-Newtonian. For breakup of ...... In-Press. Sussman M and Pukett E G 2000 A coupled level set and volume-of-fluid method for computing 3D and.

  12. Was Newtonian cosmology really inconsistent?

    Science.gov (United States)

    Vickers, Peter

    This paper follows up a debate as to the consistency of Newtonian cosmology. Whereas Malament [(1995). Is Newtonian cosmology really inconsistent? Philosophy of Science 62, 489-510] has shown that Newtonian cosmology is not inconsistent, to date there has been no analysis of Norton's claim [(1995). The force of Newtonian cosmology: Acceleration is relative. Philosophy of Science 62, 511-522.] that Newtonian cosmology was inconsistent prior to certain advances in the 1930s, and in particular prior to Seeliger's seminal paper of Seeliger [(1895). Über das Newton'sche Gravitationsgesetz. Astronomische Nachrichten 137 (3273), 129-136.] In this paper I agree that there are assumptions, Newtonian and cosmological in character, and relevant to the real history of science, which are inconsistent. But there are some important corrections to make to Norton's account. Here I display for the first time the inconsistencies-four in total-in all their detail. Although this extra detail shows there to be several different inconsistencies, it also goes some way towards explaining why they went unnoticed for 200 years.

  13. Post-Newtonian Jeans Analysis

    International Nuclear Information System (INIS)

    Nazari, Elham; Kazemi, Ali; Roshan, Mahmood; Abbassi, Shahram

    2017-01-01

    The Jeans analysis is studied in the first post-Newtonian limit. In other words, the relativistic effects on local gravitational instability are considered for systems whose characteristic velocities and corresponding gravitational fields are higher than those permitted in the Newtonian limit. The dispersion relation for the propagation of small perturbations is found in the post-Newtonian approximation using two different techniques. A new Jeans mass is derived and compared to the standard Jeans mass. In this limit, the relativistic effects make the new Jeans mass smaller than the Newtonian Jeans mass. Furthermore, the fractional difference between these two masses increases when the temperature/pressure of the system increases. Interestingly, in this limit, pressure can enhance gravitational instability instead of preventing it. Finally, the results are applied to high-temperature astrophysical systems, and the possibility of local fragmentation in some relativistic systems is investigated.

  14. Post-Newtonian Jeans Analysis

    Energy Technology Data Exchange (ETDEWEB)

    Nazari, Elham; Kazemi, Ali; Roshan, Mahmood; Abbassi, Shahram, E-mail: mroshan@um.ac.ir [Department of Physics, Ferdowsi University of Mashhad, P.O. Box 1436, Mashhad (Iran, Islamic Republic of)

    2017-04-20

    The Jeans analysis is studied in the first post-Newtonian limit. In other words, the relativistic effects on local gravitational instability are considered for systems whose characteristic velocities and corresponding gravitational fields are higher than those permitted in the Newtonian limit. The dispersion relation for the propagation of small perturbations is found in the post-Newtonian approximation using two different techniques. A new Jeans mass is derived and compared to the standard Jeans mass. In this limit, the relativistic effects make the new Jeans mass smaller than the Newtonian Jeans mass. Furthermore, the fractional difference between these two masses increases when the temperature/pressure of the system increases. Interestingly, in this limit, pressure can enhance gravitational instability instead of preventing it. Finally, the results are applied to high-temperature astrophysical systems, and the possibility of local fragmentation in some relativistic systems is investigated.

  15. Influence of fluid structure upon the shape of RTD curve at a sugar crystallizer

    International Nuclear Information System (INIS)

    Griffith, J.; Borroto, J.I.; Leclerc, J.P.

    2004-01-01

    The influence of fluid structure over the shape of the RTD curve at a pilot sugar crystallizer has been tested by the radiotracer method. For Newtonian pure molasses B sugar fluid the pattern flux was close to a perfect mixing cells with backmixing model with a back flow-rate ratio lower than one. In the case of molasses B transformed to a non-Newtonian fluid the pattern flux approaches the same model but with extreme values of the back flow-rate ration (higher than one). A direct relationship was founded between the back flow rate ratio and the flow index of the tested fluids, showing that a special attention has to be pay during data processing of the RTD curves for non-Newtonian fluids. (author)

  16. Onset of Absolute Instability Induced by Viscous Dissipation in the Poiseuille-Darcy-Benard Convection of a Newtonian Fluid

    International Nuclear Information System (INIS)

    Brandão, P V; Alves, L S de B; Barletta, A

    2014-01-01

    The present paper investigates the transition from convective to absolute instability induced by viscous dissipation. As far as the authors are aware, this is the first time such a study is reported in the literature. Its framework is provided by the Poiseuille-Darcy-Benard convection of a Newtonian fluid. We found the same behaviour observed in the absence of viscous dissipation whenever the Gebhart number is smaller than Ge < 0.95, which is the stabilising effect of the cross flow. When 0.95 < Ge < 4.31, weak cross flows still stabilise the onset of absolute instability but stronger cross flows destabilise it. For a stronger viscous dissipation, i.e. Ge > 4.31, the cross flow always destabilises this onset. The latter two conditions create a scenario where viscous dissipation is capable of inducing a transition to absolute instability in the absence of wall heating, i.e. with a zero Rayleigh number

  17. The turbulent mixing of non-Newtonian fluids

    Science.gov (United States)

    Demianov, A. Yu; Doludenko, A. N.; Inogamov, N. A.; Son, E. E.

    2013-07-01

    The turbulence caused by the Rayleigh-Taylor instability represents a complicated phenomenon. It is usually related to the major hydrodynamic activities, the tangling of the media contact boundary, merging, separation and intermixing of originally smoothed initial structures. An important role in the theory of the Rayleigh-Taylor instability is played by the discontinuity of density on a contact interface between two homogeneous (in terms of density) fluids. A numerical modeling of the intermixing of two fluids with different rheology whose densities differ twice as a result of the Rayleigh-Taylor instability has been carried out. The coefficients of turbulent intermixing in a multimode statement of the problem for the Bingham, dilatant and pseudo-plastic fluids have been obtained.

  18. Modern fluid dynamics

    CERN Document Server

    Kleinstreuer, Clement

    2018-01-01

    Modern Fluid Dynamics, Second Edition provides up-to-date coverage of intermediate and advanced fluids topics. The text emphasizes fundamentals and applications, supported by worked examples and case studies. Scale analysis, non-Newtonian fluid flow, surface coating, convection heat transfer, lubrication, fluid-particle dynamics, microfluidics, entropy generation, and fluid-structure interactions are among the topics covered. Part A presents fluids principles, and prepares readers for the applications of fluid dynamics covered in Part B, which includes computer simulations and project writing. A review of the engineering math needed for fluid dynamics is included in an appendix.

  19. Non Newtonian gravity creeping flow

    International Nuclear Information System (INIS)

    Gratton, J.; Mahajan, S.M.; Minotti, F.

    1988-11-01

    We derive the governing equations for creeping gravity currents of non Newtonian liquids having a power law rheology, using a lubrication approximation. We consider unidirectional and axisymmetric currents. The equations differ from those for Newtonian liquids, being nonlinear in the spatial derivative of the thickness of the current. However, many solutions are closely analogous to those for Newtonian rheology; in particular the spreading relations can also be expressed as power laws of time, with exponents that depend on the rheological index. Similarity solutions for currents whose volume varies as a power of time are obtained. For the spread of a constant volume of liquid, analytic solutions are found. We also derive solutions of the waiting-time type, as well as the ones describing steady flows from a constant source to a sink. General travelling wave solutions are given, and analytic formulae for a simple case are derived. A phase plane formalism, that allows the systematic derivation of self similar solutions, is introduced. The application of the Boltzmann transform is briefly discussed. Present results are closely analogous to those for Newtonian liquids; all the solutions obtained here have their counterparts in Newtonian flows. This happens because the power law rheology, like the Newtonian constitutive relation, involves a single dimensional parameter. Thus one finds similarity solutions whenever the analogous Newtonian problem is self similar. Although the spreading relations are rheology-dependent, in most cases the dependence is rather weak. The present results may be of interest for geophysics since the lithosphere deforms according to an average power law rheology. (author). 17 refs

  20. A Lagrangian finite element method for the simulation of flow of non-newtonian liquids

    DEFF Research Database (Denmark)

    Hassager, Ole; Bisgaard, C

    1983-01-01

    A Lagrangian method for the simulation of flow of non-Newtonian liquids is implemented. The fluid mechanical equations are formulated in the form of a variational principle, and a discretization is performed by finite elements. The method is applied to the slow of a contravariant convected Maxwell...

  1. Solitons in Newtonian gravity

    International Nuclear Information System (INIS)

    Goetz, G.

    1988-01-01

    It is shown that the plane-wave solutions for the equations governing the motion of a self-gravitating isothermal fluid in Newtonian hydrodynamics are generated by a sine-Gordon equation which is solvable by an 'inverse scattering' transformation. A transformation procedure is outlined by means of which one can construct solutions of the gravity system out of a pair of solutions of the sine-Gordon equation, which are interrelated via an auto-Baecklund transformation. In general the solutions to the gravity system are obtained in a parametric representation in terms of characteristic coordinates. All solutions of the gravity system generated by the one-and two-soliton solutions of the sine-Gordon equation can be constructed explicitly. These might provide models for the evolution of flat structures as they are predicted to arise in the process of galaxy formation. (author)

  2. Gravitational radiation from nearly Newtonian systems

    International Nuclear Information System (INIS)

    Kirk, E.M.

    1989-09-01

    A method of examining gravitational radiation from nearly Newtonian systems is presented. Using the Cartan formulation of Newtonian gravity, a one parameter family of space-times which have a strict Newtonian limit is constructed. An expression for the initial null data in terms of the Newtonian potential is obtained in the Newtonian limit. Using this, the problem is formulated as a series in the Newtonian parameter. The series expansions for the sources of the Bianchi identities are obtained to third order in both the vacuum and non-vacuum cases. A simple technique is presented for determining whether a particular source term gives rise to asymptotically flat null data. The far field quadrupole formula is derived in a leading approximation and a method for obtaining error bounds is discussed. Additionally, a method for solving Einstein's equations is shown. This involves expressing the Ricci identities as a matrix, Riccati equation and a system of linear matrix equations. A comparison of the formalisms of Bondi and Newman Penrose is presented and explicit correspondences between the supersurface constrain equations and the Ricci identities are shown. (author)

  3. Three-dimensional blade coating of complex fluid

    Science.gov (United States)

    Singh, Vachitar; Grimaldi, Emma; Sauret, Alban; Dressaire, Emilie

    2015-11-01

    The application of a layer of non-newtonian fluid on a solid substrate is an important industrial problem involved in polymer or paint coatings, and an everyday life challenge when it comes to spreading peanut butter on a toast. Most experimental and theoretical work has focused on the two-dimensional situation, i.e. the scraping of a fixed blade on a moving substrate to turn a thick layer of liquid into a thin coat. However the spreading of a finite volume of non-newtonian fluid using a blade has received less attention, despite significant practical and fundamental implications. In this study, we investigate experimentally the spreading of a finite volume of a model non-newtonian fluid, carbopol, initially deposited against the fixed blade. As the substrate is translated at constant speed, we characterize the dynamics of spreading and the final shape of the coated layer. We measure and rationalize the influence of the liquid volume, the height and orientation of the blade, and the speed of the substrate on the spreading.

  4. Solitons as Newtonian particles

    International Nuclear Information System (INIS)

    Eboli, O.J.P.; Marques, G.C.

    1982-07-01

    The effect of external electromagnetic fields on non relativistic solitons is studied. Although the solitons are distorted by external fields, they still exhibit a Newtonian behavior. Some explicit examples of such a phenomenon are given, presenting solutions which exhibit Newtonian behavior for simple external fields. Furthermore, general results like charge and flux quantization are shown. (Author) [pt

  5. CFD study of the thermal transfer of a non-Newtonian fluid within a tank mechanically stirred by an anchor-shaped impeller

    Science.gov (United States)

    Rahmani, L.; Seghier, O.; Benmoussa, A.; Draoui, B.

    2018-06-01

    The most of operations of chemical, biochemical or petrochemical industries are carried out in tanks or in reactors which are mechanically-controlled. The optimum mode of operation of these devices requires a finalized knowledge of the thermo-hydrodynamic behavior induced by the agitator. In the present work, the characterization of the incompressible hydrodynamic and thermal fields of a non-Newtonian fluid (Bingham) in a flat, non-baffled cylindrical vessel fitted with anchor agitator was undertaken by numerical simulation, using the CFD code Fluent (6.3.26) based on the finite volume discretization method of the energy equation and the Navier-Stokes equations which are formulated in (U.V.P) variables. We have summarized this simulated system by comparing of the consumed power and the Nusselt number for this type of mobile (Anchor agitator).

  6. Reduced viscosity interpreted for fluid/gas mixtures

    Science.gov (United States)

    Lewis, D. H.

    1981-01-01

    Analysis predicts decrease in fluid viscosity by comparing pressure profile of fluid/gas mixture with that of power-law fluid. Fluid is taken to be viscous, non-Newtonian, and incompressible; the gas to be ideal; the flow to be inertia-free, isothermal, and one dimensional. Analysis assists in design of flow systems for petroleum, coal, polymers, and other materials.

  7. Heat and mass transfer in magnetohydrodynamic Casson fluid over an exponentially permeable stretching surface

    Directory of Open Access Journals (Sweden)

    C.S.K. Raju

    2016-03-01

    Full Text Available In this study we analyzed the flow, heat and mass transfer behavior of Casson fluid past an exponentially permeable stretching surface in presence of thermal radiation, magneticfield, viscous dissipation, heat source and chemical reaction. We presented dual solutions by comparing the results of the Casson fluid with the Newtonian fluid. The governing partial nonlinear differential equations of the flow, heat and mass transfer are transformed into ordinary differential equations by using similarity transformation and solved numerically by using Matlab bvp4c package. The effects of various non-dimensional governing parameters on velocity, temperature and concentration profiles are discussed and presented graphically. Also, the friction factor, Nusselt and Sherwood numbers are analyzed and presented in tabular form for both Casson and Newtonian fluids separately. Under some special conditions the results of the present study have an excellent agreement with existing studies for both Casson and Newtonian fluid cases.

  8. Pseudo-Newtonian planar circular restricted 3-body problem

    International Nuclear Information System (INIS)

    Dubeibe, F.L.; Lora-Clavijo, F.D.; González, Guillermo A.

    2017-01-01

    We study the dynamics of the planar circular restricted three-body problem in the context of a pseudo-Newtonian approximation. By using the Fodor–Hoenselaers–Perjés procedure, we perform an expansion in the mass potential of a static massive spherical source up to the first non-Newtonian term, giving place to a gravitational potential that includes first-order general relativistic effects. With this result, we model a system composed by two pseudo-Newtonian primaries describing circular orbits around their common center of mass, and a test particle orbiting the system in the equatorial plane. The dynamics of the new system of equations is studied in terms of the Poincaré section method and the Lyapunov exponents, where the introduction of a new parameter ϵ, allows us to observe the transition from the Newtonian to the pseudo-Newtonian regime. We show that when the Jacobian constant is fixed, a chaotic orbit in the Newtonian regime can be either chaotic or regular in the pseudo-Newtonian approach. As a general result, we find that most of the pseudo-Newtonian configurations are less stable than their Newtonian equivalent.

  9. Pseudo-Newtonian planar circular restricted 3-body problem

    Energy Technology Data Exchange (ETDEWEB)

    Dubeibe, F.L., E-mail: fldubeibem@unal.edu.co [Facultad de Ciencias Humanas y de la Educación, Universidad de los Llanos, Villavicencio (Colombia); Grupo de Investigación en Relatividad y Gravitación, Escuela de Física, Universidad Industrial de Santander, A.A. 678, Bucaramanga (Colombia); Lora-Clavijo, F.D., E-mail: fadulora@uis.edu.co [Grupo de Investigación en Relatividad y Gravitación, Escuela de Física, Universidad Industrial de Santander, A.A. 678, Bucaramanga (Colombia); González, Guillermo A., E-mail: guillermo.gonzalez@saber.uis.edu.co [Grupo de Investigación en Relatividad y Gravitación, Escuela de Física, Universidad Industrial de Santander, A.A. 678, Bucaramanga (Colombia)

    2017-02-12

    We study the dynamics of the planar circular restricted three-body problem in the context of a pseudo-Newtonian approximation. By using the Fodor–Hoenselaers–Perjés procedure, we perform an expansion in the mass potential of a static massive spherical source up to the first non-Newtonian term, giving place to a gravitational potential that includes first-order general relativistic effects. With this result, we model a system composed by two pseudo-Newtonian primaries describing circular orbits around their common center of mass, and a test particle orbiting the system in the equatorial plane. The dynamics of the new system of equations is studied in terms of the Poincaré section method and the Lyapunov exponents, where the introduction of a new parameter ϵ, allows us to observe the transition from the Newtonian to the pseudo-Newtonian regime. We show that when the Jacobian constant is fixed, a chaotic orbit in the Newtonian regime can be either chaotic or regular in the pseudo-Newtonian approach. As a general result, we find that most of the pseudo-Newtonian configurations are less stable than their Newtonian equivalent.

  10. Post-Newtonian gravitational bremsstrahlung

    International Nuclear Information System (INIS)

    Turner, M.; Will, C.M.

    1977-07-01

    Formulae and numerical results are presented for the gravitational radiation emitted during a low-deflection encounter between two massive bodies. Results are valid through post-Newtonian order within general relativity. The gravitational waveform, the total luminosity and total emitted energy, the angular distribution of emitted energy, and the frequency spectrum are discussed in detail. A method boosting the accuracy of these quantities to post Newtonian order is also presented. A numerical comparison of results with those of Peters, and of Kovacs and Thorne shows that the post Newtonian method is reliable to better than 0.1 percent at v = 0.1 c, to a few percent at v = 0.35 c, and to 10 to 20 percent at v = 0.5 c

  11. Introduction to mathematical fluid dynamics

    CERN Document Server

    Meyer, Richard E

    2010-01-01

    An introduction to the behavior of liquids and gases, this volume provides excellent coverage of kinematics, momentum principle, Newtonian fluid, rotating fluids, compressibility, and more. It is geared toward advanced undergraduate and graduate students of mathematics and general science, and it requires a background in calculus and vector analysis. 1971 edition.

  12. Quasi-local mass in the covariant Newtonian spacetime

    International Nuclear Information System (INIS)

    Wu, Y-H; Wang, C-H

    2008-01-01

    In general relativity, quasi-local energy-momentum expressions have been constructed from various formulae. However, the Newtonian theory of gravity gives a well-known and a unique quasi-local mass expression (surface integration). Since geometrical formulation of Newtonian gravity has been established in the covariant Newtonian spacetime, it provides a covariant approximation from relativistic to Newtonian theories. By using this approximation, we calculate the Komar integral, the Brown-York quasi-local energy and the Dougan-Mason quasi-local mass in the covariant Newtonian spacetime. It turns out that the Komar integral naturally gives the Newtonian quasi-local mass expression; however, further conditions (spherical symmetry) need to be made for Brown-York and Dougan-Mason expressions

  13. Two-Fluid Mathematical Models for Blood Flow in Stenosed Arteries: A Comparative Study

    Directory of Open Access Journals (Sweden)

    Sankar DS

    2009-01-01

    Full Text Available The pulsatile flow of blood through stenosed arteries is analyzed by assuming the blood as a two-fluid model with the suspension of all the erythrocytes in the core region as a non-Newtonian fluid and the plasma in the peripheral layer as a Newtonian fluid. The non-Newtonian fluid in the core region of the artery is assumed as a (i Herschel-Bulkley fluid and (ii Casson fluid. Perturbation method is used to solve the resulting system of non-linear partial differential equations. Expressions for various flow quantities are obtained for the two-fluid Casson model. Expressions of the flow quantities obtained by Sankar and Lee (2006 for the two-fluid Herschel-Bulkley model are used to get the data for comparison. It is found that the plug flow velocity and velocity distribution of the two-fluid Casson model are considerably higher than those of the two-fluid Herschel-Bulkley model. It is also observed that the pressure drop, plug core radius, wall shear stress and the resistance to flow are significantly very low for the two-fluid Casson model than those of the two-fluid Herschel-Bulkley model. Hence, the two-fluid Casson model would be more useful than the two-fluid Herschel-Bulkley model to analyze the blood flow through stenosed arteries.

  14. Numerical analysis of capillary compensated micropolar fluid lubricated hole-entry journal bearings

    Directory of Open Access Journals (Sweden)

    Nathi Ram

    2016-06-01

    Full Text Available The micropolar lubricated symmetric/asymmetric hole-entry bearings using capillary restrictor have been analyzed in the present work. Reynolds equation for micropolar lubricant has been derived and solved by FEM. The results have been computed using selected parameters of micropolar lubricant for hole-entry hydrostatic/hybrid journal bearings. A significant increase in damping and stiffness coefficients is observed for bearings having micropolar parameter N2=0.9, lm=10 than similar bearings under Newtonian lubricant. The threshold speed gets increased when symmetric bearing lubricated under micropolar fluid than Newtonian lubricant. The threshold speed gets increased when symmetric bearing lubricated under micropolar fluid than Newtonian lubricant.

  15. Numerical methods for multi-scale modeling of non-Newtonian flows

    Science.gov (United States)

    Symeonidis, Vasileios

    This work presents numerical methods for the simulation of Non-Newtonian fluids in the continuum as well as the mesoscopic level. The former is achieved with Direct Numerical Simulation (DNS) spectral h/p methods, while the latter employs the Dissipative Particle Dynamics (DPD) technique. Physical results are also presented as a motivation for a clear understanding of the underlying numerical approaches. The macroscopic simulations employ two non-Newtonian models, namely the Reiner-Ravlin (RR) and the viscoelastic FENE-P model. (1) A spectral viscosity method defined by two parameters ε, M is used to stabilize the FENE-P conformation tensor c. Convergence studies are presented for different combinations of these parameters. Two boundary conditions for the tensor c are also investigated. (2) Agreement is achieved with other works for Stokes flow of a two-dimensional cylinder in a channel. Comparison of the axial normal stress and drag coefficient on the cylinder is presented. Further, similar results from unsteady two- and three-dimensional turbulent flows past a flat plate in a channel are shown. (3) The RR problem is formulated for nearly incompressible flows, with the introduction of a mathematically equivalent tensor formulation. A spectral viscosity method and polynomial over-integration are studied. Convergence studies, including a three-dimensional channel flow with a parallel slot, investigate numerical problems arising from elemental boundaries and sharp corners. (4) The round hole pressure problem is presented for Newtonian and RR fluids in geometries with different hole sizes. Comparison with experimental data is made for the Newtonian case. The flaw in the experimental assumptions of undisturbed pressure opposite the hole is revealed, while good agreement with the data is shown. The Higashitani-Pritchard kinematical theory for RR, fluids is recovered for round holes and an approximate formula for the RR Stokes hole pressure is presented. The mesoscopic

  16. The Post-Newtonian Approximation for Relativistic Compact Binaries

    Directory of Open Access Journals (Sweden)

    Futamase Toshifumi

    2007-03-01

    Full Text Available We discuss various aspects of the post-Newtonian approximation in general relativity. After presenting the foundation based on the Newtonian limit, we show a method to derive post-Newtonian equations of motion for relativistic compact binaries based on a surface integral approach and the strong field point particle limit. As an application we derive third post-Newtonian equations of motion for relativistic compact binaries which respect the Lorentz invariance in the post-Newtonian perturbative sense, admit a conserved energy, and are free from any ambiguity.

  17. Perturbed Newtonian description of the Lemaître model with non-negligible pressure

    International Nuclear Information System (INIS)

    Yamamoto, Kazuhiro; Marra, Valerio; Mukhanov, Viatcheslav; Sasaki, Misao

    2016-01-01

    We study the validity of the Newtonian description of cosmological perturbations using the Lemaître model, an exact spherically symmetric solution of Einstein's equation. This problem has been investigated in the past for the case of a dust fluid. Here, we extend the previous analysis to the more general case of a fluid with non-negligible pressure, and, for the numerical examples, we consider the case of radiation (P=ρ/3). We find that, even when the density contrast has a nonlinear amplitude, the Newtonian description of the cosmological perturbations using the gravitational potential ψ and the curvature potential φ is valid as long as we consider sub-horizon inhomogeneities. However, the relation ψ+φ=O(φ 2 )—which holds for the case of a dust fluid—is not valid for a relativistic fluid, and an effective anisotropic stress is generated. This demonstrates the usefulness of the Lemaître model which allows us to study in an exact nonlinear fashion the onset of anisotropic stress in fluids with non-negligible pressure. We show that this happens when the characteristic scale of the inhomogeneity is smaller than the sound horizon and that the deviation is caused by the nonlinear effect of the fluid's fast motion. We also find that ψ+φ= [O(φ 2 ),O(c s 2φ  δ)] for an inhomogeneity with density contrast δ whose characteristic scale is smaller than the sound horizon, unless w is close to −1, where w and c s are the equation of state parameter and the sound speed of the fluid, respectively. On the other hand, we expect ψ+φ=O(φ 2 ) to hold for an inhomogeneity whose characteristic scale is larger than the sound horizon, unless the amplitude of the inhomogeneity is large and w is close to −1

  18. Study of blood flow in several benchmark micro-channels using a two-fluid approach.

    Science.gov (United States)

    Wu, Wei-Tao; Yang, Fang; Antaki, James F; Aubry, Nadine; Massoudi, Mehrdad

    2015-10-01

    It is known that in a vessel whose characteristic dimension (e.g., its diameter) is in the range of 20 to 500 microns, blood behaves as a non-Newtonian fluid, exhibiting complex phenomena, such as shear-thinning, stress relaxation, and also multi-component behaviors, such as the Fahraeus effect, plasma-skimming, etc. For describing these non-Newtonian and multi-component characteristics of blood, using the framework of mixture theory, a two-fluid model is applied, where the plasma is treated as a Newtonian fluid and the red blood cells (RBCs) are treated as shear-thinning fluid. A computational fluid dynamic (CFD) simulation incorporating the constitutive model was implemented using OpenFOAM® in which benchmark problems including a sudden expansion and various driven slots and crevices were studied numerically. The numerical results exhibited good agreement with the experimental observations with respect to both the velocity field and the volume fraction distribution of RBCs.

  19. Study of blood flow in several benchmark micro-channels using a two-fluid approach

    Science.gov (United States)

    Wu, Wei-Tao; Yang, Fang; Antaki, James F.; Aubry, Nadine; Massoudi, Mehrdad

    2015-01-01

    It is known that in a vessel whose characteristic dimension (e.g., its diameter) is in the range of 20 to 500 microns, blood behaves as a non-Newtonian fluid, exhibiting complex phenomena, such as shear-thinning, stress relaxation, and also multi-component behaviors, such as the Fahraeus effect, plasma-skimming, etc. For describing these non-Newtonian and multi-component characteristics of blood, using the framework of mixture theory, a two-fluid model is applied, where the plasma is treated as a Newtonian fluid and the red blood cells (RBCs) are treated as shear-thinning fluid. A computational fluid dynamic (CFD) simulation incorporating the constitutive model was implemented using OpenFOAM® in which benchmark problems including a sudden expansion and various driven slots and crevices were studied numerically. The numerical results exhibited good agreement with the experimental observations with respect to both the velocity field and the volume fraction distribution of RBCs. PMID:26240438

  20. Transient flows of a Burgers' fluid

    International Nuclear Information System (INIS)

    Khan, M.

    2005-12-01

    An analysis is performed to develop the analytical solutions for some unsteady magnetohydrodynamic (MHD) flows of a Burgers' fluid between two plates. A uniform magnetic field is applied transversely to the fluid motion. The exact solutions are given for three problems. Results for the velocity fields are discussed and compared with the flows of Oldroyd-B, Maxwell, second grade and Newtonian fluids. (author)

  1. Equilibrium configurations of fluids and their stability in higher dimensions

    International Nuclear Information System (INIS)

    Cardoso, Vitor; Gualtieri, Leonardo

    2006-01-01

    We study equilibrium shapes, stability and possible bifurcation diagrams of fluids in higher dimensions, held together by either surface tension or self-gravity. We consider the equilibrium shape and stability problem of self-gravitating spheroids, establishing the formalism to generalize the MacLaurin sequence to higher dimensions. We show that such simple models, of interest on their own, also provide accurate descriptions of their general relativistic relatives with event horizons. The examples worked out here hint at some model-independent dynamics, and thus at some universality: smooth objects seem always to be well described by both 'replicas' (either self-gravity or surface tension). As an example, we exhibit an instability afflicting self-gravitating (Newtonian) fluid cylinders. This instability is the exact analogue, within Newtonian gravity, of the Gregory-Laflamme instability in general relativity. Another example considered is a self-gravitating Newtonian torus made of a homogeneous incompressible fluid. We recover the features of the black ring in general relativity

  2. Effect of radiation and magnetohydrodynamic free convection boundary layer flow on a solid sphere with Newtonian heating in a micropolar fluid

    International Nuclear Information System (INIS)

    Alkasasbeh, Hamzeh Taha; Sarif, Norhafizah Md; Salleh, Mohd Zuki; Tahar, Razman Mat; Nazar, Roslinda; Pop, Ioan

    2015-01-01

    In this paper, the effect of radiation on magnetohydrodynamic free convection boundary layer flow on a solid sphere with Newtonian heating in a micropolar fluid, in which the heat transfer from the surface is proportional to the local surface temperature, is considered. The transformed boundary layer equations in the form of nonlinear partial differential equations are solved numerically using an implicit finite difference scheme known as the Keller-box method. Numerical solutions are obtained for the local wall temperature and the local skin friction coefficient, as well as the velocity, angular velocity and temperature profiles. The features of the flow and heat transfer characteristics for various values of the Prandtl number Pr, micropolar parameter K, magnetic parameter M, radiation parameter N R , the conjugate parameter γ and the coordinate running along the surface of the sphere, x are analyzed and discussed

  3. Effect of radiation and magnetohydrodynamic free convection boundary layer flow on a solid sphere with Newtonian heating in a micropolar fluid

    Energy Technology Data Exchange (ETDEWEB)

    Alkasasbeh, Hamzeh Taha, E-mail: zukikuj@yahoo.com; Sarif, Norhafizah Md, E-mail: zukikuj@yahoo.com; Salleh, Mohd Zuki, E-mail: zukikuj@yahoo.com [Futures and Trends Research Group, Faculty of Industrial Science and Technology, Universiti Malaysia Pahang, 26300 UMP Kuantan, Pahang (Malaysia); Tahar, Razman Mat [Faculty of Technology, Universiti Malaysia Pahang, 26300 UMP Kuantan, Pahang (Malaysia); Nazar, Roslinda [School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor (Malaysia); Pop, Ioan [Department of Mathematics, Babeş-Bolyai University, R-400084 Cluj-Napoca (Romania)

    2015-02-03

    In this paper, the effect of radiation on magnetohydrodynamic free convection boundary layer flow on a solid sphere with Newtonian heating in a micropolar fluid, in which the heat transfer from the surface is proportional to the local surface temperature, is considered. The transformed boundary layer equations in the form of nonlinear partial differential equations are solved numerically using an implicit finite difference scheme known as the Keller-box method. Numerical solutions are obtained for the local wall temperature and the local skin friction coefficient, as well as the velocity, angular velocity and temperature profiles. The features of the flow and heat transfer characteristics for various values of the Prandtl number Pr, micropolar parameter K, magnetic parameter M, radiation parameter N{sub R}, the conjugate parameter γ and the coordinate running along the surface of the sphere, x are analyzed and discussed.

  4. Engineering Fracking Fluids with Computer Simulation

    Science.gov (United States)

    Shaqfeh, Eric

    2015-11-01

    There are no comprehensive simulation-based tools for engineering the flows of viscoelastic fluid-particle suspensions in fully three-dimensional geometries. On the other hand, the need for such a tool in engineering applications is immense. Suspensions of rigid particles in viscoelastic fluids play key roles in many energy applications. For example, in oil drilling the ``drilling mud'' is a very viscous, viscoelastic fluid designed to shear-thin during drilling, but thicken at stoppage so that the ``cuttings'' can remain suspended. In a related application known as hydraulic fracturing suspensions of solids called ``proppant'' are used to prop open the fracture by pumping them into the well. It is well-known that particle flow and settling in a viscoelastic fluid can be quite different from that which is observed in Newtonian fluids. First, it is now well known that the ``fluid particle split'' at bifurcation cracks is controlled by fluid rheology in a manner that is not understood. Second, in Newtonian fluids, the presence of an imposed shear flow in the direction perpendicular to gravity (which we term a cross or orthogonal shear flow) has no effect on the settling of a spherical particle in Stokes flow (i.e. at vanishingly small Reynolds number). By contrast, in a non-Newtonian liquid, the complex rheological properties induce a nonlinear coupling between the sedimentation and shear flow. Recent experimental data have shown both the shear thinning and the elasticity of the suspending polymeric solutions significantly affects the fluid-particle split at bifurcations, as well as the settling rate of the solids. In the present work, we use the Immersed Boundary Method to develop computer simulations of viscoelastic flow in suspensions of spheres to study these problems. These simulations allow us to understand the detailed physical mechanisms for the remarkable physical behavior seen in practice, and actually suggest design rules for creating new fluid recipes.

  5. The rheology applied to the fluids used in perforation of wells of petroleum

    International Nuclear Information System (INIS)

    Sierra Restrepo, Carlos Mario

    1997-01-01

    The properties of flow of the drilling fluids should be controlled, because they play a very important paper when we are drilling a well and a wrong behaviour could occasion serious problems. These properties are in great part consequence of their viscosity or more exactly of their rheology. The drilling fluids are too complex and the relationship between shear stress and shear rate is not considered as a linear relation that passes for the origin, like it is the case of the Newtonian fluids for the one which they are classified like n on Newtonian fluids . Also, they should conquer a certain grade of internal resistance in order to begin to flow. There is not a mathematical equation that describes the rheology of all the non-Newtonian fluids exactly. On the other hand, they have proposed several equations that approach the true relationship shear stress -shear rate. Those that have shown more satisfactory outputs are: The Bingham plastic model, the power-law model, and the power-law modified model

  6. Post-Newtonian gravitational bremsstrahlung

    International Nuclear Information System (INIS)

    Turner, M.; Will, C.M.

    1978-01-01

    We present formulae and numerical results for the gravitational radiation emitted during a low-deflection encounter between two massive bodies (''gravitational bremsstrahlung''). Our results are valid through post-Newtonian order within general relativity. We discuss in detail the gravitational waveform (transverse-traceless part of the metric perturbation tensor), the toal luminosity and total emitted energy, the angular distribution of emitted energy (antenna pattern), and the frequency spectrum. We also present a method of ''boosting'' the accuracy of these quantities to post-3/2-Newtonian order. A numerical comparison of our results with those of Peters and of Kovacs and Thorne shows that the post-Newtonian method is reliable to better than 0.1% at v=0.1c, to a few percent at v=0.35c, and to 10--20% at v=0.5c. We also compare our results with those of Smarr

  7. The interaction of two spheres in a simple-shear flow of complex fluids

    Science.gov (United States)

    Firouznia, Mohammadhossein; Metzger, Bloen; Ovarlez, Guillaume; Hormozi, Sarah

    2017-11-01

    We study the interaction of two small freely-moving spheres in a linear flow field of Newtonian, shear thinning and yield stress fluids. We perform a series of experiments over a range of shear rates as well as different shear histories using an original apparatus and with the aid of conventional rheometry, Particle Image Velocimetry and Particle Tracking Velocimetry. Showing that the non-Newtonian nature of the suspending fluid strongly affects the shape of particle trajectories and the irreversibility. An important point is that non-Newtonian effects can be varied and unusual. Depending on the shear rate, nonideal shear thinning and yield stress suspending fluids might show elasticity that needs to be taken into account. The flow field around one particle is studied in different fluids when subjected to shear. Then using these results to explain the two particle interactions in a simple-shear flow we show how particle-particle contact and non-Newtonian behaviors result in relative trajectories with fore-aft asymmetry. Well-resolved velocity and stress fields around the particles are presented here. Finally, we discuss how the relative particle trajectories may affect the microstructure of complex suspensions and consequently the bulk rheology. NSF (Grant No. CBET-1554044-CAREER).

  8. Are Non-Newtonian Effects Important in Hemodynamic Simulations of Patients With Autogenous Fistula?

    Science.gov (United States)

    Javid Mahmoudzadeh Akherat, S. M.; Cassel, Kevin; Boghosian, Michael; Dhar, Promila; Hammes, Mary

    2017-01-01

    Given the current emphasis on accurate computational fluid dynamics (CFD) modeling of cardiovascular flows, which incorporates realistic blood vessel geometries and cardiac waveforms, it is necessary to revisit the conventional wisdom regarding the influences of non-Newtonian effects. In this study, patient-specific reconstructed 3D geometries, whole blood viscosity data, and venous pulses postdialysis access surgery are used as the basis for the hemodynamic simulations of renal failure patients with native fistula access. Rheological analysis of the viscometry data initially suggested that the correct choice of constitutive relations to capture the non-Newtonian behavior of blood is important because the end-stage renal disease (ESRD) patient cohort under observation experience drastic variations in hematocrit (Hct) levels and whole blood viscosity throughout the hemodialysis treatment. For this purpose, various constitutive relations have been tested and implemented in CFD practice, namely Quemada and Casson. Because of the specific interest in neointimal hyperplasia and the onset of stenosis in this study, particular attention is placed on differences in nonhomeostatic wall shear stress (WSS) as that drives the venous adaptation process that leads to venous geometric evolution over time in ESRD patients. Surprisingly, the CFD results exhibit no major differences in the flow field and general flow characteristics of a non-Newtonian simulation and a corresponding identical Newtonian counterpart. It is found that the vein's geometric features and the dialysis-induced flow rate have far greater influence on the WSS distribution within the numerical domain. PMID:28249082

  9. Are Non-Newtonian Effects Important in Hemodynamic Simulations of Patients With Autogenous Fistula?

    Science.gov (United States)

    Javid Mahmoudzadeh Akherat, S M; Cassel, Kevin; Boghosian, Michael; Dhar, Promila; Hammes, Mary

    2017-04-01

    Given the current emphasis on accurate computational fluid dynamics (CFD) modeling of cardiovascular flows, which incorporates realistic blood vessel geometries and cardiac waveforms, it is necessary to revisit the conventional wisdom regarding the influences of non-Newtonian effects. In this study, patient-specific reconstructed 3D geometries, whole blood viscosity data, and venous pulses postdialysis access surgery are used as the basis for the hemodynamic simulations of renal failure patients with native fistula access. Rheological analysis of the viscometry data initially suggested that the correct choice of constitutive relations to capture the non-Newtonian behavior of blood is important because the end-stage renal disease (ESRD) patient cohort under observation experience drastic variations in hematocrit (Hct) levels and whole blood viscosity throughout the hemodialysis treatment. For this purpose, various constitutive relations have been tested and implemented in CFD practice, namely Quemada and Casson. Because of the specific interest in neointimal hyperplasia and the onset of stenosis in this study, particular attention is placed on differences in nonhomeostatic wall shear stress (WSS) as that drives the venous adaptation process that leads to venous geometric evolution over time in ESRD patients. Surprisingly, the CFD results exhibit no major differences in the flow field and general flow characteristics of a non-Newtonian simulation and a corresponding identical Newtonian counterpart. It is found that the vein's geometric features and the dialysis-induced flow rate have far greater influence on the WSS distribution within the numerical domain.

  10. Active learning of constitutive relation from mesoscopic dynamics for macroscopic modeling of non-Newtonian flows

    Science.gov (United States)

    Zhao, Lifei; Li, Zhen; Caswell, Bruce; Ouyang, Jie; Karniadakis, George Em

    2018-06-01

    We simulate complex fluids by means of an on-the-fly coupling of the bulk rheology to the underlying microstructure dynamics. In particular, a continuum model of polymeric fluids is constructed without a pre-specified constitutive relation, but instead it is actively learned from mesoscopic simulations where the dynamics of polymer chains is explicitly computed. To couple the bulk rheology of polymeric fluids and the microscale dynamics of polymer chains, the continuum approach (based on the finite volume method) provides the transient flow field as inputs for the (mesoscopic) dissipative particle dynamics (DPD), and in turn DPD returns an effective constitutive relation to close the continuum equations. In this multiscale modeling procedure, we employ an active learning strategy based on Gaussian process regression (GPR) to minimize the number of expensive DPD simulations, where adaptively selected DPD simulations are performed only as necessary. Numerical experiments are carried out for flow past a circular cylinder of a non-Newtonian fluid, modeled at the mesoscopic level by bead-spring chains. The results show that only five DPD simulations are required to achieve an effective closure of the continuum equations at Reynolds number Re = 10. Furthermore, when Re is increased to 100, only one additional DPD simulation is required for constructing an extended GPR-informed model closure. Compared to traditional message-passing multiscale approaches, applying an active learning scheme to multiscale modeling of non-Newtonian fluids can significantly increase the computational efficiency. Although the method demonstrated here obtains only a local viscosity from the polymer dynamics, it can be extended to other multiscale models of complex fluids whose macro-rheology is unknown.

  11. Adomian decomposition method for Hall and ion-slip effects on mixed convection flow of a chemically reacting Newtonian fluid between parallel plates with heat generation/absorption

    Directory of Open Access Journals (Sweden)

    Ch.Ram Reddy

    2017-12-01

    Full Text Available This paper analyzes the heat and mass transfer characteristics on mixed convective fully developed flow in an electrically conducting Newtonian fluid between vertical parallel plates. The chemical reaction, heat generation, Hall and ion-slip effects are taken into consideration. By using similarity transformations the nonlinear governing equations are reduced into dimensionless form and hence solved using Adomian decomposition method (ADM. The influence of magnetic parameter, Hall parameter, ion-slip parameter, chemical reaction parameter, and heat generation/absorption parameter on non-dimensional velocities, temperature and concentration profiles are exhibited graphically. In addition, the numerical data for skin friction, heat and mass transfer rates are shown in tabular form.

  12. Moving interface problems and applications in fluid dynamics

    CERN Document Server

    Khoo, Boo Cheong; Lin, Ping

    2008-01-01

    This volume is a collection of research papers presented at the program on Moving Interface Problems and Applications in Fluid Dynamics, which was held between January 8 and March 31, 2007 at the Institute for Mathematical Sciences (IMS) of the National University of Singapore. The topics discussed include modeling and simulations of biological flow coupled to deformable tissue/elastic structure, shock wave and bubble dynamics and various applications including biological treatments with experimental verification, multi-medium flow or multi-phase flow and various applications including cavitation/supercavitation, detonation problems, Newtonian and non-Newtonian fluid, and many other areas. Readers can benefit from some recent research results in these areas.

  13. Non-Newtonian Hele-Shaw Flow and the Saffman-Taylor Instability

    International Nuclear Information System (INIS)

    Kondic, L.; Shelley, M.J.; Palffy-Muhoray, P.

    1998-01-01

    We explore the Saffman-Taylor instability of a gas bubble expanding into a shear thinning liquid in a radial Hele-Shaw cell. Using Darcy close-quote s law generalized for non-Newtonian fluids, we perform simulations of the full dynamical problem. The simulations show that shear thinning significantly influences the developing interfacial patterns. Shear thinning can suppress tip splitting, and produce fingers which oscillate during growth and shed side branches. Emergent length scales show reasonable agreement with a general linear stability analysis. copyright 1998 The American Physical Society

  14. Cosmology with modified Newtonian dynamics (MOND)

    NARCIS (Netherlands)

    Sanders, R. H.

    1998-01-01

    It is well known that the application of Newtonian dynamics to an expanding spherical region leads to the correct relativistic expression (the Friedmann equation) for the evolution of the cosmic scalefactor. Here, the cosmological implications of Milgrom's modified Newtonian dynamics (MOND) are

  15. A review on rising bubble dynamics in viscosity-stratified fluids

    Indian Academy of Sciences (India)

    Kirti Chandra Sahu

    Multiphase flow; non-Newtonian; immiscible fluids; bubbles; numerical simulations. 1. Introduction. The fluid dynamics of a gas bubble rising due to buoyancy in a surrounding .... Figure 2. Behaviour of a single bubble rising in quiescent liquid.

  16. Turbulent characteristics of shear-thinning fluids in recirculating flows

    Energy Technology Data Exchange (ETDEWEB)

    Pereira, A.S. [Inst. Superior de Engenharia do Porto (Portugal). Dept. de Engenharia Quimica; Pinho, F.T. [Centro de Estudos de Fenomenos de Transporte, Departamento de Engenharia Mecanica e Gestao Industrial, Faculdade de Engenharia da Universidade do Porto, Rua dos Bragas, 4050-123 Porto (Portugal)

    2000-03-01

    A miniaturised fibre optic laser-Doppler anemometer was used to carry out a detailed hydrodynamic investigation of the flow downstream of a sudden expansion with 0.1-0.2% by weight shear-thinning aqueous solutions of xanthan gum. Upstream of the sudden expansion the pipe flow was fully-developed and the xanthan gum solutions exhibited drag reduction with corresponding lower radial and tangential normal Reynolds stresses, but higher axial Reynolds stress near the wall and a flatter axial mean velocity profile in comparison with Newtonian flow. The recirculation bubble length was reduced by more than 20% relative to the high Reynolds number Newtonian flow, and this was attributed to the occurrence further upstream of high turbulence for the non-Newtonian solutions, because of advection of turbulence and earlier high turbulence production in the shear layer. Comparisons with the measurements of Escudier and Smith (1999) with similar fluids emphasized the dominating role of inlet turbulence. The present was less anisotropic, and had lower maximum axial Reynolds stresses (by 16%) but higher radial turbulence (20%) than theirs. They reported considerably longer recirculating bubble lengths than we do for similar non-Newtonian fluids and Reynolds numbers. (orig.)

  17. Modelling non-dust fluids in cosmology

    International Nuclear Information System (INIS)

    Christopherson, Adam J.; Hidalgo, Juan Carlos; Malik, Karim A.

    2013-01-01

    Currently, most of the numerical simulations of structure formation use Newtonian gravity. When modelling pressureless dark matter, or 'dust', this approach gives the correct results for scales much smaller than the cosmological horizon, but for scenarios in which the fluid has pressure this is no longer the case. In this article, we present the correspondence of perturbations in Newtonian and cosmological perturbation theory, showing exact mathematical equivalence for pressureless matter, and giving the relativistic corrections for matter with pressure. As an example, we study the case of scalar field dark matter which features non-zero pressure perturbations. We discuss some problems which may arise when evolving the perturbations in this model with Newtonian numerical simulations and with CMB Boltzmann codes

  18. Spreading law of non-Newtonian power-law liquids on a spherical substrate by an energy-balance approach.

    Science.gov (United States)

    Iwamatsu, Masao

    2017-07-01

    The spreading of a cap-shaped spherical droplet of non-Newtonian power-law liquids, both shear-thickening and shear-thinning liquids, that completely wet a spherical substrate is theoretically investigated in the capillary-controlled spreading regime. The crater-shaped droplet model with the wedge-shaped meniscus near the three-phase contact line is used to calculate the viscous dissipation near the contact line. Then the energy balance approach is adopted to derive the equation that governs the evolution of the contact line. The time evolution of the dynamic contact angle θ of a droplet obeys a power law θ∼t^{-α} with the spreading exponent α, which is different from Tanner's law for Newtonian liquids and those for non-Newtonian liquids on a flat substrate. Furthermore, the line-tension dominated spreading, which could be realized on a spherical substrate for late-stage of spreading when the contact angle becomes low and the curvature of the contact line becomes large, is also investigated.

  19. Shear-induced structural transitions in Newtonian non-Newtonian two-phase flow

    Science.gov (United States)

    Cristobal, G.; Rouch, J.; Colin, A.; Panizza, P.

    2000-09-01

    We show the existence under shear flow of steady states in a two-phase region of a brine-surfactant system in which lyotropic dilute lamellar (non-Newtonian) and sponge (Newtonian) phases are coexisting. At high shear rates and low sponge phase-volume fractions, we report on the existence of a dynamic transition corresponding to the formation of a colloidal crystal of multilamellar vesicles (or ``onions'') immersed in the sponge matrix. As the sponge phase-volume fraction increases, this transition exhibits a hysteresis loop leading to a structural bistability of the two-phase flow. Contrary to single phase lamellar systems where it is always 100%, the onion volume fraction can be monitored continuously from 0 to 100 %.

  20. Perturbed Newtonian description of the Lemaître model with non-negligible pressure

    Energy Technology Data Exchange (ETDEWEB)

    Yamamoto, Kazuhiro [Department of Physical Sciences, Hiroshima University, Higashi-hiroshima, Kagamiyama 1-3-1, 739-8526 (Japan); Marra, Valerio [Departamento de Física, Universidade Federal do Espírito Santo, Av. F. Ferrari, 514, 29075-910, Vitória, ES (Brazil); Mukhanov, Viatcheslav [Theoretical Physics, Ludwig Maxmillians University, Theresienstr. 37, 80333 Munich (Germany); Sasaki, Misao, E-mail: kazuhiro@hiroshima-u.ac.jp, E-mail: valerio.marra@me.com, E-mail: Viatcheslav.Mukhanov@physik.lmu.de, E-mail: misao@yukawa.kyoto-u.ac.jp [Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-Oiwakecho, Sakyo-Ku, Kyoto 606-8502 (Japan)

    2016-03-01

    We study the validity of the Newtonian description of cosmological perturbations using the Lemaître model, an exact spherically symmetric solution of Einstein's equation. This problem has been investigated in the past for the case of a dust fluid. Here, we extend the previous analysis to the more general case of a fluid with non-negligible pressure, and, for the numerical examples, we consider the case of radiation (P=ρ/3). We find that, even when the density contrast has a nonlinear amplitude, the Newtonian description of the cosmological perturbations using the gravitational potential ψ and the curvature potential φ is valid as long as we consider sub-horizon inhomogeneities. However, the relation ψ+φ=O(φ{sup 2})—which holds for the case of a dust fluid—is not valid for a relativistic fluid, and an effective anisotropic stress is generated. This demonstrates the usefulness of the Lemaître model which allows us to study in an exact nonlinear fashion the onset of anisotropic stress in fluids with non-negligible pressure. We show that this happens when the characteristic scale of the inhomogeneity is smaller than the sound horizon and that the deviation is caused by the nonlinear effect of the fluid's fast motion. We also find that ψ+φ= [O(φ{sup 2}),O(c{sub s}{sup 2φ} δ)] for an inhomogeneity with density contrast δ whose characteristic scale is smaller than the sound horizon, unless w is close to −1, where w and c{sub s} are the equation of state parameter and the sound speed of the fluid, respectively. On the other hand, we expect ψ+φ=O(φ{sup 2}) to hold for an inhomogeneity whose characteristic scale is larger than the sound horizon, unless the amplitude of the inhomogeneity is large and w is close to −1.

  1. Fluid Dynamics for Physicists

    Science.gov (United States)

    Faber, T. E.

    1995-08-01

    This textbook provides an accessible and comprehensive account of fluid dynamics that emphasizes fundamental physical principles and stresses connections with other branches of physics. Beginning with a basic introduction, the book goes on to cover many topics not typically treated in texts, such as compressible flow and shock waves, sound attenuation and bulk viscosity, solitary waves and ship waves, thermal convection, instabilities, turbulence, and the behavior of anisotropic, non-Newtonian and quantum fluids. Undergraduate or graduate students in physics or engineering who are taking courses in fluid dynamics will find this book invaluable.

  2. Heat transfer analysis in a second grade fluid over and oscillating vertical plate using fractional Caputo-Fabrizio derivatives

    International Nuclear Information System (INIS)

    Shah, Nehad Ali; Khan, Ilyas

    2016-01-01

    This paper presents a Caputo-Fabrizio fractional derivatives approach to the thermal analysis of a second grade fluid over an infinite oscillating vertical flat plate. Together with an oscillating boundary motion, the heat transfer is caused by the buoyancy force induced by temperature differences between the plate and the fluid. Closed form solutions of the fluid velocity and temperature are obtained by means of the Laplace transform. The solutions of ordinary second grade and Newtonian fluids corresponding to time derivatives of integer and fractional orders are obtained as particular cases of the present solutions. Numerical computations and graphical illustrations are used in order to study the effects of the Caputo-Fabrizio time-fractional parameter α, the material parameter α 2 , and the Prandtl and Grashof numbers on the velocity field. A comparison for time derivative of integer order versus fractional order is shown graphically for both Newtonian and second grade fluids. It is found that fractional fluids (second grade and Newtonian) have highest velocities. This shows that the fractional parameter enhances the fluid flow. (orig.)

  3. An integrated in-line fluid characterization system for industrial applications(In-situ fluid mechanics experiments)

    OpenAIRE

    Johan, Wiklund; Reinhardt, Kotze; Beat, Birkhofer; Stefano, Ricci; Valentino, Meacci; Mats, Stading; Rainer, Haldenwang; SP-Technical Research Institute of Sweden; FPRC, Cape Peninsula University of Technology; Sika Services AG; Information Engineering Department - University of Florence; Information Engineering Department - University of Florence; SP-Technical Research Institute of Sweden; FPRC, Cape Peninsula University of Technology

    2015-01-01

    In this work we have presented the world's first commercially available embedded in-line fluids characterization system, "Flow-Viz". It has been specifically designed for the non-invasive, in-line, continuous, real-time velocity profile and rheological assessment of opaque, non-Newtonian industrial fluids. The Flow-Viz system has been successfully installed in pilot plants of international companies and used also for academic research. The technology has been applied to a wide range of fluids...

  4. Post-Newtonian celestial dynamics in cosmology: Field equations

    Science.gov (United States)

    Kopeikin, Sergei M.; Petrov, Alexander N.

    2013-02-01

    Post-Newtonian celestial dynamics is a relativistic theory of motion of massive bodies and test particles under the influence of relatively weak gravitational forces. The standard approach for development of this theory relies upon the key concept of the isolated astronomical system supplemented by the assumption that the background spacetime is flat. The standard post-Newtonian theory of motion was instrumental in the explanation of the existing experimental data on binary pulsars, satellite, and lunar laser ranging, and in building precise ephemerides of planets in the Solar System. Recent studies of the formation of large-scale structures in our Universe indicate that the standard post-Newtonian mechanics fails to describe more subtle dynamical effects in motion of the bodies comprising the astronomical systems of larger size—galaxies and clusters of galaxies—where the Riemann curvature of the expanding Friedmann-Lemaître-Robertson-Walker universe interacts with the local gravitational field of the astronomical system and, as such, cannot be ignored. The present paper outlines theoretical principles of the post-Newtonian mechanics in the expanding Universe. It is based upon the gauge-invariant theory of the Lagrangian perturbations of cosmological manifold caused by an isolated astronomical N-body system (the Solar System, a binary star, a galaxy, and a cluster of galaxies). We postulate that the geometric properties of the background manifold are described by a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker metric governed by two primary components—the dark matter and the dark energy. The dark matter is treated as an ideal fluid with the Lagrangian taken in the form of pressure along with the scalar Clebsch potential as a dynamic variable. The dark energy is associated with a single scalar field with a potential which is hold unspecified as long as the theory permits. Both the Lagrangians of the dark matter and the scalar field are

  5. Eye rotation induced dynamics of a Newtonian fluid within the vitreous cavity: the effect of the chamber shape

    International Nuclear Information System (INIS)

    Stocchino, Alessandro; Repetto, Rodolfo; Cafferata, Chiara

    2007-01-01

    The dynamics of the vitreous body induced by eye rotations is studied experimentally. In particular, we consider the case in which the vitreous cavity is filled by a Newtonian fluid, either because the vitreous is liquefied or because it has been replaced, after vitrectomy, by a viscous fluid. We employ a rigid Perspex container which models, in a magnified scale, the vitreous cavity of the human eye. The shape of the cavity closely resembles that of the real vitreous chamber; in particular, the anterior part of the container is concave in order to model the presence of the eye lens. The container is filled with glycerol and is mounted on the shaft of a computer-controlled motor which rotates according to a periodic time law. PIV (particle image velocimetry) measurements are taken on the equatorial plane orthogonal to the axis of rotation. The experimental measurements show that the velocity field is strongly influenced by the deformed geometry of the domain. In particular, the formation of a vortex in the vicinity of the lens, which migrates in time towards the core of the domain, is invariably observed. The vortex path is tracked in time by means of a vortex identification technique and it is found that it is significantly influenced by the Womersley number of the flow. Particle trajectories are computed from the PIV measurements. Particles initially located at different positions on the equatorial horizontal plane (perpendicular to the axis of rotation) tend to concentrate in narrow regions adjacent to the lens, thus suggesting the existence, in such regions, of a vertical fluid ejection. Such a strong flow three-dimensionality, which is essentially induced by the irregular shape of the domain, may play a significant role in the mixing processes taking place inside the eye globe. The tangential stresses acting on the rigid boundary of the domain are also computed from the experimental measurements showing that regions subject to particularly intense stresses

  6. Newtonian versus black-hole scattering

    International Nuclear Information System (INIS)

    Siopsis, G.

    1999-01-01

    We discuss non-relativistic scattering by a Newtonian potential. We show that the gray-body factors associated with scattering by a black hole exhibit the same functional dependence as scattering amplitudes in the Newtonian limit, which should be the weak-field limit of any quantum theory of gravity. This behavior arises independently of the presence of supersymmetry. The connection to two-dimensional conformal field theory is also discussed. copyright 1999 The American Physical Society

  7. Sphere interaction in bounded shear flow of Oldroyd-B fluids

    Science.gov (United States)

    Chiu, Shang-Huan; Pan, Tsorng-Whay; Glowinski, Roland

    2017-11-01

    It is well-known that, up to the initial sphere displacement, binary encounters of spheres in bounded shear flow of a Newtonian fluid can have either swapping or non-swapping trajectories under creeping flow conditions. The motion of dilute sphere suspensions in bounded shear flow of Oldroyd-B fluids at zero Reynolds number has been studied. The pass and return trajectories of the two ball mass centers in a two wall driven shear flow are similar to those in a Newtonian fluid; but they lose the symmetry due to the effect of elastic force arising from viscoelastic fluids. A tumbling chain of two balls (a dipole) may occur, depending on the value of the Weissenberg number and the initial vertical displacement of the ball mass center to the middle plane between two walls. The two ball tumbling motion has also been compared with that of an ellipsoid in bounded shear flow Oldroyd-B fluids. This work was supported by NSF (Grant DMS-1418308).

  8. Irreversibility analysis for gravity driven non-Newtonian liquid film along an inclined isothermal plate

    International Nuclear Information System (INIS)

    Makinde, O.D.

    2005-10-01

    In this paper, the first and second law of thermodynamics are employed in order to study the inherent irreversibility for a gravity driven non-Newtonian Ostwald-de Waele power law liquid film along an inclined isothermal plate. Based on some simplified assumptions, the governing equations are obtained and solved analytically. Expressions for fluid velocity, temperature, volumetric entropy generation numbers, irreversibility distribution ratio and the Bejan number are also determined. (author)

  9. Inertia effects in the laminar radial flow of a power law fluid with an electromagnetic field

    International Nuclear Information System (INIS)

    Chen, C.-K.; Chen, K.-H.; Wu, C.-Y.

    1984-01-01

    An approximate study of the pressure distribution for the radial flow of a non-newtonian (power law) fluid between two parallel disks in the presence of an axial electrical field is obtained by using the momentum and energy integral methods. For a non-newtonian fluid it is shown that the inertia effect must be considered to be significant for the pressure distribution, especially for the power law fluids with n >= 1. Furthermore, it is seen that the inertia effect will also lower the load capacity of the disks. (Auth.)

  10. Particle migration using local variation of the viscosity (LVOV) model in flow of a non-Newtonian fluid for ceramic tape casting

    DEFF Research Database (Denmark)

    Jabbaribehnam, Mirmasoud; Spangenberg, Jon; Hattel, Jesper Henri

    2016-01-01

    In this paper, the migration of secondary particles in a non-Newtonian ceramic slurry inthe tape casting process is investigated with the purpose of understanding the particle distribution patterns along the casting direction. The Ostwald-de Waele power law model for the non-Newtonian flow...... the substratevelocity (casting speed) leads to a more uniform distribution of the particles inside the ceramic slurry, in which case the shear induced particle migration is dominating over the gravity induced one....

  11. Simulation of fault-bend fold by incompressible Newtonian fluid; Hiasshukusei Newton ryutai ni yoru danso oremagari shukyoku kozo no simulation

    Energy Technology Data Exchange (ETDEWEB)

    Tamagawa, T; Matsuoka, T [Japan Petroleum Exploration Corp., Tokyo (Japan); Tsukui, R [Japan National Oil Corp., Tokyo (Japan). Technology Research Center

    1997-10-22

    Incompressible Newtonian fluid simulation is experimentally applied to faults typical of the compression and extension fields. A fault-bend folding structure of the flat-ramp flat fault in the compression field and a folding structure of a normal fault in the extension field are studied, and the results are compared with those obtained by the balanced cross section method. The result of calculation indicates that the velocity gradient with the ramp angle set at 30deg is correspondent to stress and that stress concentration is taking place at the ramp section of the fault. This solution is an approximation and does not necessary support the conservation of area but, when the ramp angle is allowed to change from 10 through 40deg, it is found that the conservation of area holds though roughly. It is found that the configuration of the folding structure formed by a flat-ramp flat fault is positioned between the anomalous-mode layer parallel shear typical of a balanced cross section and the folding structure formed by a vertical shear. 7 refs., 7 figs.

  12. Relativistic generalization of the Newtonian force

    International Nuclear Information System (INIS)

    Qadir, A.; Quamar, J.

    1982-06-01

    Whereas there is no denying the essential contribution of geometrodynamics, it must be admitted that our physical intuition is still firmly based in the Newtonian concept of force. Here we extend some earlier work re-introducing the Newtonian force concept into relativity theory. Some fundamentally new insights into the relativistic effects due to charge and rotation are presented. (author)

  13. Extensional flow of low-viscosity fluids in capillary bridges formed by pulsed surface acoustic wave jetting

    International Nuclear Information System (INIS)

    Bhattacharjee, P K; McDonnell, A G; Prabhakar, R; Yeo, L Y; Friend, J

    2011-01-01

    Forming capillary bridges of low-viscosity (∼<10 mPa s) fluids is difficult, making the study of their capillary-thinning behavior and the measurement of the fluid's extensional viscosity difficult as well. Current techniques require some time to form a liquid bridge from the stretching of a droplet. Rapidly stretching a liquid bridge using these methods can cause its breakup if the viscosity is too low. Stretching more slowly allows the bridge to thin and break up before a suitable bridge geometry can be established to provide reliable and accurate rheological data. Using a pulsed surface acoustic wave to eject a jet from a sessile droplet, a capillary bridge may be formed in about 7.5 ms, about seven times quicker than current methods. With this approach, capillary bridges may be formed from Newtonian and non-Newtonian fluids having much lower viscosities-water, 0.04% by weight solution of high-molecular-weight (7 MDa) polystyrene in dioctyl phthalate and 0.25% fibrinogen solution in demineralized water, for example. Details of the relatively simple system used to achieve these results are provided, as are experimental results indicating deviations from a Newtonian response by the low-viscosity non-Newtonian fluids used in our study.

  14. Extensional flow of low-viscosity fluids in capillary bridges formed by pulsed surface acoustic wave jetting

    Energy Technology Data Exchange (ETDEWEB)

    Bhattacharjee, P K; McDonnell, A G; Prabhakar, R; Yeo, L Y; Friend, J, E-mail: james.friend@monash.edu.au [MicroNanophysics Research Laboratory, Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, VIC 3800 (Australia); Melbourne Centre for Nanofabrication, Melbourne, VIC 3800 (Australia)

    2011-02-15

    Forming capillary bridges of low-viscosity ({approx}<10 mPa s) fluids is difficult, making the study of their capillary-thinning behavior and the measurement of the fluid's extensional viscosity difficult as well. Current techniques require some time to form a liquid bridge from the stretching of a droplet. Rapidly stretching a liquid bridge using these methods can cause its breakup if the viscosity is too low. Stretching more slowly allows the bridge to thin and break up before a suitable bridge geometry can be established to provide reliable and accurate rheological data. Using a pulsed surface acoustic wave to eject a jet from a sessile droplet, a capillary bridge may be formed in about 7.5 ms, about seven times quicker than current methods. With this approach, capillary bridges may be formed from Newtonian and non-Newtonian fluids having much lower viscosities-water, 0.04% by weight solution of high-molecular-weight (7 MDa) polystyrene in dioctyl phthalate and 0.25% fibrinogen solution in demineralized water, for example. Details of the relatively simple system used to achieve these results are provided, as are experimental results indicating deviations from a Newtonian response by the low-viscosity non-Newtonian fluids used in our study.

  15. Oscillating flow of a Burgers' fluid in a pipe

    International Nuclear Information System (INIS)

    Khan, M.; Asghar, S.; Hayat, T.

    2005-12-01

    An analysis is made to see the influences of Hall current on the flow of a Burgers' fluid. The velocity field corresponding to flow in a pipe is determined. The closed form analytical solutions for several Newtonian and non-Newtonian fluid models can be obtained from the present analysis as the limiting cases. The purpose of this work is twofold. Firstly, to investigate the oscillating flow in a pipe using Burgers? fluid model. Secondly, to see the effects of Hall current on the velocity field. The flow in a pipe is induced due to imposition of an oscillating pressure gradient. An exact analytical solution to the governing problem is given using the Fourier transform technique. The obtained expression for the velocity field shows that there are pronounced effects of Hall and rheological parameters. The considered fluid model is a viscoelastic model and has been used to characterize food products such as cheese, soil, asphalt and asphalt mixes etc. (author)

  16. Study of blood flow in several benchmark micro-channels using a two-fluid approach

    OpenAIRE

    Wu, Wei-Tao; Yang, Fang; Antaki, James F.; Aubry, Nadine; Massoudi, Mehrdad

    2015-01-01

    It is known that in a vessel whose characteristic dimension (e.g., its diameter) is in the range of 20 to 500 microns, blood behaves as a non-Newtonian fluid, exhibiting complex phenomena, such as shear-thinning, stress relaxation, and also multi-component behaviors, such as the Fahraeus effect, plasma-skimming, etc. For describing these non-Newtonian and multi-component characteristics of blood, using the framework of mixture theory, a two-fluid model is applied, where the plasma is treated ...

  17. Analytic solutions of Oldroyd-B fluid with fractional derivatives in a circular duct that applies a constant couple

    Directory of Open Access Journals (Sweden)

    M.B. Riaz

    2016-12-01

    Full Text Available The aim of this article was to analyze the rotational flow of an Oldroyd-B fluid with fractional derivatives, induced by an infinite circular cylinder that applies a constant couple to the fluid. Such kind of problem in the settings of fractional derivatives has not been found in the literature. The solutions are based on an important remark regarding the governing equation for the non-trivial shear stress. The solutions that have been obtained satisfy all imposed initial and boundary conditions and can easily be reduced to the similar solutions corresponding to ordinary Oldroyd-B, fractional/ordinary Maxwell, fractional/ordinary second-grade, and Newtonian fluids performing the same motion. The obtained results are expressed in terms of Newtonian and non-Newtonian contributions. Finally, the influence of fractional parameters on the velocity, shear stress and a comparison between generalized and ordinary fluids is graphically underlined.

  18. Does general relativity theory possess the classical newtonian limit

    International Nuclear Information System (INIS)

    Denisov, V.I.; Logunov, A.A.

    1980-01-01

    A detailed comparison of newtonian approximation of the Einstein theory and the Newton theory of gravity is made. A difference of principle between these two theories is clarified at the stage of obtaining integrals of motion. Exact eqautions of motion and Einstein equations shows the existence only zero integrals of motion as well as in the newtonian approximation. A conclusion is that GRT has no classical newtonian limit, since the integrals of motion in the Newton theory of gravity and in the newtonian approximation of the Einstein theory do not coincide [ru

  19. A two-phase theory for non-Newtonian suspensions

    Science.gov (United States)

    Varsakelis, Christos

    In this talk, a continuum and thermodynamically consistent theory for macroscopic particles immersed in a non-Newtonian fluid is presented. According to the employed methodology, each phase of the mixture is treated as a thermodynamic system, endowed with its own set of thermodynamic and kinetic variables, and is required to separately satisfy the equations for the balance of mass, momentum and energy. As both constituents of the mixture are not simple fluids, additional degrees of freedom are introduced for the proper description of their thermodynamic state. A subsequent exploitation of the entropy inequality asserts that the accommodation of the complicated rheological characteristics of both phases requires a departure from a linear current-force relationship. For this reason, a subtle nonlinear representation of the stress tensors is employed. Importantly, the inclusion of additional degrees of freedom allows us to obtain a rate equation for the evolution of the volume fraction of the particulate phase. Following a delineation of the fundamentals of the proposed theory, the talk concludes with the presentation of some limiting cases that also serve as preliminary, sanity tests.

  20. Fluid/gravity correspondence and the CFM black brane solutions

    Energy Technology Data Exchange (ETDEWEB)

    Casadio, R. [Universita di Bologna, Dipartimento di Fisica e Astronomia, Bologna (Italy); I.N.F.N., Sezione di Bologna, Bologna (Italy); Cavalcanti, R.T. [Universita di Bologna, Dipartimento di Fisica e Astronomia, Bologna (Italy); Universidade Federal do ABC-UFABC, Centro de Ciencias Naturais e Humanas, Santo Andre (Brazil); Rocha, Roldao da [Universidade Federal do ABC-UFABC, Centro de Matematica, Computacao e Cognicao, Santo Andre (Brazil)

    2016-10-15

    We consider the lower bound for the shear viscosity-to-entropy density ratio, obtained from the fluid/gravity correspondence, in order to constrain the post-Newtonian parameter of brane-world metrics. In particular, we analyse the Casadio-Fabbri-Mazzacurati (CFM) effective solutions for the gravity side of the correspondence and argue that including higher-order terms in the hydrodynamic expansion can lead to a full agreement with the experimental bounds, for the Eddington-Robertson-Schiff post-Newtonian parameter in the CFM metrics. This lends further support to the physical relevance of the viscosity-to-entropy ratio lower bound and fluid/gravity correspondence. Hence we show that CFM black branes are, effectively, Schwarzschild black branes. (orig.)

  1. Low Density Lipoprotein and Non-Newtonian Oscillating Flow Biomechanical Parameters for Normal Human Aorta.

    Science.gov (United States)

    Soulis, Johannes V; Fytanidis, Dimitrios K; Lampri, Olga P; Giannoglou, George D

    2016-04-01

    The temporal variation of the hemodynamic mechanical parameters during cardiac pulse wave is considered as an important atherogenic factor. Applying non-Newtonian blood molecular viscosity simulation is crucial for hemodynamic analysis. Understanding low density lipoprotein (LDL) distribution in relation to flow parameters will possibly spot the prone to atherosclerosis aorta regions. The biomechanical parameters tested were averaged wall shear stress (AWSS), oscillatory shear index (OSI) and relative residence time (RRT) in relation to the LDL concentration. Four non-Newtonian molecular viscosity models and the Newtonian one were tested for the normal human aorta under oscillating flow. The analysis was performed via computational fluid dynamic. Tested viscosity blood flow models for the biomechanical parameters yield a consistent aorta pattern. High OSI and low AWSS develop at the concave aorta regions. This is most noticeable in downstream flow region of the left subclavian artery and at concave ascending aorta. Concave aorta regions exhibit high RRT and elevated LDL. For the concave aorta site, the peak LDL value is 35.0% higher than its entrance value. For the convex site, it is 18.0%. High LDL endothelium regions located at the aorta concave site are well predicted with high RRT. We are in favor of using the non-Newtonian power law model for analysis. It satisfactorily approximates the molecular viscosity, WSS, OSI, RRT and LDL distribution. Concave regions are mostly prone to atherosclerosis. The flow biomechanical factor RRT is a relatively useful tool for identifying the localization of the atheromatic plaques of the normal human aorta.

  2. Handbook of mathematical analysis in mechanics of viscous fluids

    CERN Document Server

    Novotný, Antonín

    2018-01-01

    Mathematics has always played a key role for researches in fluid mechanics. The purpose of this handbook is to give an overview of items that are key to handling problems in fluid mechanics. Since the field of fluid mechanics is huge, it is almost impossible to cover many topics. In this handbook, we focus on mathematical analysis on viscous Newtonian fluid. The first part is devoted to mathematical analysis on incompressible fluids while part 2 is devoted to compressible fluids.

  3. Fundamentals of convection in non-Newtonian fluids

    International Nuclear Information System (INIS)

    Chen, J.L.S.; Ekmann, J.M.; Peterson, G.P.

    1987-01-01

    There are five papers in this book. They are: Pressure Drop and Heat Transfer in Viscoelastic Duct Flow - A New Look, A Heat Transfer Correlation for Viscoelastic Pipe Flows under Constant Wall Heat Flux, Three-Dimensional Solidification and Flow of Polymers in Curved Square Ducts, Natural Convecon Heat Transfer Between a Power-Law Fluid and a Permeable Isothermal Vertical Wall, and On Nonisothermal Flows of Bingham Plastics

  4. Hydrodynamic characteristics and mixing behaviour of Sclerotium glucanicum culture fluids in an airlift reactor with an internal loop used for scleroglucan production.

    Science.gov (United States)

    Kang, X; Wang, H; Wang, Y; Harvey, L M; McNeil, B

    2001-10-01

    The filamentous fungus, Sclerotium glucanicum NRRL 3006, was cultivated in a 0.008 m(3) airlift bioreactor with internal recirculation loop (ARL-IL) for production of the biopolymer, scleroglucan. The rheological behaviour of the culture fluid was characterised by measurement of the fluid consistency coefficient (K) and the flow behaviour index (n). Based on these measurements, the culture fluid changed from a low viscosity Newtonian system early in the process, to a viscous non-Newtonian (pseudoplastic) system. In addition, reactor hydrodynamics and mixing behaviour were characterised by measurement of whole mean gas hold-up (epsilon(g)), liquid re-circulation velocity (U(ld)) and mixing time (t(m)). Under identical process conditions, the effects of the viscosity of the culture fluid and air flow rate on epsilon(g), U(ld) and t(m) were examined and empirical correlations for epsilon(g), U(ld) and t(m) with both superficial velocity U(g) and consistency coefficient K were obtained and expressed separately. The correlations obtained are likely to describe the behaviour of real fungal culture fluids more accurately than previous correlations based on Newtonian or simulated non-Newtonian systems.

  5. Change in the flow curves of non-Newtonian oils due to a magnetic field

    International Nuclear Information System (INIS)

    Veliev, F.G.

    1979-01-01

    The effect of a variable magnetic field on the rheological properties of non-Newtonian fluids is evaluated. Bituminous pitch oils were analyzed by recording the flow curves Q.Q(Δp) - the dependence of the volumetric flow rate on the pressure gradient - with and without a field. The results obtained indicate that variable magnetic fields can produce obvious changes in the rheological properties of bituminous pitch oils, although they are nonmagnetoactive and practically electrically nonconducting

  6. Non-Newtonian behavior and molecular structure of Cooee bitumen under shear flow

    DEFF Research Database (Denmark)

    Lemarchand, Claire; Bailey, Nicholas; Daivis, Peter

    2015-01-01

    The rheology and molecular structure of a model bitumen (Cooee bitumen) under shear are investigated in the non-Newtonian regime using non-equilibrium molecular dynamics simulations. The shear viscosity, normal stress differences, and pressure of the bitumen mixture are computed at different shear...... rates and different temperatures. The model bitumen is shown to be a shear-thinning fluid at all temperatures. In addition, the Cooee model is able to reproduce experimental results showing the formation of nanoaggregates composed of stacks of flat aromatic molecules in bitumen. These nanoaggregates...

  7. Interplay between inertial and non-Newtonian effects on the flow in weakly modulated channel

    International Nuclear Information System (INIS)

    Abu-Ramadan, E.; Khayat, R.E.

    2002-01-01

    The flow inside a spatially modulated channel is examined for shear-thinning and shear-thickening fluids. The modulation amplitude is assumed to be small. A regular perturbation expansion of the flow field is used, coupled to a variable-step finite-difference scheme, to solve the problem. Since this method is intended to provide a fast and accurate alternative to conventional methods in the limit of small modulation amplitude, establishing the accuracy of the solution is critical. Numerical accuracy and convergence will be assessed, therefore. The influence of the wall geometry, inertia and non-Newtonian effects are investigated systematically. In particular, the influence of the flow and fluid parameters is examined on the conditions for the onset of separation. (author)

  8. Experimental and computational fluid dynamics studies of mixing of complex oral health products

    Science.gov (United States)

    Cortada-Garcia, Marti; Migliozzi, Simona; Weheliye, Weheliye Hashi; Dore, Valentina; Mazzei, Luca; Angeli, Panagiota; ThAMes Multiphase Team

    2017-11-01

    Highly viscous non-Newtonian fluids are largely used in the manufacturing of specialized oral care products. Mixing often takes place in mechanically stirred vessels where the flow fields and mixing times depend on the geometric configuration and the fluid physical properties. In this research, we study the mixing performance of complex non-Newtonian fluids using Computational Fluid Dynamics models and validate them against experimental laser-based optical techniques. To this aim, we developed a scaled-down version of an industrial mixer. As test fluids, we used mixtures of glycerol and a Carbomer gel. The viscosities of the mixtures against shear rate at different temperatures and phase ratios were measured and found to be well described by the Carreau model. The numerical results were compared against experimental measurements of velocity fields from Particle Image Velocimetry (PIV) and concentration profiles from Planar Laser Induced Fluorescence (PLIF).

  9. Nonlinear convective flow of Powell-Erying magneto nanofluid with Newtonian heating

    Directory of Open Access Journals (Sweden)

    Sajid Qayyum

    Full Text Available Objective of present article is to describe magnetohydrodynamic (MHD non-linear convective flow of Powell-Erying nanofluid over a stretching surface. Characteristics of Newtonian heat and mass conditions in this attempt is given attention. Heat and mass transfer analysis is examined in the frame of thermal radiation and chemical reaction. Brownian motion and thermophoresis concept is introduced due to presence of nanoparticles. Nonlinear equations of momentum, energy and concentration are transformed into dimensionless expression by invoking suitable variables. The series solutions are obtained through homotopy analysis method (HAM. Impact of embedded variables on the velocity, temperature and nanoparticles concentration is graphically presented. Numerical values of skin friction coefficient, local Nusselt and Sherwood numbers are computed and analyzed. It is concluded that velocity field enhances for fluid variable while reverse situation is noticed regarding Hartman number. Temperature and heat transfer rate behave quite reverse for Prandtl number. It is also noted that the concentration and local Sherwood number have opposite behavior in the frame of Brownian motion. Keywords: Powell-Erying nanofluid, Magnetohydrodynamic (MHD, Nonlinear convection, Thermal radiation, Chemical reaction, Newtonian heat and mass conditions

  10. Mathematical modeling for laminar flow of power law fluid in porous media

    Energy Technology Data Exchange (ETDEWEB)

    Silva, Renato A.; Mesquita, Maximilian S. [Universidade Federal do Espirito Santo (UFES), Sao Mateus, ES (Brazil). Centro Universitario Norte do Espirito Santo. Dept. de Engenharias e Computacao

    2010-07-01

    In this paper, the macroscopic equations for laminar power-law fluid flow is obtained for a porous medium starting from traditional equations (Navier-Stokes). Then, the volume averaging is applied in traditional transport equations with the power-law fluid model. This procedure leads to macroscopic transport equations set for non-Newtonian fluid. (author)

  11. Instability of displacement of Oldroyd-B fluid by air in a Hele-Shaw cell

    Science.gov (United States)

    Daripa, Prabir

    2014-03-01

    We study the displacement of an Oldroyd-B fluid in a Hele-Shaw cell when driven by air. In particular, we explicitly obtain an analytical expression for the growth rate of instability which depends on the relaxation and retardation (time) constants, denoted by λ, and λ1 respectively, appearing in the Oldroyd-B constitutive relations. When these two constants are zero, we recover the classical Saffman-Taylor result for a Newtonian liquid displaced by air. Our results show that this displacement process is more unstable than the case when a Newtonian fluid is displaced by air. The analytical results are plotted and compared with numerical results on this unstable displacement process available in the literature. The agreement is found to be excellent. In particular, results show that the non-Newtonian case (i.e., Oldroyd-B) is more unstable than the Newtonian case. Supported by an NPRP Grant # 08-777-1-141 from the Qatar National Research Fund (a member of the Qatar Foundation). The statements made herein are solely the responsibility of the author.

  12. Orbital motions as gradiometers for post-Newtonian tidal effects

    Energy Technology Data Exchange (ETDEWEB)

    Iorio, Lorenzo, E-mail: lorenzo.iorio@libero.it [Ministero dell' Istruzione, dell' Università e della Ricerca, Istruzione, Bari (Italy)

    2014-08-14

    The direct long-term changes occurring in the orbital dynamics of a local gravitationally bound binary system S due to the post-Newtonian tidal acceleration caused by an external massive source are investigated. A class of systems made of a test particle m rapidly orbiting with orbital frequency n{sub b} an astronomical body of mass M which, in turn, slowly revolves around a distant object of mass M′ with orbital frequency n{sub b}′ « n{sub b} is considered. The characteristic frequencies of the non-Keplerian orbital variations of m and of M itself are assumed to be negligible with respect to both n{sub b} and n{sub b}′. General expressions for the resulting Newtonian and post-Newtonian tidal orbital shifts of m are obtained. The future missions BepiColombo and JUICE to Mercury and Ganymede, respectively, are considered in view of a possible detection. The largest effects, of the order of ≈ 0.1-0.5 milliarcseconds per year (mas yr{sup −1}), occur for the Ganymede orbiter of the JUICE mission. Although future improvements in spacecraft tracking and orbit determination might, perhaps, reach the required sensitivity, the systematic bias represented by the other known orbital perturbations of both Newtonian and post-Newtonian origin would be overwhelming. The realization of a dedicated artificial mini-planetary system to be carried onboard and Earth-orbiting spacecraft is considered as well. Post-Newtonian tidal precessions as large as ≈ 1−10{sup 2} mas yr{sup −1} could be obtained, but the quite larger Newtonian tidal effects would be a major source of systematic bias because of the present-day percent uncertainty in the product of the Earth's mass times the Newtonian gravitational parameter.

  13. Analysis of flow and LDL concentration polarization in siphon of internal carotid artery: Non-Newtonian effects.

    Science.gov (United States)

    Sharifi, Alireza; Niazmand, Hamid

    2015-10-01

    Carotid siphon is known as one of the risky sites among the human intracranial arteries, which is prone to formation of atherosclerotic lesions. Indeed, scientists believe that accumulation of low density lipoprotein (LDL) inside the lumen is the major cause of atherosclerosis. To this aim, three types of internal carotid artery (ICA) siphon have been constructed to examine variations of hemodynamic parameters in different regions of the arteries. Providing real physiological conditions, blood considered as non-Newtonian fluid and real velocity and pressure waveforms have been employed as flow boundary conditions. Moreover, to have a better estimation of risky sites, the accumulation of LDL particles has been considered, which has been usually ignored in previous relevant studies. Governing equations have been discretized and solved via open source OpenFOAM software. A new solver has been built to meet essential parameters related to the flow and mass transfer phenomena. In contrast to the common belief regarding negligible effect of blood non-Newtonian behavior inside large arteries, current study suggests that the non-Newtonian blood behavior is notable, especially on the velocity field of the U-type model. In addition, it is concluded that neglecting non-Newtonian effects underestimates the LDL accumulation up to 3% in the U-type model at the inner side of both its bends. However, in the V and C type models, non-Newtonian effects become relatively small. Results also emphasize that the outer part of the second bend at the downstream is also at risk similar to the inner part of the carotid bends. Furthermore, from findings it can be implied that the risky sites strongly depend on the ICA shape since the extension of the risky sites are relatively larger for the V-type model, while the LDL concentrations are higher for the C-type model. Copyright © 2015 Elsevier Ltd. All rights reserved.

  14. Thermal Marangoni convection in two-phase flow of dusty Casson fluid

    Science.gov (United States)

    Mahanthesh, B.; Gireesha, B. J.

    2018-03-01

    This paper deals with the thermal Marangoni convection effects in magneto-Casson liquid flow through suspension of dust particles. The transpiration cooling aspect is accounted. The surface tension is assumed to be fluctuating linearly with temperature. The fluid and dust particle's temperature of the interface is chosen as a quadratic function of interface arc length. The governing problem is modelled by conservation laws of mass, momentum and energy for fluid and dust particle phase. Stretching transformation technique is utilized to form ordinary differential equations from the partial differential equations. Later, the numerical solutions based on Runge-Kutta-Fehlberg method are established. The momentum and heat transport distributions are focused on the outcome of distinct governing parameters. The results of Nusselt number is also presented and discussed. It is established that the heat transfer rate is higher in the case of dusty non-Newtonian fluid than dusty Newtonian fluid. The rate of heat transfer can be enhanced by suspending dust particles in a base liquid.

  15. Laminar flow of a shear-thickening fluid in a 90∘ pipe bend

    Science.gov (United States)

    Marn, Jure; Ternik, Primož

    2006-05-01

    The non-Newtonian fluid flow in a sharp 90∘ curved pipe is studied numerically to obtain the pressure loss coefficient prompted by disagreement between the existing empirical correlations and results obtained by computer codes. This disagreement results from presumption of fully developed flow throughout the curvature (correlations) while the actual flow is partially developed for the Newtonian and sharp 90∘ curved bend non-Newtonian flows, and fully developed for slightly bent 90∘ curvature non-Newtonian flow. The Quadratic model is employed to accommodate the shear-thickening behavior of an electrostatic ash and water mixture. Numerical results are obtained for different values of Reynolds number. Finally, results for local pressure loss coefficient are compared with values obtained for the Power law rheological model.

  16. Numerical investigation of non-Newtonian nanofluid flow in a converging microchannel

    Energy Technology Data Exchange (ETDEWEB)

    Mohsenian, S.; Ramiar, A.; Ranjbar, A. A. [Faculty of Mechanical Engineering, Babol Noshirvani University of Technology, Babol (Iran, Islamic Republic of)

    2017-01-15

    In the present study the flow of non-Newtonian nanofluid through a converging microchannel is investigated numerically. TiO{sub 2} nanoparticles with 10 nm diameter are dispersed in an aqueous solution of 0.5 %.wt Carboxymethyl cellulose (CMC) to produce the nanofluid. Both nanofluid and the base fluid show pseudoplastic behavior. The equations have been solved with finite volume approach using collocated grid. It has been found that by increasing the volume fraction and Reynolds number and the convergence angle, the Nusselt number increases. Also, it has been observed that by increasing convergence angle and decreasing aspect ratio of the channel, the velocity of the channel increases.

  17. Orbital motions as gradiometers for post-Newtonian tidal effects

    Directory of Open Access Journals (Sweden)

    Lorenzo eIorio

    2014-08-01

    Full Text Available The direct long-term changes occurring in the orbital dynamics of a local gravitationally bound binary system S due to the post-Newtonian tidal acceleration caused by an external massive source are investigated. A class of systems made of a test particle m rapidly orbiting with orbital frequency nb an astronomical body of mass M which, in turn, slowly revolves around a distantobject of mass M with orbital frequency nb'<< □ nb is considered. The characteristic frequenciesof the non-Keplerian orbital variations of m and of M itself are assumed to be negligible withrespect to both nb and nb'. General expressions for the resulting Newtonian and post-Newtoniantidal orbital shifts of m are obtained. The future missions BepiColombo and JUICE to Mercuryand Ganymede, respectively, are considered in view of a possible detection. The largest effects,of the order of □ 0:1 □□ 0:5 milliarcseconds per year (mas yr□□1, occur for the Ganymede orbiterof the JUICE mission. Although future improvements in spacecraft tracking and orbit determina14tion might, perhaps, reach the required sensitivity, the systematic bias represented by the otherknown orbital perturbations of both Newtonian and post-Newtonian origin would be overwhel16ming. The realization of a dedicated artificial mini-planetary system to be carried onboard andEarth-orbiting spacecraft is considered as well. Post-Newtonian tidal precessions as large as1 □□ 102 mas yr□□1 could be obtained, but the quite larger Newtonian tidal effects would be amajor source of systematic bias because of the present-day percent uncertainty in the product of the Earth’s mass times the Newtonian gravitational parameter.

  18. Microgravity Fluids for Biology, Workshop

    Science.gov (United States)

    Griffin, DeVon; Kohl, Fred; Massa, Gioia D.; Motil, Brian; Parsons-Wingerter, Patricia; Quincy, Charles; Sato, Kevin; Singh, Bhim; Smith, Jeffrey D.; Wheeler, Raymond M.

    2013-01-01

    Microgravity Fluids for Biology represents an intersection of biology and fluid physics that present exciting research challenges to the Space Life and Physical Sciences Division. Solving and managing the transport processes and fluid mechanics in physiological and biological systems and processes are essential for future space exploration and colonization of space by humans. Adequate understanding of the underlying fluid physics and transport mechanisms will provide new, necessary insights and technologies for analyzing and designing biological systems critical to NASAs mission. To enable this mission, the fluid physics discipline needs to work to enhance the understanding of the influence of gravity on the scales and types of fluids (i.e., non-Newtonian) important to biology and life sciences. In turn, biomimetic, bio-inspired and synthetic biology applications based on physiology and biology can enrich the fluid mechanics and transport phenomena capabilities of the microgravity fluid physics community.

  19. Inverse solutions for a second-grade fluid for porous medium ...

    Indian Academy of Sciences (India)

    R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

    to the free spiraling of electrons and ions about the magnetic lines of force before ... An understanding of the dynamics of fluids in porous media has practical ... viscous term in order to account for the vorticity diffusion caused by the boundary resis- ... The governing equations that describe the flow of a Newtonian fluid is the ...

  20. A novel investigation of a micropolar fluid characterized by nonlinear constitutive diffusion model in boundary layer flow and heat transfer

    Science.gov (United States)

    Sui, Jize; Zhao, Peng; Cheng, Zhengdong; Zheng, Liancun; Zhang, Xinxin

    2017-02-01

    The rheological and heat-conduction constitutive models of micropolar fluids (MFs), which are important non-Newtonian fluids, have been, until now, characterized by simple linear expressions, and as a consequence, the non-Newtonian performance of such fluids could not be effectively captured. Here, we establish the novel nonlinear constitutive models of a micropolar fluid and apply them to boundary layer flow and heat transfer problems. The nonlinear power law function of angular velocity is represented in the new models by employing generalized "n-diffusion theory," which has successfully described the characteristics of non-Newtonian fluids, such as shear-thinning and shear-thickening fluids. These novel models may offer a new approach to the theoretical understanding of shear-thinning behavior and anomalous heat transfer caused by the collective micro-rotation effects in a MF with shear flow according to recent experiments. The nonlinear similarity equations with a power law form are derived and the approximate analytical solutions are obtained by the homotopy analysis method, which is in good agreement with the numerical solutions. The results indicate that non-Newtonian behaviors involving a MF depend substantially on the power exponent n and the modified material parameter K 0 introduced by us. Furthermore, the relations of the engineering interest parameters, including local boundary layer thickness, local skin friction, and Nusselt number are found to be fitted by a quadratic polynomial to n with high precision, which enables the extraction of the rapid predictions from a complex nonlinear boundary-layer transport system.

  1. RESONANT POST-NEWTONIAN ECCENTRICITY EXCITATION IN HIERARCHICAL THREE-BODY SYSTEMS

    Energy Technology Data Exchange (ETDEWEB)

    Naoz, Smadar; Kocsis, Bence; Loeb, Abraham [Institute for Theory and Computation, Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States); Yunes, Nicolas, E-mail: snaoz@cfa.harvard.edu [Department of Physics, Montana State University, Bozeman, MT 59718 (United States)

    2013-08-20

    We study the secular, hierarchical three-body problem to first-order in a post-Newtonian expansion of general relativity (GR). We expand the first-order post-Newtonian Hamiltonian to leading-order in the ratio of the semi-major axis of the two orbits. In addition to the well-known terms that correspond to the GR precession of the inner and outer orbits, we find a new secular post-Newtonian interaction term that can affect the long-term evolution of the triple. We explore the parameter space for highly inclined and eccentric systems, where the Kozai-Lidov mechanism can produce large-amplitude oscillations in the eccentricities. The standard lore, i.e., that GR effects suppress eccentricity, is only consistent with the parts of phase space where the GR timescales are several orders of magnitude shorter than the secular Newtonian one. In other parts of phase space, however, post-Newtonian corrections combined with the three-body ones can excite eccentricities. In particular, for systems where the GR timescale is comparable to the secular Newtonian timescales, the three-body interactions give rise to a resonant-like eccentricity excitation. Furthermore, for triples with a comparable-mass inner binary, where the eccentric Kozai-Lidov mechanism is suppressed, post-Newtonian corrections can further increase the eccentricity and lead to orbital flips even when the timescale of the former is much longer than the timescale of the secular Kozai-Lidov quadrupole perturbations.

  2. Deposition Velocities of Newtonian and Non-Newtonian Slurries in Pipelines

    Energy Technology Data Exchange (ETDEWEB)

    Poloski, Adam P. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Adkins, Harold E. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Abrefah, John [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Casella, Andrew M. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Hohimer, Ryan E. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Nigl, Franz [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Minette, Michael J. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Toth, James J. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Tingey, Joel M. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Yokuda, Satoru T. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

    2009-03-01

    correlation used in the WTP design guide has been shown to be inaccurate for Hanford waste feed materials. The use of the Thomas (1979) correlation in the design guide is not conservative—In cases where 100% of the particles are smaller than 74 μm or particles are considered to be homogeneous due to yield stress forces suspending the particles the homogeneous fraction of the slurry can be set to 100%. In such cases, the predicted critical velocity based on the conservative Oroskar and Turian (1980) correlation is reduced to zero and the design guide returns a value from the Thomas (1979) correlation. The measured data in this report show that the Thomas (1979) correlation predictions often fall below that measured experimental values. A non-Newtonian deposition velocity design guide should be developed for the WTP— Since the WTP design guide is limited to Newtonian fluids and the WTP expects to process large quantities of such materials, the existing design guide should be modified address such systems. A central experimental finding of this testing is that the flow velocity required to reach turbulent flow increases with slurry rheological properties due to viscous forces dampening the formation of turbulent eddies. The flow becomes dominated by viscous forces rather than turbulent eddies. Since the turbulent eddies necessary for particle transport are not present, the particles will settle when crossing this boundary called the transitional deposition boundary. This deposition mechanism should be expected and designed for in the WTP.

  3. The Stokes boundary layer for a thixotropic or antithixotropic fluid

    KAUST Repository

    McArdle, Catriona R.

    2012-10-01

    We present a mathematical investigation of the oscillatory boundary layer in a semi-infinite fluid bounded by an oscillating wall (the so-called \\'Stokes problem\\'), when the fluid has a thixotropic or antithixotropic rheology. We obtain asymptotic solutions in the limit of small-amplitude oscillations, and we use numerical integration to validate the asymptotic solutions and to explore the behaviour of the system for larger-amplitude oscillations. The solutions that we obtain differ significantly from the classical solution for a Newtonian fluid. In particular, for antithixotropic fluids the velocity reaches zero at a finite distance from the wall, in contrast to the exponential decay for a thixotropic or a Newtonian fluid.For small amplitudes of oscillation, three regimes of behaviour are possible: the structure parameter may take values defined instantaneously by the shear rate, or by a long-term average; or it may behave hysteretically. The regime boundaries depend on the precise specification of structure build-up and breakdown rates in the rheological model, illustrating the subtleties of complex fluid models in non-rheometric settings. For larger amplitudes of oscillation the dominant behaviour is hysteretic. We discuss in particular the relationship between the shear stress and the shear rate at the oscillating wall. © 2012 Elsevier B.V.

  4. Numerical solution of chemically reactive non-Newtonian fluid flow: Dual stratification

    Science.gov (United States)

    Rehman, Khalil Ur; Malik, M. Y.; Khan, Abid Ali; Zehra, Iffat; Zahri, Mostafa; Tahir, M.

    2017-12-01

    We have found that only a few attempts are available in the literature relatively to the tangent hyperbolic fluid flow induced by stretching cylindrical surfaces. In particular, temperature and concentration stratification effects have not been investigated until now with respect to the tangent hyperbolic fluid model. Therefore, we have considered the tangent hyperbolic fluid flow induced by an acutely inclined cylindrical surface in the presence of both temperature and concentration stratification effects. To be more specific, the fluid flow is attained with the no slip condition, which implies that the bulk motion of the fluid particles is the same as the stretching velocity of a cylindrical surface. Additionally, the flow field situation is manifested with heat generation, mixed convection and chemical reaction effects. The flow partial differential equations give a complete description of the present problem. Therefore, to trace out the solution, a set of suitable transformations is introduced to convert these equations into ordinary differential equations. In addition, a self-coded computational algorithm is executed to inspect the numerical solution of these reduced equations. The effect logs of the involved parameters are provided graphically. Furthermore, the variations of the physical quantities are examined and given with the aid of tables. It is observed that the fluid temperature is a decreasing function of the thermal stratification parameter and a similar trend is noticed for the concentration via the solutal stratification parameter.

  5. Effect on Non-Newtonian Rheology on Mixing in Taylor-Couette Flow

    Science.gov (United States)

    Cagney, Neil; Balabani, Stavroula

    2017-11-01

    Mixing processes within many industry applications are strongly affected by the rheology of the working fluid. This is particularly relevant for pharmaceutical, food and waste treatment industries, where the working fluids are often strongly non-Newtonian, and significant variations in rheology between batches may occur. We approach the question of how rheology affects mixing by focussing on a the classical case of Taylor-Couette flow, which exhibits a number of instabilities and flow regimes as a function of Reynolds number. We examine Taylor-Couette flow generated for a range of aqueous solutions of xantham gum or corn starch, such that the rheology varies from shear-thinning to shear-thickening. For each case, we measure the power consumption using a torque meter and the flow field using high speed, time-resolved Particle-Image Velocimetry. The mixing characteristics are quantified using a number of Lagrangian and Eulerian approaches, including the coarse grained density method and vortex strength. By comparing these metrics to the power number, we discuss how the mixing efficiency (ratio of mixing effectiveness to power input) varies with the flow index of the fluid.

  6. Viscous-elastic dynamics of power-law fluids within an elastic cylinder

    Science.gov (United States)

    Boyko, Evgeniy; Bercovici, Moran; Gat, Amir D.

    2017-07-01

    In a wide range of applications, microfluidic channels are implemented in soft substrates. In such configurations, where fluidic inertia and compressibility are negligible, the propagation of fluids in channels is governed by a balance between fluid viscosity and elasticity of the surrounding solid. The viscous-elastic interactions between elastic substrates and non-Newtonian fluids are particularly of interest due to the dependence of viscosity on the state of the system. In this work, we study the fluid-structure interaction dynamics between an incompressible non-Newtonian fluid and a slender linearly elastic cylinder under the creeping flow regime. Considering power-law fluids and applying the thin shell approximation for the elastic cylinder, we obtain a nonhomogeneous p-Laplacian equation governing the viscous-elastic dynamics. We present exact solutions for the pressure and deformation fields for various initial and boundary conditions for both shear-thinning and shear-thickening fluids. We show that in contrast to Stokes' problem where a compactly supported front is obtained for shear-thickening fluids, here the role of viscosity is inversed and such fronts are obtained for shear-thinning fluids. Furthermore, we demonstrate that for the case of a step in inlet pressure, the propagation rate of the front has a tn/n +1 dependence on time (t ), suggesting the ability to indirectly measure the power-law index (n ) of shear-thinning liquids through measurements of elastic deformation.

  7. Flow modelling of a newtonian fluid by two regions- the region of pure fluid and porous region

    International Nuclear Information System (INIS)

    Sampaio, R.; Gama, R.M.S. da

    1983-01-01

    A model of flow with two regions is presented using mixture theory. One region contains only pure fluid and the other a mixture of fluid and porous rigid solid. Compatibility conditons on the pure fluid-mixture interface are carefully discussed. The theory is used to solve a problem of a flow induced by pressure gradient and helicoidal motion of an impermeable cylinder on two rings one of pure fluid and another of mixture. (Author) [pt

  8. Fluid dynamics following flow shut-off in bottle filling

    Science.gov (United States)

    Thete, Sumeet; Appathurai, Santosh; Gao, Haijing; Basaran, Osman

    2012-11-01

    Bottle filling is ubiquitous in industry. Examples include filling of bottles with shampoos and cleaners, engine oil and pharmaceuticals. In these examples, fluid flows out of a nozzle to fill bottles in an assembly line. Once the required volume of fluid has flowed out of the nozzle, the flow is shut off. However, an evolving fluid thread or string may remain suspended from the nozzle following flow shut-off and persist. This stringing phenomenon can be detrimental to a bottle filling operation because it can adversely affect line speed and filling accuracy by causing uncertainty in fill volume, product loss and undesirable marring of the bottles' exterior surfaces. The dynamics of stringing are studied numerically primarily by using the 1D, slender-jet approximation of the flow equations. A novel feature entails development and use of a new boundary condition downstream of the nozzle exit to expedite the computations. While the emphasis is on stringing of Newtonian fluids and use of 1D approximations, results will also be presented for situations where (a) the fluids are non-Newtonian and (b) the full set of equations are solved without invoking the 1D approximation. Phase diagrams will be presented that identify conditions for which stringing can be problematic.

  9. Non-Darcy Free Convection of Power-Law Fluids Over a Two-Dimensional Body Embedded in a Porous Medium

    KAUST Repository

    El-Amin, Mohamed

    2010-11-27

    A boundary layer analysis was presented to study the non-Darcy-free convection of a power-law fluid over a non-isothermal two-dimensional body embedded in a porous medium. The Ostwald-de Waele power-law model was used to characterize the non-Newtonian fluid behavior. Similarity solutions were obtained with variations in surface temperature or surface heat flux. In view of the fact that most of the non-Newtonian fluids have large Prandtl numbers, this study was directed toward such fluids. The effects of the porous medium parameters, k1 and k2, body shape parameter, m, and surface thermal variations parameter, p, as well as the power-law index, n, were examined. © 2010 Springer Science+Business Media B.V.

  10. Non-Darcy Free Convection of Power-Law Fluids Over a Two-Dimensional Body Embedded in a Porous Medium

    KAUST Repository

    El-Amin, Mohamed; Sun, Shuyu; El-Ameen, M. A.; Jaha, Y. A.; Gorla, Rama Subba Reddy

    2010-01-01

    A boundary layer analysis was presented to study the non-Darcy-free convection of a power-law fluid over a non-isothermal two-dimensional body embedded in a porous medium. The Ostwald-de Waele power-law model was used to characterize the non-Newtonian fluid behavior. Similarity solutions were obtained with variations in surface temperature or surface heat flux. In view of the fact that most of the non-Newtonian fluids have large Prandtl numbers, this study was directed toward such fluids. The effects of the porous medium parameters, k1 and k2, body shape parameter, m, and surface thermal variations parameter, p, as well as the power-law index, n, were examined. © 2010 Springer Science+Business Media B.V.

  11. Point-of-care Devices: Non-Newtonian Whole Blood Behavior and Capillary Flow on Reagent-coated Walls

    Directory of Open Access Journals (Sweden)

    Jean BERTHIER

    2016-08-01

    Full Text Available Most point-of-care (POC and patient self-testing (PST devices are based on the analysis of whole blood taken from a finger prick. Whole blood contains a bountiful of information about the donor’s health. We analyze here two particularities of microsystems for blood analysis: the blood non-Newtonian behavior, and the capillary flow in reagent-coated channels. Capillarity is the most commonly used method to move fluids in portable systems. It is shown first that the capillary flow of blood does not follow the Lucas-Washburn-Rideal law when the capillary flow velocity is small, due to its non-Newtonian rheology and to the formation of rouleaux of RBCs. In a second step, the capillary flow of blood on reagent-coated surfaces is investigated; first experimentally by observing the spreading of a droplet of blood on different reagent-coated substrates; second theoretically and numerically using the general law for spontaneous capillary flows and the Evolver numerical program.

  12. Numerical investigation on hydraulic fracture cleanup and its impact on the productivity of a gas well with a non-Newtonian fluid model

    Energy Technology Data Exchange (ETDEWEB)

    Friedel, T. [Schlumberger Data and Consulting Services, Sugar Land, TX (United States)

    2006-07-01

    There are many damage mechanisms associated with hydraulically fractured gas wells. These include hydraulic damage caused by invading fluids during the treatment and damage due to the stresses exerted on the fracture face. Damage to the proppant pack can also reduce conductivity and non-Darcy flow. However, these are not the only impacts of impaired productivity in tight-gas reservoirs, which do not respond to hydraulic fracturing as expected. Some sustain a flat production profile or show only a slow increase in production rate for several weeks or months. This is due to poor rock quality, strong stress dependency in permeability, hydraulic and mechanical damage. Another reason for the poor performance is related to the cleanup of the cross-linked fracturing fluid with its non-Newtonian characteristics. This paper presented an improved 3-phase cleanup model for the investigation of polymer gel cleanup. Yield stress was considered according to the Herschel-Bulkley rheology model. The viscosity model is based on the exact analytical solution, including the plug flow zone. According to data in the published literature, half of the gel phase can be recovered. The gel saturation gradually increases towards the fracture tips, thereby lowering the fracture conductivities. The residing gel damages the permeability and porosity of the proppant pack or causes damage to the fracture face, thereby reducing production potential. These results are in agreement with field observations where fracture half-lengths, conductivities and productivity are also lower than expected. Preliminary results suggest that capillary forces and load-water recovery have little influence on gel cleanup. 16 refs., 2 tabs., 17 figs.

  13. Rayleigh Taylor instability of two superposed compressible fluids in un-magnetized plasma

    International Nuclear Information System (INIS)

    Sharma, P K; Tiwari, A; Argal, S; Chhajlani, R K

    2014-01-01

    The linear Rayleigh Taylor instability of two superposed compressible Newtonian fluids is discussed with the effect of surface tension which can play important roles in space plasma. As in both the superposed Newtonian fluids, the system is stable for potentially stable case and unstable for potentially unstable case in the present problem also. The equations of the problem are solved by normal mode method and a dispersion relation is obtained for such a system. The behaviour of growth rate is examined in the presence of surface tension and it is found that the surface tension has stabilizing influence on the Rayleigh Taylor instability of two superposed compressible fluids. Numerical analysis is performed to show the effect of sound velocity and surface tension on the growth rate of Rayleigh Taylor instability. It is found that both parameters have stabilizing influence on the growth rate of Rayleigh Taylor instability.

  14. Newtonian cosmology with a quantum bounce

    Energy Technology Data Exchange (ETDEWEB)

    Bargueno, P.; Bravo Medina, S.; Nowakowski, M. [Universidad de los Andes, Departamento de Fisica, Bogota (Colombia); Batic, D. [University of West Indies, Department of Mathematics, Kingston 6 (Jamaica)

    2016-10-15

    It has been known for some time that the cosmological Friedmann equation deduced from general relativity can also be obtained within the Newtonian framework under certain assumptions. We use this result together with quantum corrections to the Newtonian potentials to derive a set a of quantum corrected Friedmann equations. We examine the behavior of the solutions of these modified cosmological equations paying special attention to the sign of the quantum corrections. We find different quantum effects crucially depending on this sign. One such a solution displays a qualitative resemblance to other quantum models like Loop quantum gravity or non-commutative geometry. (orig.)

  15. Flow of power-law fluids in fixed beds of cylinders or spheres

    KAUST Repository

    Singh, John P.; Padhy, Sourav; Shaqfeh, Eric S. G.; Koch, Donald L.

    2012-01-01

    is influenced by the Newtonian fluid stress and a body force representing the linear drag on the surrounding particles. We consider a similar analysis for a power-law fluid where the stress τ is related to the rate of strain e by τ = 2m en-1e, where m and n

  16. Post-Newtonian parameter γ in generalized non-local gravity

    Science.gov (United States)

    Zhang, Xue; Wu, YaBo; Yang, WeiQiang; Zhang, ChengYuan; Chen, BoHai; Zhang, Nan

    2017-10-01

    We investigate the post-Newtonian parameter γ and derive its formalism in generalized non-local (GNL) gravity, which is the modified theory of general relativity (GR) obtained by adding a term m 2 n-2 R☐-n R to the Einstein-Hilbert action. Concretely, based on parametrizing the generalized non-local action in which gravity is described by a series of dynamical scalar fields ϕ i in addition to the metric tensor g μν, the post-Newtonian limit is computed, and the effective gravitational constant as well as the post-Newtonian parameters are directly obtained from the generalized non-local gravity. Moreover, by discussing the values of the parametrized post-Newtonian parameters γ, we can compare our expressions and results with those in Hohmann and Järv et al. (2016), as well as current observational constraints on the values of γ in Will (2006). Hence, we draw restrictions on the nonminimal coupling terms F̅ around their background values.

  17. Equations of motion according to the asymptotic post-Newtonian scheme for general relativity in the harmonic gauge

    Science.gov (United States)

    Arminjon, Mayeul

    2005-10-01

    The asymptotic scheme of post-Newtonian approximation defined for general relativity in the harmonic gauge by Futamase & Schutz (1983) is based on a family of initial data for the matter fields of a perfect fluid and for the initial metric, defining a family of weakly self-gravitating systems. We show that Weinberg’s (1972) expansion of the metric and his general expansion of the energy-momentum tensor T, as well as his expanded equations for the gravitational field and his general form of the expanded dynamical equations, apply naturally to this family. Then, following the asymptotic scheme, we derive the explicit form of the expansion of T for a perfect fluid, and the expanded fluid-dynamical equations. (These differ from those written by Weinberg.) By integrating these equations in the domain occupied by a body, we obtain a general form of the translational equations of motion for a 1PN perfect-fluid system in general relativity. To put them into a tractable form, we use an asymptotic framework for the separation parameter η, by defining a family of well-separated 1PN systems. We calculate all terms in the equations of motion up to the order η3 included. To calculate the 1PN correction part, we assume that the Newtonian motion of each body is a rigid one, and that the family is quasispherical, in the sense that in all bodies the inertia tensor comes close to being spherical as η→0. Apart from corrections that cancel for exact spherical symmetry, there is in the final equations of motion one additional term, as compared with the Lorentz-Droste (Einstein-Infeld-Hoffmann) acceleration. This term depends on the spin of the body and on its internal structure.

  18. Flow pattern-based mass and heat transfer and frictional drag of gas-non-Newtonian liquid flow in helical coil: two- and three-phase systems

    Science.gov (United States)

    Thandlam, Anil Kumar; Das, Chiranjib; Majumder, Subrata Kumar

    2017-04-01

    Investigation of wall-liquid mass transfer and heat transfer phenomena with gas-Newtonian and non-Newtonian fluids in vertically helical coil reactor have been reported in this article. Experiments were conducted to investigate the effect of various dynamic and geometric parameters on mass and heat transfer coefficients in the helical coil reactor. The flow pattern-based heat and mass transfer phenomena in the helical coil reactor are highlighted at different operating conditions. The study covered a wide range of geometric parameters such as diameter of the tube ( d t ), diameter of the coil ( D c ), diameter of the particle ( d p ), pitch difference ( p/D c ) and concentrations of non-Newtonian liquid. The correlation models for the heat and mass transfer coefficient based on the flow pattern are developed which may be useful in process scale-up of the helical coil reactor for industrial application. The frictional drag coefficient was also estimated and analyzed by mass transfer phenomena based on the electrochemical method.

  19. Non-Newtonian flow of pathological bile in the biliary system: experimental investigation and CFD simulations

    Science.gov (United States)

    Kuchumov, Alex G.; Gilev, Valeriy; Popov, Vitaliy; Samartsev, Vladimir; Gavrilov, Vasiliy

    2014-02-01

    The paper presents an experimental study of pathological human bile taken from the gallbladder and bile ducts. The flow dependences were obtained for different types of bile from patients with the same pathology, but of different age and sex. The parameters of the Casson's and Carreau's equations were found for bile samples. Results on the hysteretic bile behavior at loading-unloading tests are also presented, which proved that the pathologic bile is a non-Newtonian thixotropic liquid. The viscosity of the gallbladder bile was shown to be higher compared to the duct bile. It was found that at higher shear stress the pathological bile behaves like Newtonian fluid, which is explained by reorientation of structural components. Moreover, some pathological bile flow in the biliary system CFD simulations were performed. The velocity and pressure distributions as well as flow rates in the biliary segments during the gallbladder refilling and emptying phases are obtained. The results of CFD simulations can be used for surgeons to assess the patient's condition and choose an adequate treatment.

  20. Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries

    Directory of Open Access Journals (Sweden)

    Luc Blanchet

    2014-02-01

    Full Text Available To be observed and analyzed by the network of gravitational wave detectors on ground (LIGO, VIRGO, etc. and by the future detectors in space (eLISA, etc., inspiralling compact binaries -- binary star systems composed of neutron stars and/or black holes in their late stage of evolution -- require high-accuracy templates predicted by general relativity theory. The gravitational waves emitted by these very relativistic systems can be accurately modelled using a high-order post-Newtonian gravitational wave generation formalism. In this article, we present the current state of the art on post-Newtonian methods as applied to the dynamics and gravitational radiation of general matter sources (including the radiation reaction back onto the source and inspiralling compact binaries. We describe the post-Newtonian equations of motion of compact binaries and the associated Lagrangian and Hamiltonian formalisms, paying attention to the self-field regularizations at work in the calculations. Several notions of innermost circular orbits are discussed. We estimate the accuracy of the post-Newtonian approximation and make a comparison with numerical computations of the gravitational self-force for compact binaries in the small mass ratio limit. The gravitational waveform and energy flux are obtained to high post-Newtonian order and the binary's orbital phase evolution is deduced from an energy balance argument. Some landmark results are given in the case of eccentric compact binaries -- moving on quasi-elliptical orbits with non-negligible eccentricity. The spins of the two black holes play an important role in the definition of the gravitational wave templates. We investigate their imprint on the equations of motion and gravitational wave phasing up to high post-Newtonian order (restricting to spin-orbit effects which are linear in spins, and analyze the post-Newtonian spin precession equations as well as the induced precession of the orbital plane.

  1. Experimental investigation of the flow of a blood analogue fluid in a replica of a bifurcated small artery.

    Science.gov (United States)

    Anastasiou, A D; Spyrogianni, A S; Koskinas, K C; Giannoglou, G D; Paras, S V

    2012-03-01

    The scope of this work is to study the pulsatile flow of a blood mimicking fluid in a micro channel that simulates a bifurcated small artery, in which the Fahraeus-Lindqvist effect is insignificant. An aqueous glycerol solution with small amounts of xanthan gum was used for simulating viscoelastic properties of blood and in vivo flow conditions were reproduced. Local flow velocities were measured using micro Particle Image Velocimetry (μ-PIV). From the measured velocity distributions, the wall shear stress (WSS) and its variation during a pulse were estimated. The Reynolds numbers employed are relatively low, i.e. similar to those prevailing during blood flow in small arteries. Experiments both with a Newtonian and a non-Newtonian fluid (having asymptotic viscosity equal to the viscosity of the Newtonian one) proved that the common assumption that blood behaves as a Newtonian fluid is not valid for blood flow in small arteries. It was also shown that the outer wall of the bifurcation, which is exposed to a lower WSS, is more predisposed to atherosclerotic plaque formation. Moreover, this region in small vessels is shorter than the one in large arteries, as the developed secondary flow decays faster. Finally, the WSS values in small arteries were found to be lower than those in large ones. Copyright © 2011 IPEM. Published by Elsevier Ltd. All rights reserved.

  2. Viscoelastic fluid-structure interactions between a flexible cylinder and wormlike micelle solution

    Science.gov (United States)

    Dey, Anita A.; Modarres-Sadeghi, Yahya; Rothstein, Jonathan P.

    2018-06-01

    It is well known that when a flexible or flexibly mounted structure is placed perpendicular to the flow of a Newtonian fluid, it can oscillate due to the shedding of separated vortices at high Reynolds numbers. Unlike Newtonian fluids, the flow of viscoelastic fluids can become unstable even at infinitesimal Reynolds numbers due to a purely elastic flow instability that can occur at large Weissenberg numbers. Recent work has shown that these elastic flow instabilities can drive the motion of flexible sheets. The fluctuating fluid forces exerted on the structure from the elastic flow instabilities can lead to a coupling between an oscillatory structural motion and the state of stress in the fluid flow. In this paper, we present the results of an investigation into the flow of a viscoelastic wormlike micelle solution past a flexible circular cylinder. The time variation of the flow field and the state of stress in the fluid are shown using a combination of particle image tracking and flow-induced birefringence images. The static and dynamic responses of the flexible cylinder are presented for a range of flow velocities. The nonlinear dynamics of the structural motion is studied to better understand an observed transition from a symmetric to an asymmetric structural deformation and oscillation behavior.

  3. Nonrotating black hole in a post-Newtonian tidal environment

    International Nuclear Information System (INIS)

    Taylor, Stephanne; Poisson, Eric

    2008-01-01

    We examine the motion and tidal dynamics of a nonrotating black hole placed within a post-Newtonian external spacetime. The black hole's gravity is described accurately to all orders in Gm/c 2 r, where m is the black-hole mass and r is the distance to the black hole. The tidal perturbation created by the external environment is treated as a small perturbation. At a large distance from the black hole, the gravitational field of the external distribution of matter is assumed to be sufficiently weak to be adequately described by the (first) post-Newtonian approximation to general relativity. There, the black hole is treated as a monopole contribution to the total gravitational field. There exists an overlap in the domains of validity of each description, and the black-hole and post-Newtonian metrics are matched in the overlap. The matching procedure produces (i) a justification of the statement that a nonrotating black hole is a post-Newtonian monopole; (ii) a complete characterization of the coordinate transformation between the inertial, barycentric frame and the accelerated, black-hole frame; (iii) the equations of motion for the black hole; and (iv) the gravito-electric and gravito-magnetic tidal fields acting on the black hole. We first calculate the equations of motion and tidal fields by making no assumptions regarding the nature of the post-Newtonian environment; this could contain a continuous distribution of matter (so as to model a galactic core) or any number of condensed bodies. We next specialize our discussion to a situation in which the black hole is a member of a post-Newtonian two-body system. As an application of our results, we examine the geometry of the deformed event horizon and calculate the tidal heating of the black hole, the rate at which it acquires mass as a result of its tidal interaction with the companion body.

  4. Flow of power-law fluids in fixed beds of cylinders or spheres

    KAUST Repository

    Singh, John P.

    2012-10-29

    An ensemble average of the equations of motion for a Newtonian fluid over particle configurations in a dilute fixed bed of spheres or cylinders yields Brinkman\\'s equations of motion, where the disturbance velocity produced by a test particle is influenced by the Newtonian fluid stress and a body force representing the linear drag on the surrounding particles. We consider a similar analysis for a power-law fluid where the stress τ is related to the rate of strain e by τ = 2m en-1e, where m and n are constants. In this case, the ensemble-averaged momentum equation includes a body force resulting from the nonlinear drag exerted on the surrounding particles, a power-law stress associated with the disturbance velocity of the test particle, and a stress term that is linear with respect to the test particle\\'s disturbance velocity. The latter term results from the interaction of the test particle\\'s velocity disturbance with the random straining motions produced by the neighbouring particles and is important only in shear-thickening fluids where the velocity disturbances of the particles are long-ranged. The solutions to these equations using scaling analyses for dilute beds and numerical simulations using the finite element method are presented. We show that the drag force acting on a particle in a fixed bed can be written as a function of a particle-concentration-dependent length scale at which the fluid velocity disturbance produced by a particle is modified by hydrodynamic interactions with its neighbours. This is also true of the drag on a particle in a periodic array where the length scale is the lattice spacing. The effects of particle interactions on the drag in dilute arrays (periodic or random) of cylinders and spheres in shear-thickening fluids is dramatic, where it arrests the algebraic growth of the disturbance velocity with radial position when n≥ 1 for cylinders and n≥ 2 for spheres. For concentrated random arrays of particles, we adopt an

  5. Theoretical frameworks for testing relativistic gravity. V - Post-Newtonian limit of Rosen's theory

    Science.gov (United States)

    Lee, D. L.; Ni, W.-T.; Caves, C. M.; Will, C. M.

    1976-01-01

    The post-Newtonian limit of Rosen's theory of gravity is evaluated and is shown to be identical to that of general relativity, except for the post-Newtonian parameter alpha sub 2 (which is related to the difference in propagation speeds for gravitational and electromagnetic waves). Both the value of alpha sub 2 and the value of the Newtonian gravitational constant depend on the present cosmological structure of the Universe. If the cosmological structure has a specific (but presumably special) form, the Newtonian gravitational constant assumes its current value, alpha sub 2 is zero, the post-Newtonian limit of Rosen's theory is identical to that of general relativity - and standard solar system experiments cannot distinguish between the two theories.

  6. Parameterized Post-Newtonian Expansion of Scalar-Vector-Tensor Theory of Gravity

    International Nuclear Information System (INIS)

    Arianto; Zen, Freddy P.; Gunara, Bobby E.; Hartanto, Andreas

    2010-01-01

    We investigate the weak-field, post-Newtonian expansion to the solution of the field equations in scalar-vector-tensor theory of gravity. In the calculation we restrict ourselves to the first post Newtonian. The parameterized post Newtonian (PPN) parameters are determined by expanding the modified field equations in the metric perturbation. Then, we compare the solution to the PPN formalism in first PN approximation proposed by Will and Nordtvedt and read of the coefficients (the PPN parameters) of post Newtonian potentials of the theory. We find that the values of γ PPN and β PPN are the same as in General Relativity but the coupling functions β 1 , β 2 , and β 3 are the effect of the preferred frame.

  7. Newtonian quantum gravity

    International Nuclear Information System (INIS)

    Jones, K.R.W.

    1995-01-01

    We develop a nonlinear quantum theory of Newtonian gravity consistent with an objective interpretation of the wavefunction. Inspired by the ideas of Schroedinger, and Bell, we seek a dimensional reduction procedure to map complex wavefunctions in configuration space onto a family of observable fields in space-time. Consideration of quasi-classical conservation laws selects the reduced one-body quantities as the basis for an explicit quasi-classical coarse-graining. These we interpret as describing the objective reality of the laboratory. Thereafter, we examine what may stand in the role of the usual Copenhagen observer to localise this quantity against macroscopic dispersion. Only a tiny change is needed, via a generically attractive self-potential. A nonlinear treatment of gravitational self-energy is thus advanced. This term sets a scale for all wavepackets. The Newtonian cosmology is thus closed, without need of an external observer. Finally, the concept of quantisation is re-interpreted as a nonlinear eigenvalue problem. To illustrate, we exhibit an elementary family of gravitationally self-bound solitary waves. Contrasting this theory with its canonically quantised analogue, we find that the given interpretation is empirically distinguishable, in principle. This result encourages deeper study of nonlinear field theories as a testable alternative to canonically quantised gravity. (author). 46 refs., 5 figs

  8. Characteristics of gas-liquid dynamics in operation of oil fields producing non-Newtonian crude oils

    Energy Technology Data Exchange (ETDEWEB)

    Mirzadzhanzade, A Kh; Khasaev, A M; Gurbanov, R S; Akhmedov, Z M

    1968-08-01

    Experimental studies have shown that crude oils from Azerbaidzhan, Uzbekistan, Tataria, Kazakhstan and other areas have anomalous properties under reservoir conditions. Such crude oils are non-Newtonian and (1) obey Darcys Law at low velocities; (2) obey an exponential law at higher velocities; and (3) obey a modified Darcys Law at most velocities. A discussion is given of (1) flow of non-Newtonian crude oils together with gas or water; (2) flow of non-Newtonian crude oils in well tubing; (3) behavior of wells producing non-Newtonian crude oils; and (4) pumping of non-Newtonian oils in wells. Experiments have shown that a visco-plastic liquid does not fill pump inlets completely; as the diameter of the pump inlet decreases so also does the degree of liquid filling. A statistical analysis of production data from 160 fields with Newtonian oil and 129 fields with non- Newtonian oil has shown that much higher production is obtained from fields with Newtonian crude oils.

  9. Newtonian hydrodynamic equations with relativistic pressure and velocity

    Energy Technology Data Exchange (ETDEWEB)

    Hwang, Jai-chan [Department of Astronomy and Atmospheric Sciences, Kyungpook National University, Daegu 702-701 (Korea, Republic of); Noh, Hyerim [Korea Astronomy and Space Science Institute, Daejeon 305-348 (Korea, Republic of); Fabris, Júlio; Piattella, Oliver F.; Zimdahl, Winfried, E-mail: jchan@knu.ac.kr, E-mail: hr@kasi.re.kr, E-mail: fabris@pq.cnpq.br, E-mail: oliver.piattella@pq.cnpq.br, E-mail: winfried.zimdahl@pq.cnpq.br [Departamento de Fisica, Universidade Federal do Espirito Santo, Vitória (Brazil)

    2016-07-01

    We present a new approximation to include fully general relativistic pressure and velocity in Newtonian hydrodynamics. The energy conservation, momentum conservation and two Poisson's equations are consistently derived from Einstein's gravity in the zero-shear gauge assuming weak gravity and action-at-a-distance limit. The equations show proper special relativity limit in the absence of gravity. Our approximation is complementary to the post-Newtonian approximation and the equations are valid in fully nonlinear situations.

  10. Shear Rheology of a Suspension of Deformable Solids in Viscoelastic Fluid via Immersed Boundary Techniques

    Science.gov (United States)

    Guido, Christopher; Shaqfeh, Eric

    2017-11-01

    The simulation of fluids with suspended deformable solids is important to the design of microfluidic devices with soft particles and the examination of blood flow in complex channels. The fluids in these applications are often viscoelastic, motivating the development of a high-fidelity simulation tool with general constitutive model implementations for both the viscoelastic fluid and deformable solid. The Immersed Finite Element Method (IFEM) presented by Zhang et al. (2007) allows for distinct fluid and solid grids to be utilized reducing the need for costly re-meshing when particles translate. We discuss a modified version of the IFEM that allows for the simulation of deformable particles in viscoelastic flows. This simulation tool is validated for simple Newtonian shear flows with elastic particles that obey a Neo-Hookean Law. The tool is used to further explore the rheology of a dilute suspension of Neo-Hookean particles in a Giesekus fluid. The results show that dilute suspensions of soft particles have viscosities that decrease as the Capillary number becomes higher in both the case of a Newtonian and viscoelastic fluid. A discussion of multiple particle results will be included. NSF CBET-1066263 and 1066334.

  11. Possible evidence for non-Newtonian gravity in the Greenland ice gap

    International Nuclear Information System (INIS)

    Ander, M.E.

    1988-01-01

    An Airy-type geophysical experiment was conducted down a 2 km deep hole in the Greenland ice cap in order to test for possible violations of Newton's inverse square law by making gravity measurements over a range of 213 m to 1460 m. A significant departure from Newtonian gravity was observed. This result can be explained by the existence of an attractive non-Newtonian component of gravity with a strength of about 3.4% that of Newtonian gravity at a scale of 1460 m. Unfortunately, we cannot completely, unambiguously attribute it to a breakdown of Newtonian gravity because we have shown that lateral density variations in the bedrock beneath the ice can cause such apparent departures. If such variations existed, they would have to be rather unusual but certainly no impossible. 8 refs

  12. Acoustic geometry for general relativistic barotropic irrotational fluid flow

    International Nuclear Information System (INIS)

    Visser, Matt; Molina-ParIs, Carmen

    2010-01-01

    'Acoustic spacetimes', in which techniques of differential geometry are used to investigate sound propagation in moving fluids, have attracted considerable attention over the last few decades. Most of the models currently considered in the literature are based on non-relativistic barotropic irrotational fluids, defined in a flat Newtonian background. The extension, first to special relativistic barotropic fluid flow and then to general relativistic barotropic fluid flow in an arbitrary background, is less straightforward than it might at first appear. In this paper, we provide a pedagogical and simple derivation of the general relativistic 'acoustic spacetime' in an arbitrary (d+1)-dimensional curved-space background.

  13. Second-order perturbations of cosmological fluids: Relativistic effects of pressure, multicomponent, curvature, and rotation

    International Nuclear Information System (INIS)

    Hwang, Jai-chan; Noh, Hyerim

    2007-01-01

    We present general relativistic correction terms appearing in Newton's gravity to the second-order perturbations of cosmological fluids. In our previous work we have shown that to the second-order perturbations, the density and velocity perturbation equations of general relativistic zero-pressure, irrotational, single-component fluid in a spatially flat background coincide exactly with the ones known in Newton's theory without using the gravitational potential. We also have shown the effect of gravitational waves to the second order, and pure general relativistic correction terms appearing in the third-order perturbations. Here, we present results of second-order perturbations relaxing all the assumptions made in our previous works. We derive the general relativistic correction terms arising due to (i) pressure, (ii) multicomponent, (iii) background spatial curvature, and (iv) rotation. In the case of multicomponent zero-pressure, irrotational fluids under the flat background, we effectively do not have relativistic correction terms, thus the relativistic equations expressed in terms of density and velocity perturbations again coincide with the Newtonian ones. In the other three cases we generally have pure general relativistic correction terms. In the case of pressure, the relativistic corrections appear even in the level of background and linear perturbation equations. In the presence of background spatial curvature, or rotation, pure relativistic correction terms directly appear in the Newtonian equations of motion of density and velocity perturbations to the second order; to the linear order, without using the gravitational potential (or metric perturbations), we have relativistic/Newtonian correspondences for density and velocity perturbations of a single-component fluid including the rotation even in the presence of background spatial curvature. In the small-scale limit (far inside the horizon), to the second-order, relativistic equations of density and

  14. Empirical Correlations and CFD Simulations of Vertical Two-Phase Gas-Liquid (Newtonian and Non-Newtonian) Flow Compared Against Experimental Data of Void Fraction and Pressure Drop

    DEFF Research Database (Denmark)

    Ratkovich, Nicolas Rios; Bentzen, Thomas Ruby; Majumder, S.K.

    2012-01-01

    Gas-Newtonian liquid two-phase flows (TPFs) are presented in several industrial processes (i.e. oil-gas industry). In spite of the common occurrence of these TPFs, their understanding is limited compared to single-phase flows. Different studies on TPF have focus on developing empirical correlations...... based in large sets of experiment data for void fraction and pressure drop which have proven to be accurate for specific condition that their where developed for, which limit their applicability. On the other hand, scarce studies focus on gas-non-Newtonian liquids TPFs, which are very common in chemical...... processes. The main reason for it is due to the characterization of the viscosity, which determines the hydraulic regime and flow behaviours on the system. The focus of this study is the analysis of the TPF for Newtonian and non-Newtonian liquids in a vertical pipe in terms of void fraction and total...

  15. Computational Fluid Dynamics Simulation of Hydrodynamics and Stresses in the PhEur/USP Disintegration Tester Under Fed and Fasted Fluid Characteristics.

    Science.gov (United States)

    Kindgen, Sarah; Wachtel, Herbert; Abrahamsson, Bertil; Langguth, Peter

    2015-09-01

    Disintegration of oral solid dosage forms is a prerequisite for drug dissolution and absorption and is to a large extent dependent on the pressures and hydrodynamic conditions in the solution that the dosage form is exposed to. In this work, the hydrodynamics in the PhEur/USP disintegration tester were investigated using computational fluid dynamics (CFD). Particle image velocimetry was used to validate the CFD predictions. The CFD simulations were performed with different Newtonian and non-Newtonian fluids, representing fasted and fed states. The results indicate that the current design and operating conditions of the disintegration test device, given by the pharmacopoeias, are not reproducing the in vivo situation. This holds true for the hydrodynamics in the disintegration tester that generates Reynolds numbers dissimilar to the reported in vivo situation. Also, when using homogenized US FDA meal, representing the fed state, too high viscosities and relative pressures are generated. The forces acting on the dosage form are too small for all fluids compared to the in vivo situation. The lack of peristaltic contractions, which generate hydrodynamics and shear stress in vivo, might be the major drawback of the compendial device resulting in the observed differences between predicted and in vivo measured hydrodynamics. © 2015 Wiley Periodicals, Inc. and the American Pharmacists Association.

  16. The parameterized post-Newtonian limit of bimetric theories of gravity

    International Nuclear Information System (INIS)

    Clifton, Timothy; Banados, Maximo; Skordis, Constantinos

    2010-01-01

    We consider the post-Newtonian limit of a general class of bimetric theories of gravity, in which both metrics are dynamical. The established parameterized post-Newtonian approach is followed as closely as possible, although new potentials are found that do not exist within the standard framework. It is found that these theories can evade solar system tests of post-Newtonian gravity remarkably well. We show that perturbations about Minkowski space in these theories contain both massless and massive degrees of freedom, and that in general there are two different types of massive mode, each with a different mass parameter. If both of these masses are sufficiently large then the predictions of the most general class of theories we consider are indistinguishable from those of general relativity, up to post-Newtonian order in a weak-field, low-velocity expansion. In the limit that the massive modes become massless, we find that these general theories do not exhibit a van Dam-Veltman-Zakharov-like discontinuity in their γ parameter, although there are discontinuities in other post-Newtonian parameters as the massless limit is approached. This smooth behaviour in γ is due to the discontinuities from each of the two different massive modes cancelling each other out. Such cancellations cannot occur in special cases with only one massive mode, such as the Isham-Salam-Strathdee theory.

  17. Second post-Newtonian Lagrangian dynamics of spinning compact binaries

    Energy Technology Data Exchange (ETDEWEB)

    Huang, Li; Wu, Xin [Nanchang University, Department of Physics and Institute of Astronomy, Nanchang (China); Ma, DaZhu [Hubei University for Nationalities, School of Science, Enshi (China)

    2016-09-15

    The leading-order spin-orbit coupling is included in a post-Newtonian Lagrangian formulation of spinning compact binaries, which consists of the Newtonian term, first post-Newtonian (1PN) and 2PN non-spin terms and 2PN spin-spin coupling. This leads to a 3PN spin-spin coupling occurring in the derived Hamiltonian. The spin-spin couplings are mainly responsible for chaos in the Hamiltonians. However, the 3PN spin-spin Hamiltonian is small and has different signs, compared with the 2PN spin-spin Hamiltonian equivalent to the 2PN spin-spin Lagrangian. As a result, the probability of the occurrence of chaos in the Lagrangian formulation without the spin-orbit coupling is larger than that in the Lagrangian formulation with the spin-orbit coupling. Numerical evidences support this claim. (orig.)

  18. Topics in the Foundations of General Relativity and Newtonian Gravitation Theory

    CERN Document Server

    Malament, David B

    2012-01-01

    In Topics in the Foundations of General Relativity and Newtonian Gravitation Theory, David B. Malament presents the basic logical-mathematical structure of general relativity and considers a number of special topics concerning the foundations of general relativity and its relation to Newtonian gravitation theory. These special topics include the geometrized formulation of Newtonian theory (also known as Newton-Cartan theory), the concept of rotation in general relativity, and Gödel spacetime. One of the highlights of the book is a no-go theorem that can be understood to show that there is

  19. Relativistic thermodynamics of Fluids. l

    International Nuclear Information System (INIS)

    Havas, P.; Swenson, R.J.

    1979-01-01

    In 1953, Stueckelberg and Wanders derived the basic laws of relativistic linear nonequilibrium thermodynamics for chemically reacting fluids from the relativistic local conservation laws for energy-momentum and the local laws of production of substances and of nonnegative entropy production by the requirement that the corresponding currents (assumed to depend linearly on the derivatives of the state variables) should not be independent. Generalizing their method, we determine the most general allowed form of the energy-momentum tensor T/sup alphabeta/ and of the corresponding rate of entropy production under the same restriction on the currents. The problem of expressing this rate in terms of thermodynamic forces and fluxes is discussed in detail; it is shown that the number of independent forces is not uniquely determined by the theory, and seven possibilities are explored. A number of possible new cross effects are found, all of which persist in the Newtonian (low-velocity) limit. The treatment of chemical reactions is incorporated into the formalism in a consistent manner, resulting in a derivation of the law for rate of production, and in relating this law to transport processes differently than suggested previously. The Newtonian limit is discussed in detail to establish the physical interpretation of the various terms of T/sup alphabeta/. In this limit, the interpretation hinges on that of the velocity field characterizing the fluid. If it is identified with the average matter velocity following from a consideration of the number densities, the usual local conservation laws of Newtonian nonequilibrium thermodynamics are obtained, including that of mass. However, a slightly different identification allows conversion of mass into energy even in this limit, and thus a macroscopic treatment of nuclear or elementary particle reactions. The relation of our results to previous work is discussed in some detail

  20. Peristaltic Transport of a Rheological Fluid: Model for Movement of Food Bolus Through Esophagus

    OpenAIRE

    Misra, J. C.; Maiti, S.

    2011-01-01

    Fluid mechanical peristaltic transport through esophagus has been of concern in the paper. A mathematical model has been developed with an aim to study the peristaltic transport of a rheological fluid for arbitrary wave shapes and tube lengths. The Ostwald-de Waele power law of viscous fluid is considered here to depict the non-Newtonian behaviour of the fluid. The model is formulated and analyzed with the specific aim of exploring some important information concerning the movement of food bo...

  1. Undulatory swimming in viscoelastic fluids under geometric confinement: experiments with C. elegans

    Science.gov (United States)

    Gagnon, David; Shih, Jerry; Arratia, Paulo

    2017-11-01

    Many natural biological processes, such as bacteria moving through vesicles in the circulatory system and spermatozoa swimming through millimeter-scale fallopian tubes, require low Reynolds number swimmers to move between two fluid-solid interfaces. Furthermore, these biological systems typically involve non-Newtonian fluids (e.g. blood and mucus), which can be shear-thinning, viscoelastic, or both. Using the model biological organism C. elegans, we introduce two far-field no-slip boundary conditions in the beating plane by observing swimming through thin channels in viscosified Newtonian and viscoelastic fluids. Using image processing and particle tracking velocimetry techniques, we measure both the swimming kinematics and the resulting flow fields as a function of decreasing channel width. As this width approaches the characteristic transverse length scale of the nematode's swimming gate, we observe (i) swimming speed decreases with increasing De, (ii) this decrease in speed can be non-monotonic with decreasing channel width at a given De, and (iii) the change in nematode kinematics appears to be associated with a structural change in the flow field around the swimmer quantified using the flow type parameter.

  2. Measurement and characterization of slippage and slip-law using a rigorous analysis in dynamics of oscillating rheometer: Newtonian fluid

    Science.gov (United States)

    Azese, Martin Ndi

    2018-02-01

    This article presents a rigorous calculation involving velocity slip of Newtonian fluid where we analyze and solve the unsteady Navier-Stokes equation with emphasis on its rheological implication. The goal of which is to model a simple yet effective non-invasive way of quantifying and characterizing slippage. Indeed this contrasts with previous techniques that exhibit inherent limitations whereby injecting foreign objects usually alter the flow. This problem is built on the Couette rheological flow system such that μ-Newton force and μ-stress are captured and processed to obtain wall slip. Our model leads to a linear partial differential equation and upon enforcing linear-Navier slip boundary conditions (BC) yields inhomogeneous and unsteady "Robin-type" BC. A dimensional analysis reveals salient dimensionless parameters: Roshko, Strouhal, and Reynolds while highlighting slip-numbers from BC. We also solve the slip-free case to corroborate and validate our results. Several graphs are generated showing slip effects, particularly, studying how slip-numbers, a key input, differentiate themselves to the outputs. We also confirm this in a graphical fashion by presenting the flow profile across channel width, velocity, and stress at both walls. A perturbation scheme is introduced to calculate long-time behavior when the system seats for long. More importantly, in the end, we justify the existence of a reverse mechanism, where an inverse transformation like Fourier transform uses the output data to retrieve slip-numbers and slip law, thus quantifying and characterizing slip. Therefore, we not only substantiate our analysis, but we also justify our claim, measurement and characterization, and theorize realizability of our proposition.

  3. The LS-STAG immersed boundary/cut-cell method for non-Newtonian flows in 3D extruded geometries

    Science.gov (United States)

    Nikfarjam, F.; Cheny, Y.; Botella, O.

    2018-05-01

    The LS-STAG method is an immersed boundary/cut-cell method for viscous incompressible flows based on the staggered MAC arrangement for Cartesian grids, where the irregular boundary is sharply represented by its level-set function, results in a significant gain in computer resources (wall time, memory usage) compared to commercial body-fitted CFD codes. The 2D version of LS-STAG method is now well-established (Cheny and Botella, 2010), and this paper presents its extension to 3D geometries with translational symmetry in the z direction (hereinafter called 3D extruded configurations). This intermediate step towards the fully 3D implementation can be applied to a wide variety of canonical flows and will be regarded as the keystone for the full 3D solver, since both discretization and implementation issues on distributed memory machines are tackled at this stage of development. The LS-STAG method is then applied to various Newtonian and non-Newtonian flows in 3D extruded geometries (axisymmetric pipe, circular cylinder, duct with an abrupt expansion) for which benchmark results and experimental data are available. The purpose of these investigations are (a) to investigate the formal order of accuracy of the LS-STAG method, (b) to assess the versatility of method for flow applications at various regimes (Newtonian and shear-thinning fluids, steady and unsteady laminar to turbulent flows) (c) to compare its performance with well-established numerical methods (body-fitted and immersed boundary methods).

  4. The magnetic interaction of Janus magnetic particles suspended in a viscous fluid

    NARCIS (Netherlands)

    Seong, Y.; Kang, T.G.; Hulsen, M.A.; den Toonder, J.M.J.; Anderson, P.D.

    2016-01-01

    We studied the magnetic interaction between circular Janus magnetic particles suspended in a Newtonian fluid under the influence of an externally applied uniform magnetic field. The particles are equally compartmentalized into paramagnetic and non-magnetic sides. A direct numerical scheme is

  5. A note on the post-Newtonian limit of quasi-local energy expressions

    International Nuclear Information System (INIS)

    Frauendiener, Jörg; Szabados, László B

    2011-01-01

    An 'effective' quasi-local energy expression, motivated by the (relativistically corrected) Newtonian theory, is introduced in exact general relativity as the volume integral of all the source terms in the field equation for the Newtonian potential in static spacetimes. In particular, we exhibit a new post-Newtonian correction in the source term in the field equation for the Newtonian gravitational potential. In asymptotically flat spacetimes, this expression tends to the Arnowitt-Deser-Misner energy at spatial infinity as a monotonically decreasing set function. We prove its positivity in spherically symmetric spacetimes under certain energy conditions, and that its vanishing characterizes flatness. We argue that any physically acceptable quasi-local energy expression should behave qualitatively like this 'effective' energy expression in this limit. (paper)

  6. Contracting bubbles in Hele-Shaw cells with a power-law fluid

    International Nuclear Information System (INIS)

    McCue, Scott W; King, John R

    2011-01-01

    The problem of bubble contraction in a Hele-Shaw cell is studied for the case in which the surrounding fluid is of power-law type. A small perturbation of the radially symmetric problem is first considered, focussing on the behaviour just before the bubble vanishes, it being found that for shear-thinning fluids the radially symmetric solution is stable, while for shear-thickening fluids the aspect ratio of the bubble boundary increases. The borderline (Newtonian) case considered previously is neutrally stable, the bubble boundary becoming elliptic in shape with the eccentricity of the ellipse depending on the initial data. Further light is shed on the bubble contraction problem by considering a long thin Hele-Shaw cell: for early times the leading-order behaviour is one-dimensional in this limit; however, as the bubble contracts its evolution is ultimately determined by the solution of a Wiener–Hopf problem, the transition between the long thin limit and the extinction limit in which the bubble vanishes being described by what is in effect a similarity solution of the second kind. This same solution describes the generic (slit-like) extinction behaviour for shear-thickening fluids, the interface profiles that generalize the ellipses that characterize the Newtonian case being constructed by the Wiener–Hopf calculation

  7. Relativistic gravitation theory for the modified Newtonian dynamics paradigm

    International Nuclear Information System (INIS)

    Bekenstein, Jacob D.

    2004-01-01

    The modified Newtonian dynamics (MOND) paradigm of Milgrom can boast of a number of successful predictions regarding galactic dynamics; these are made without the assumption that dark matter plays a significant role. MOND requires gravitation to depart from Newtonian theory in the extragalactic regime where dynamical accelerations are small. So far relativistic gravitation theories proposed to underpin MOND have either clashed with the post-Newtonian tests of general relativity, or failed to provide significant gravitational lensing, or violated hallowed principles by exhibiting superluminal scalar waves or an a priori vector field. We develop a relativistic MOND inspired theory which resolves these problems. In it gravitation is mediated by metric, a scalar, and a 4-vector field, all three dynamical. For a simple choice of its free function, the theory has a Newtonian limit for nonrelativistic dynamics with significant acceleration, but a MOND limit when accelerations are small. We calculate the β and γ parameterized post-Newtonian coefficients showing them to agree with solar system measurements. The gravitational light deflection by nonrelativistic systems is governed by the same potential responsible for dynamics of particles. To the extent that MOND successfully describes dynamics of a system, the new theory's predictions for lensing by that system's visible matter will agree as well with observations as general relativity's predictions made with a dynamically successful dark halo model. Cosmological models based on the theory are quite similar to those based on general relativity; they predict slow evolution of the scalar field. For a range of initial conditions, this last result makes it easy to rule out superluminal propagation of metric, scalar, and vector waves

  8. Newtonian cosmology with a time-varying constant of gravitation

    International Nuclear Information System (INIS)

    McVittie, G.C.

    1978-01-01

    Newtonian cosmology is based on the Eulerian equations of fluid mechanics combined with Poisson's equation modified by the introduction of a time-varying G. Spherically symmetric model universes are worked out with instantaneously uniform densities. They are indeterminate unless instantaneous uniformity of the pressure is imposed. When G varies as an inverse power of the time, the models can in some cases be shown to depend on the solution of a second-order differential equation which also occurs in the Friedmann models of general relativity. In Section 3, a method for 'passing through' a singularity of this equation is proposed which entails making four arbitrary mathematical assumptions. When G varies as (time) -1 , models with initially cycloidal motion are possible, each cycle becoming longer as time progresses. Finally, gravitation becomes so weak that the model expands to infinity. Kinetic and potential energies for the whole model are derived from the basic equations; their sum is not constant. (author)

  9. Analytical solutions of couple stress fluid flows with slip boundary conditions

    Directory of Open Access Journals (Sweden)

    Devakar M.

    2014-09-01

    Full Text Available In the present article, the exact solutions for fundamental flows namely Couette, Poiseuille and generalized Couette flows of an incompressible couple stress fluid between parallel plates are obtained using slip boundary conditions. The effect of various parameters on velocity for each problem is discussed. It is found that, for each of the problems, the solution in the limiting case as couple stresses approaches to zero is similar to that of classical viscous Newtonian fluid. The results indicate that, the presence of couple stresses decreases the velocity of the fluid.

  10. Two-Phase Acto-Cytosolic Fluid Flow in a Moving Keratocyte: A 2D Continuum Model.

    Science.gov (United States)

    Nikmaneshi, M R; Firoozabadi, B; Saidi, M S

    2015-09-01

    The F-actin network and cytosol in the lamellipodia of crawling cells flow in a centripetal pattern and spout-like form, respectively. We have numerically studied this two-phase flow in the realistic geometry of a moving keratocyte. Cytosol has been treated as a low viscosity Newtonian fluid flowing through the high viscosity porous medium of F-actin network. Other involved phenomena including myosin activity, adhesion friction, and interphase interaction are also discussed to provide an overall view of this problem. Adopting a two-phase coupled model by myosin concentration, we have found new accurate perspectives of acto-cytosolic flow and pressure fields, myosin distribution, as well as the distribution of effective forces across the lamellipodia of a keratocyte with stationary shape. The order of magnitude method is also used to determine the contribution of forces in the internal dynamics of lamellipodia.

  11. Pressure drop coefficient of laminar Newtonian flow in axisymmetric diffusers

    International Nuclear Information System (INIS)

    Rosa, S.; Pinho, F.T.

    2006-01-01

    The laminar flow of Newtonian fluids in axisymmetric diffusers has been numerically investigated to evaluate the pressure-loss coefficient as a function of Reynolds number, diffusion angle and expansion ratio. The numerical simulations were carried out with a finite-volume based code using non-orthogonal collocated grids and second order accurate differencing schemes to discretize all terms of the transport equations. The calculations were carried out for Reynolds numbers between 2 and 200, diffusion angles from 0 deg. to 90 deg. and expansion ratios of 1.5 and 2 and the data are presented in tabular form and as correlations. A simplified 1D theoretical analysis helped explain the various contributions to the loss coefficient and its difference relative to the reversible pressure variation due to differences between the actual and fully developed friction losses, distortions of the velocity profiles and pressure non-uniformity upstream and downstream of the expansion section

  12. Pressure drop coefficient of laminar Newtonian flow in axisymmetric diffusers

    Energy Technology Data Exchange (ETDEWEB)

    Rosa, S. [Escola Superior de Tecnologia e Gestao, Instituto Politecnico, Campus de Santa Apolonia, 5301-857 Braganca (Portugal)]. E-mail: srosa@ipb.pt; Pinho, F.T. [Centro de Estudos de Fenomenos de Transporte, DEM, Universidade do Minho, Campus de Azurem, 4800-058 Guimaraes (Portugal)]. E-mail: fpinho@fe.up.pt

    2006-04-15

    The laminar flow of Newtonian fluids in axisymmetric diffusers has been numerically investigated to evaluate the pressure-loss coefficient as a function of Reynolds number, diffusion angle and expansion ratio. The numerical simulations were carried out with a finite-volume based code using non-orthogonal collocated grids and second order accurate differencing schemes to discretize all terms of the transport equations. The calculations were carried out for Reynolds numbers between 2 and 200, diffusion angles from 0 deg. to 90 deg. and expansion ratios of 1.5 and 2 and the data are presented in tabular form and as correlations. A simplified 1D theoretical analysis helped explain the various contributions to the loss coefficient and its difference relative to the reversible pressure variation due to differences between the actual and fully developed friction losses, distortions of the velocity profiles and pressure non-uniformity upstream and downstream of the expansion section.

  13. Numerical Investigation of the Performance of Kenics Static Mixers for the Agitation of Shear Thinning Fluids

    OpenAIRE

    A. Mahammedi; H. Ameur; A. Ariss

    2017-01-01

    The laminar flow of non-Newtonian fluids through a Kenics static mixer is investigated by using the CFD (Computational Fluid Dynamics) tool. The working fluids have a shear thinning behavior modeled by the Ostwald De Waele law. We focus on the effect of Reynolds number, fluid properties, twist angle and blade pitch on the flow characteristics and energy cost. The pressure drop information obtained from the simulations was compared to several experimental correlations and data available in the...

  14. Parameterised post-Newtonian expansion in screened regions

    Science.gov (United States)

    McManus, Ryan; Lombriser, Lucas; Peñarrubia, Jorge

    2017-12-01

    The parameterised post-Newtonian (PPN) formalism has enabled stringent tests of static weak-field gravity in a theory-independent manner. Here we incorporate screening mechanisms of modified gravity theories into the framework by introducing an effective gravitational coupling and defining the PPN parameters as functions of position. To determine these functions we develop a general method for efficiently performing the post-Newtonian expansion in screened regimes. For illustration, we derive all the PPN functions for a cubic galileon and a chameleon model. We also analyse the Shapiro time delay effect for these two models and find no deviations from General Relativity insofar as the signal path and the perturbing mass reside in a screened region of space.

  15. Numerical investigation of fluid mud motion using a three-dimensional hydrodynamic and two-dimensional fluid mud coupling model

    Science.gov (United States)

    Yang, Xiaochen; Zhang, Qinghe; Hao, Linnan

    2015-03-01

    A water-fluid mud coupling model is developed based on the unstructured grid finite volume coastal ocean model (FVCOM) to investigate the fluid mud motion. The hydrodynamics and sediment transport of the overlying water column are solved using the original three-dimensional ocean model. A horizontal two-dimensional fluid mud model is integrated into the FVCOM model to simulate the underlying fluid mud flow. The fluid mud interacts with the water column through the sediment flux, current, and shear stress. The friction factor between the fluid mud and the bed, which is traditionally determined empirically, is derived with the assumption that the vertical distribution of shear stress below the yield surface of fluid mud is identical to that of uniform laminar flow of Newtonian fluid in the open channel. The model is validated by experimental data and reasonable agreement is found. Compared with numerical cases with fixed friction factors, the results simulated with the derived friction factor exhibit the best agreement with the experiment, which demonstrates the necessity of the derivation of the friction factor.

  16. Comparison between a generalized Newtonian model and a network-type multiscale model for hemodynamic behavior in the aortic arch: Validation with 4D MRI data for a case study.

    Science.gov (United States)

    Menut, Marine; Boussel, Loïc; Escriva, Xavier; Bou-Saïd, Benyebka; Walter-Le Berre, Hélène; Marchesse, Yann; Millon, Antoine; Della Schiava, Nellie; Lermusiaux, Patrick; Tichy, John

    2018-05-17

    Blood is a complex fluid in which the presence of the various constituents leads to significant changes in its rheological properties. Thus, an appropriate non-Newtonian model is advisable; and we choose a Modified version of the rheological model of Phan-Thien and Tanner (MPTT). The different parameters of this model, derived from the rheology of polymers, allow characterization of the non-Newtonian nature of blood, taking into account the behavior of red blood cells in plasma. Using the MPTT model that we implemented in the open access software OpenFOAM, numerical simulations have been performed on blood flow in the thoracic aorta for a healthy patient. We started from a patient-specific model which was constructed from medical images. Exiting flow boundary conditions have been developped, based on a 3-element Windkessel model to approximate physiological conditions. The parameters of the Windkessel model were calibrated with in vivo measurements of flow rate and pressure. The influence of the selected viscosity of red blood cells on the flow and wall shear stress (WSS) was investigated. Results obtained from this model were compared to those of the Newtonian model, and to those of a generalized Newtonian model, as well as to in vivo dynamic data from 4D MRI during a cardiac cycle. Upon evaluating the results, the MPTT model shows better agreement with the MRI data during the systolic and diastolic phases than the Newtonian or generalized Newtonian model, which confirms our interest in using a complex viscoelastic model. Copyright © 2018 Elsevier Ltd. All rights reserved.

  17. Numerical simulation of the planar extrudate swell of pseudoplastic and viscoelastic fluids with the streamfunction and the VOF methods

    DEFF Research Database (Denmark)

    Comminal, Raphaël; Pimenta, Francisco; Hattel, Jesper H.

    2018-01-01

    , as well as with numerical simulations performed with the open-source rheoTool toolbox in OpenFOAM®. While the simulations of the generalized Newtonian fluids achieved mesh independence for all the methods tested, the flow simulations of the viscoelastic fluids are more sensitive to mesh refinement...

  18. Theoretical frameworks for testing relativistic gravity. 5: Post-Newtonian limit of Rosen's theory

    Science.gov (United States)

    Lee, D. L.; Caves, C. M.

    1974-01-01

    The post-Newtonian limit of Rosen's theory of gravity is evaluated and is shown to be identical to that of general relativity, except for the PPN parameter alpha sub 2, which is related to the difference in propagation speeds for gravitational and electromagnetic waves. Both the value of alpha sub 2 and the value of the Newtonian gravitational constant depend on the present cosmological structure of the Universe. If the cosmological structure has a specific but presumably special form, the Newtonian gravitational constant assumes its current value, alpha sub 2 is zero, the post-Newtonian limit of Rosen's theory is identical to that of general relativity--and standard solar system experiments cannot distinguish between the two theories.

  19. Post-Newtonian approximation of the maximum four-dimensional Yang-Mills gauge theory

    International Nuclear Information System (INIS)

    Smalley, L.L.

    1982-01-01

    We have calculated the post-Newtonian approximation of the maximum four-dimensional Yang-Mills theory proposed by Hsu. The theory contains torsion; however, torsion is not active at the level of the post-Newtonian approximation of the metric. Depending on the nature of the approximation, we obtain the general-relativistic values for the classical Robertson parameters (γ = β = 1), but deviations for the Nordtvedt effect and violations of post-Newtonian conservation laws. We conclude that in its present form the theory is not a viable theory of gravitation

  20. Radiative flow of Carreau liquid in presence of Newtonian heating and chemical reaction

    Science.gov (United States)

    Hayat, T.; Ullah, Ikram; Ahmad, B.; Alsaedi, A.

    Objective of this article is to investigate the magnetohydrodynamic (MHD) boundary layer stretched flow of Carreau fluid in the presence of Newtonian heating. Sheet is presumed permeable. Analysis is studied in the presence of chemical reaction and thermal radiation. Mathematical formulation is established by using the boundary layer approximations. The resultant nonlinear flow analysis is computed for the convergent solutions. Interval of convergence via numerical data and plots are obtained and verified. Impact of numerous pertinent variables on the velocity, temperature and concentration is outlined. Numerical data for surface drag coefficient, surface heat transfer (local Nusselt number) and mass transfer (local Sherwood number) is executed and inspected. Comparison of skin friction coefficient in limiting case is made for the verification of current derived solutions.

  1. Unsteady flow of fractional Oldroyd-B fluids through rotating annulus

    Science.gov (United States)

    Tahir, Madeeha; Naeem, Muhammad Nawaz; Javaid, Maria; Younas, Muhammad; Imran, Muhammad; Sadiq, Naeem; Safdar, Rabia

    2018-04-01

    In this paper exact solutions corresponding to the rotational flow of a fractional Oldroyd-B fluid, in an annulus, are determined by applying integral transforms. The fluid starts moving after t = 0+ when pipes start rotating about their axis. The final solutions are presented in the form of usual Bessel and hypergeometric functions, true for initial and boundary conditions. The limiting cases for the solutions for ordinary Oldroyd-B, fractional Maxwell and Maxwell and Newtonian fluids are obtained. Moreover, the solution is obtained for the fluid when one pipe is rotating and the other one is at rest. At the end of this paper some characteristics of fluid motion, the effect of the physical parameters on the flow and a correlation between different fluid models are discussed. Finally, graphical representations confirm the above affirmation.

  2. The flow and spray characteristics of gelled fluids; Die Stroemungs- und Verspruehungseigenschaften gelfoermiger Fluide

    Energy Technology Data Exchange (ETDEWEB)

    Madlener, K.

    2008-07-01

    In the present study gelled fluids are investigated concerning their application as propellants in storable and thrust controllable rocket propulsion systems. The correlations between the non-Newtonian viscosity properties and the flow and spray characteristics are discussed. Based on the proposed viscosity model Herschel-Bulkley-Extended (HBE) the laminar pipe flow is calculated for the investigated propellants. With the introduction of a generalized form of the Reynolds number and the presentation of a possibility to determine the critical values of this number it is possible to calculate the laminar-turbulent transition in a pipe flow. The theoretical results are evaluated with experimental data. The spray characteristics of various gelled fluids are examined using an experimental setup with impinging-jet-injectors. (orig.)

  3. MHD flow of Kuvshinski fluid through porous medium with temperature gradient heat source

    International Nuclear Information System (INIS)

    Goyal, Mamta; Banshiwal, Anna

    2014-01-01

    MHD free convection time dependent flow of a viscous, dissipative, incompressible, electrically conducting, non Newtonian fluid name as Kuvshinski fluid past an infinite vertical plate is considered The plate is moving with uniform velocity in the direction of flow. Analytical solutions have been obtained for velocity, temperature and concentration using perturbation technique. The effects of governing parameter on flow quantities are discussed with the help of graphs. (author)

  4. Comparative study of Eyring and Carreau fluids in a suspension of dust and nickel nanoparticles with variable conductivity

    Science.gov (United States)

    Mamatha Upadhya, S.; Mahesha; Raju, C. S. K.

    2018-04-01

    A theoretical analysis is carried out to investigate the magnetohydrodynamic unsteady flow of Eyring-Powell and Carreau non-Newtonian fluids in a suspension of dust and nickel nanoparticles by considering variable thermal conductivity and thermal radiation. Dispersion of nickel nanoparticles in dusty fluids finds applications in heat exchanger systems, rechargeable batteries, chemical catalysts, metallurgy, conducting paints, magnetic recording media, drug delivery, nanofibers, textiles, etc. The initially arising set of physical governing partial differential equations is transformed to ordinary differential equations (ODEs) with the aid of similarity transformations. Consequentially, the nonlinear ODEs are solved numerically through the Runge-Kutta Fehlberg scheme (RKFS). The computational results for non-dimensional temperature and velocity profiles are presented through graphs. Furthermore, the numerical values of friction factor and heat transfer rate are tabulated numerically for the unsteady and steady cases of the Eyring and Carreau fluid cases and of the dusty non-Newtonian (φ=0) and the dusty non-Newtonian nanofluid (φ≠ 0) cases of the unsteady flow. We also validated the present results with previous published studies and found them to be highly satisfactory. The formulated model reveals that the rate of heat transfer is higher in the mixture of the nickel + Eyring-Powell case compared to the nickel + Carreau case. From this we can highlight that, depending on the industrial appliances, we can use heating or cooling processes for Eyring and Carreau fluids, respectively.

  5. Shape optimization for non-Newtonian fluids in time-dependent domains

    Czech Academy of Sciences Publication Activity Database

    Sokolowski, J.; Stebel, Jan

    2014-01-01

    Roč. 3, č. 2 (2014), s. 331-348 ISSN 2163-2480 R&D Projects: GA ČR GA201/09/0917 Institutional support: RVO:67985840 Keywords : shape optimization * time - dependent domain * incompressible viscous fluid Subject RIV: BA - General Mathematics Impact factor: 0.373, year: 2014 http://www.aimsciences.org/journals/home.jsp?journalID=25

  6. Shape optimization for non-Newtonian fluids in time-dependent domains

    Czech Academy of Sciences Publication Activity Database

    Sokolowski, J.; Stebel, Jan

    2014-01-01

    Roč. 3, č. 2 (2014), s. 331-348 ISSN 2163-2480 R&D Projects: GA ČR GA201/09/0917 Institutional support: RVO:67985840 Keywords : shape optimization * time-dependent domain * incompressible viscous fluid Subject RIV: BA - General Mathematics Impact factor: 0.373, year: 2014 http://www.aimsciences.org/journals/home.jsp?journalID=25

  7. Newtonian gravity and the Bargmann algebra

    NARCIS (Netherlands)

    Andringa, Roel; Bergshoeff, Eric; Panda, Sudhakar; de Roo, Mees

    2011-01-01

    We show how the Newton-Cartan formulation of Newtonian gravity can be obtained from gauging the Bargmann algebra, i.e. the centrally extended Galilean algebra. In this gauging procedure several curvature constraints are imposed. These convert the spatial (time) translational symmetries of the

  8. Interfacial patterns in magnetorheological fluids: Azimuthal field-induced structures.

    Science.gov (United States)

    Dias, Eduardo O; Lira, Sérgio A; Miranda, José A

    2015-08-01

    Despite their practical and academic relevance, studies of interfacial pattern formation in confined magnetorheological (MR) fluids have been largely overlooked in the literature. In this work, we present a contribution to this soft matter research topic and investigate the emergence of interfacial instabilities when an inviscid, initially circular bubble of a Newtonian fluid is surrounded by a MR fluid in a Hele-Shaw cell apparatus. An externally applied, in-plane azimuthal magnetic field produced by a current-carrying wire induces interfacial disturbances at the two-fluid interface, and pattern-forming structures arise. Linear stability analysis, weakly nonlinear theory, and a vortex sheet approach are used to access early linear and intermediate nonlinear time regimes, as well as to determine stationary interfacial shapes at fully nonlinear stages.

  9. Interacting wave fronts and rarefaction waves in a second order model of nonlinear thermoviscous fluids : Interacting fronts and rarefaction waves

    DEFF Research Database (Denmark)

    Rasmussen, Anders Rønne; Sørensen, Mads Peter; Gaididei, Yuri Borisovich

    2011-01-01

    A wave equation including nonlinear terms up to the second order for a thermoviscous Newtonian fluid is proposed. In the lossless case this equation results from an expansion to third order of the Lagrangian for the fundamental non-dissipative fluid dynamical equations. Thus it preserves the Hami...... is proposed. The dynamics of the rarefaction wave is approximated by a collective coordinate approach in the energy balance equation. © 2010 Springer Science+Business Media B.V.......A wave equation including nonlinear terms up to the second order for a thermoviscous Newtonian fluid is proposed. In the lossless case this equation results from an expansion to third order of the Lagrangian for the fundamental non-dissipative fluid dynamical equations. Thus it preserves...... the Hamiltonian structure, in contrast to the Kuznetsov equation, a model often used in nonlinear acoustics. An exact traveling wave front solution is derived from a generalized traveling wave assumption for the velocity potential. Numerical studies of the evolution of a number of arbitrary initial conditions...

  10. Entropy generation due to double diffusive convective flow of Casson fluids over nonlinearity stretching sheets with slip conditions

    Directory of Open Access Journals (Sweden)

    Sameh E. Ahmed

    2017-12-01

    Full Text Available The present paper deals with the effects of slip boundary conditions and chemical reaction on the heat and mass transfer by mixed convective boundary layer flow of a non-Newtonian fluid over a nonlinear stretching sheet. The Casson fluid model is used to characterize the non-Newtonian fluid behavior. First order chemical reactions are considered. Similar solutions are used to convert the partial differential equations governing the problem to ordinary differential equations. The velocity, temperature and concentration profiles are obtained, numerically, using the MATLAB function bvp4c and those are used to compute the entropy generation number. The effect of increasing values of the Casson parameter is found to suppress the velocity field and temperature distribution. But the concentration is enhanced with the increasing of Casson parameter. The viscous dissipation, temperature and concentration irreversibility are determined and discussed in details.

  11. Unsteady Hydromagnetic Flow of Radiating Fluid Past a Convectively Heated Vertical Plate with the Navier Slip

    Directory of Open Access Journals (Sweden)

    O. D. Makinde

    2014-01-01

    Full Text Available This paper investigates the unsteady hydromagnetic-free convection of an incompressible electrical conducting Boussinesq’s radiating fluid past a moving vertical plate in an optically thin environment with the Navier slip, viscous dissipation, and Ohmic and Newtonian heating. The nonlinear partial differential equations governing the transient problem are obtained and tackled numerically using a semidiscretization finite difference method coupled with Runge-Kutta Fehlberg integration technique. Numerical data for the local skin friction coefficient and the Nusselt number have been tabulated for various values of parametric conditions. Graphical results for the fluid velocity, temperature, skin friction, and the Nusselt number are presented and discussed. The results indicate that the skin friction coefficient decreases while the heat transfer rate at the plate surface increases as the slip parameter and Newtonian heating increase.

  12. Computational simulation of a non-newtonian model of the blood separation process.

    Science.gov (United States)

    De Gruttola, Sandro; Boomsma, Kevin; Poulikakos, Dimos

    2005-12-01

    The aim of this work is to construct a computational fluid dynamics model capable of simulating the transient non-Newtonian process of apheresis. A Lagrangian-Eulerian model has been developed which tracks the blood particles within a two-dimensional flow configuration. Within the Eulerian method, the fluid mass and momentum conservation equations within the separator are solved using the density and the viscosity is calculated from the blood particle concentrations. Subsequently, the displacement of the blood particles is calculated with a Lagrangian method. Hawksley's model for the density of supensions is used in the variable density calculation. The viscosity is calculated with two models based on Vand's rigid particle suspension viscosity concepts, followed by the flow field calculation in the separator. Simulations were performed for various inlet hematocrit values and separator lengths. The simulations are in satisfactory agreement with experimental results reported in literature, indicating a complete separation of plasma and red blood cells (RBCs), as well as nearly complete separation of red blood cells and platelets. No hemolysis was observed in the simulations because the shear rate remained under the critical value of 150 N/m2.

  13. Lyapunov spectra and conjugate-pairing rule for confined atomic fluids

    DEFF Research Database (Denmark)

    Bernadi, Stefano; Todd, B.D.; Hansen, Jesper Schmidt

    2010-01-01

    In this work we present nonequilibrium molecular dynamics simulation results for the Lyapunov spectra of atomic fluids confined in narrow channels of the order of a few atomic diameters. We show the effect that realistic walls have on the Lyapunov spectra. All the degrees of freedom of the confin...... evolved Lyapunov vectors projected into a reduced dimensional phase space. We finally observe that the phase-space compression due to the thermostat remains confined into the wall region and does not significantly affect the purely Newtonian fluid region....

  14. Presenting Newtonian gravitation

    International Nuclear Information System (INIS)

    Counihan, Martin

    2007-01-01

    The basic principles of the Newtonian theory of gravitation are presented in a way which students may find more logically coherent, mathematically accessible and physically interesting than other approaches. After giving relatively simple derivations of the circular hodograph and the elliptical orbit from the inverse-square law, the concept of gravitational energy is developed from vector calculus. It is argued that the energy density of a gravitational field may reasonably be regarded as -g 2 /8πG, and that the inverse-square law may be replaced by a Schwarzschild-like force law without the need to invoke non-Euclidean geometry

  15. Constraining Relativistic Generalizations of Modified Newtonian Dynamics with Gravitational Waves.

    Science.gov (United States)

    Chesler, Paul M; Loeb, Abraham

    2017-07-21

    In the weak-field limit of general relativity, gravitational waves obey linear equations and propagate at the speed of light. These properties of general relativity are supported by the observation of ultrahigh-energy cosmic rays as well as by LIGO's recent detection of gravitation waves. We argue that two existing relativistic generalizations of modified Newtonian dynamics, namely, the generalized Einstein-aether theory and bimetric modified Newtonian dynamics, display fatal inconsistencies with these observations.

  16. Effect of surface tension on the dynamical behavior of bubble in rotating fluids under low gravity environment

    Science.gov (United States)

    Hung, R. J.; Tsao, Y. D.; Leslie, Fred W.; Hong, B. B.

    1988-01-01

    Time dependent evolutions of the profile of free surface (bubble shapes) for a cylindrical container partially filled with a Newtonian fluid of constant density, rotating about its axis of symmetry, have been studied. Numerical computations of the dynamics of bubble shapes have been carried out with the following situations: (1) linear functions of spin-up and spin-down in low and microgravity environments, (2) linear functions of increasing and decreasing gravity enviroment in high and low rotating cylidner speeds, (3) step functions of spin-up and spin-down in a low gravity environment, and (4) sinusoidal function oscillation of gravity environment in high and low rotating cylinder speeds. The initial condition of bubble profiles was adopted from the steady-state formulations in which the computer algorithms have been developed by Hung and Leslie (1988), and Hung et al. (1988).

  17. Biorheological Model on Flow of Herschel-Bulkley Fluid through a Tapered Arterial Stenosis with Dilatation.

    Science.gov (United States)

    Priyadharshini, S; Ponalagusamy, R

    2015-01-01

    An analysis of blood flow through a tapered artery with stenosis and dilatation has been carried out where the blood is treated as incompressible Herschel-Bulkley fluid. A comparison between numerical values and analytical values of pressure gradient at the midpoint of stenotic region shows that the analytical expression for pressure gradient works well for the values of yield stress till 2.4. The wall shear stress and flow resistance increase significantly with axial distance and the increase is more in the case of converging tapered artery. A comparison study of velocity profiles, wall shear stress, and flow resistance for Newtonian, power law, Bingham-plastic, and Herschel-Bulkley fluids shows that the variation is greater for Herschel-Bulkley fluid than the other fluids. The obtained velocity profiles have been compared with the experimental data and it is observed that blood behaves like a Herschel-Bulkley fluid rather than power law, Bingham, and Newtonian fluids. It is observed that, in the case of a tapered stenosed tube, the streamline pattern follows a convex pattern when we move from r/R = 0 to r/R = 1 and it follows a concave pattern when we move from r/R = 0 to r/R = -1. Further, it is of opposite behaviour in the case of a tapered dilatation tube which forms new information that is, for the first time, added to the literature.

  18. Computational modeling of unsteady third-grade fluid flow over a vertical cylinder: A study of heat transfer visualization

    Science.gov (United States)

    Reddy, G. Janardhana; Hiremath, Ashwini; Kumar, Mahesh

    2018-03-01

    The present paper aims to investigate the effect of Prandtl number for unsteady third-grade fluid flow over a uniformly heated vertical cylinder using Bejan's heat function concept. The mathematical model of this problem is given by highly time-dependent non-linear coupled equations and are resolved by an efficient unconditionally stable implicit scheme. The time histories of average values of momentum and heat transport coefficients as well as the steady-state flow variables are displayed graphically for distinct values of non-dimensional control parameters arising in the system. As the non-dimensional parameter value gets amplified, the time taken for the fluid flow variables to attain the time-independent state is decreasing. The dimensionless heat function values are closely associated with an overall rate of heat transfer. Thermal energy transfer visualization implies that the heat function contours are compact in the neighborhood of the leading edge of the hot cylindrical wall. It is noticed that the deviations of flow-field variables from the hot wall for a non-Newtonian third-grade fluid flow are significant compared to the usual Newtonian fluid flow.

  19. Newtonian Version of the Variable Mass Theory of Gravity

    Science.gov (United States)

    Carvalho, J. C.; Lima, J. A. S.

    1990-11-01

    RESUMEN. Se presenta una versi6n Newtoniana de los modelos cosmol6gicos espacialmente e isotr6picos con masa variable. La influencia de la variaci6n de masa en la evoluci6n de la funci6n de escala est establecida para el caso de un Universo lieno de polvo bajo Ia suposici6n de que esta variaci6n es un efecto estrictamente cosmol6jico. Se muestra que el hiperb6lico, parab6lico 0 el#ptico dcl movimiento de puede ser modificado a lo larjo de la expansi6n. ABSTRACT. This paper presents a Newtonian version of the spatially homojeneous and isotropic cosmolojical models with variable mass. The influence of the mass variation on the evolution of the scale function is established for the case of a dust-filled Universe under the assumption that this variation is a strict cosmolojical effect. It is shown that the hyperbolic, parabolic or elliptic character of the fluid motion can be modified alonj the expansion. Keq : COSMOLOGY

  20. Viscous Dissipation Effects on the Motion of Casson Fluid over an Upper Horizontal Thermally Stratified Melting Surface of a Paraboloid of Revolution: Boundary Layer Analysis

    Directory of Open Access Journals (Sweden)

    T. M. Ajayi

    2017-01-01

    Full Text Available The problem of a non-Newtonian fluid flow past an upper surface of an object that is neither a perfect horizontal/vertical nor inclined/cone in which dissipation of energy is associated with temperature-dependent plastic dynamic viscosity is considered. An attempt has been made to focus on the case of two-dimensional Casson fluid flow over a horizontal melting surface embedded in a thermally stratified medium. Since the viscosity of the non-Newtonian fluid tends to take energy from the motion (kinetic energy and transform it into internal energy, the viscous dissipation term is accommodated in the energy equation. Due to the existence of internal space-dependent heat source; plastic dynamic viscosity and thermal conductivity of the non-Newtonian fluid are assumed to vary linearly with temperature. Based on the boundary layer assumptions, suitable similarity variables are applied to nondimensionalized, parameterized and reduce the governing partial differential equations into a coupled ordinary differential equations. These equations along with the boundary conditions are solved numerically using the shooting method together with the Runge-Kutta technique. The effects of pertinent parameters are established. A significant increases in Rex1/2Cfx is guaranteed with St when magnitude of β is large. Rex1/2Cfx decreases with Ec and m.

  1. Motion of a suspended charged particle in a NON-Newtonian fluid. Vol. 2

    Energy Technology Data Exchange (ETDEWEB)

    Abdel-Khalek, M M [Nuclear Research Center, Atomic Energy Authority, Cairo (Egypt)

    1996-03-01

    The path lines of a solid spherical charged particle suspended in a non-newton electrical conducting viscous fluid through two infinite parallel plates in the presence of a constant magnetic field normal to the plane of particle motion were determined. The effect of some parameters such as particle volume, fluid density, fluid viscosity, and the use magnetic field strength on these path lines were determined. The present solution requires some empirical parameters concerning the collision of the particles with the wall. The differential equations of motion were numerically solved by Runge-Kutta method. Some conclusions about width, maximum height and number of collisions with upper and lower plates were deduced. 4 figs.

  2. The effect of the expansion ratio on a turbulent non-Newtonian recirculating flow

    Energy Technology Data Exchange (ETDEWEB)

    Pereira, A.S. [Departamento de Engenharia Quimica Instituto Superior de Engenharia do Porto (Portugal); Pinho, F.T. [Centro de Estudos de Fenomenos de Transporte, DEMEGI, Faculdade de Engenharia, Universidade do Porto (Portugal)

    2002-04-01

    Measurements of the mean and turbulent flow characteristics of shear-thinning moderately elastic 0.1% and 0.2% xanthan gum aqueous solutions were carried out in a sudden expansion having a diameter ratio of 2. The inlet flow was turbulent and fully developed, and the results were compared with data for water in the same geometry and with previous published Newtonian and non-Newtonian data in a smaller expansion of diameter ratio equal to 1.538. An increase in expansion ratio led to an increase in the recirculation length and in the axial normal Reynolds stress at identical normalised locations, but the difference between Newtonian and non-Newtonian characteristics was less intense than in the smaller expansion. An extensive comparison of mean and turbulent flow characteristics was carried out in order to understand the variation of flow features. (orig.)

  3. Comparative study of Newtonian physiological blood flow through normal and stenosed carotid artery

    Science.gov (United States)

    Rahman, Mohammad Matiur; Hossain, Md. Anwar; Mamun, Khairuzzaman; Akhter, Most. Nasrin

    2017-06-01

    A numerical simulation is performed to investigate Newtonian physiological flows behavior on three dimensional idealized carotid artery (CA) and single stenosed (75% by area) carotid artery(SCA). The wall vessel is set as rigid during simulation. Bifurcated blood vessel are simulated by using three-dimensional flow analysis. Physiological and parabolic velocity profiles are set out to fix the conditions of inlet boundaries of artery. In other hand, physiological waveform is an important part of compilation and it is successfully done by utilization of Fourier series having sixteen harmonics. The investigation has a Reynolds number range of 94 to 1120. Low Reynolds number k — ω model has been used as governing equation. The investigation has been carried out to characterize the flow behavior of blood in two geometry, namely, (i) Normal carotid artery (CA) and (ii) Stenosed carotid artery (SCA). The Newtonian model has been used to study the physics of fluid. The findings of the two models are thoroughly compared in order to observe there behavioral sequence of flows. The numerical results were presented in terms of velocity, pressure, wall shear stress distributions and cross sectional velocities as well as the streamlines contour. Stenosis disturbs the normal pattern of blood flow through the artery as reduced area. At stenosis region velocity and peak Reynolds number rapidly increase and Reynolds number reach transitional and turbulent region. These flow fluctuation and turbulence have bad effect to the blood vessel which makes to accelerate the progress of stenosis.

  4. Reverse flow and vortex breakdown in a shear-thinning fluid

    International Nuclear Information System (INIS)

    Cabeza, C; Sarasua, G; Barrere, N; Marti, A C

    2011-01-01

    The effect of polymer concentration on the development of reverse secondary flow and vortex breakdown was studied using a viscoelastic solution of polyacrlylamide in water. The fluid was contained in cylindrical containers of two different radii, the top end wall of which rotated at a varying speed, thus, imparting a circulating motion to the fluid. Whereas using a newtonian fluid, streamlines will occupy the entire container, the flow of a shear-thinning fluid may divide into two cells of opposite circulating motion. The curve of critical Reynolds and elasticity numbers (Re, E) values corresponding to the development of reverse flow was obtained over a wide range of Re values. Vortex breakdown was found to occur at extremely low Re values.

  5. The Newtonian Moment - Isaac Newton and the Making of Modern Culture

    Science.gov (United States)

    Feingold, Mordechai

    2004-12-01

    Isaac Newton is a legendary figure whose mythical dimension threatens to overshadow the actual man. The story of the apple falling from the tree may or may not be true, but Isaac Newton's revolutionary discoveries and their importance to the Enlightenment era and beyond are undeniable. The Newtonian Moment , a companion volume to a forthcoming exhibition by the New York Public Library, investigates the effect that Newton's theories and discoveries had, not only on the growth of science, but also on the very shape of modern culture and thought. Newton's scientific work at Cambridge was groundbreaking. From his optical experiments with prisms during the 1660s to the publication of both Principia (1687) and Opticks (1704), Newton's achievements were widely disseminated, inciting tremendous interest and excitement. Newtonianism developed into a worldview marked by many tensions: between modernity and the old guard, between the humanities and science, and the public battles between great minds. The Newtonian Moment illuminates the many facets of his colossal accomplishments, as well as the debates over the kind of knowledge that his accomplishments engendered. The book contributes to a greater understanding of the world today by offering a panoramic view of the profound impact of Newtonianism on the science, literature, art, and religion of the Enlightenment. Copiously illustrated with items drawn from the collections of the New York Public Library as well as numerous other libraries and museums, The Newtonian Moment enlightens its audience with a guided and in-depth look at the man, his world, and his enduring legacy.

  6. Conceptual coherence of non-Newtonian worldviews in Force Concept Inventory data

    Directory of Open Access Journals (Sweden)

    Terry F. Scott

    2017-05-01

    Full Text Available The Force Concept Inventory is one of the most popular and most analyzed multiple-choice concept tests used to investigate students’ understanding of Newtonian mechanics. The correct answers poll a set of underlying Newtonian concepts and the coherence of these underlying concepts has been found in the data. However, this inventory was constructed after several years of research into the common preconceptions held by students and using these preconceptions as distractors in the questions. Their sole purpose is to deflect non-Newtonian candidates away from the correct answer. Alternatively, one can argue that the responses could also be treated as polling these preconceptions. In this paper we shift the emphasis of the analysis away from the correlation structure of the correct answers and look at the latent traits underlying the incorrect responses. Our analysis models the data employing exploratory factor analysis, which uses regularities in the data to suggest the existence of underlying structures in the cognitive processing of the students. This analysis allows us to determine whether the data support the claim that there are alternate non-Newtonian worldviews on which students’ incorrect responses are based. The existence of such worldviews, and their coherence, could explain the resilience of non-Newtonian preconceptions and would have significant implications to the design of instruction methods. We find that there are indeed coherent alternate conceptions of the world which can be categorized using the results of the research that led to the construction of the Force Concept Inventory.

  7. 3D Suspended Polymeric Microfluidics (SPMF3) with Flow Orthogonal to Bending (FOB) for Fluid Analysis through Kinematic Viscosity

    OpenAIRE

    Mostapha Marzban; Muthukumaran Packirisamy; Javad Dargahi

    2017-01-01

    Measuring of fluid properties such as dynamic viscosity and density has tremendous potential for various applications from physical to biological to chemical sensing. However, it is almost impossible to affect only one of these properties, as dynamic viscosity and density are coupled. Hence, this paper proposes kinematic viscosity as a comprehensive parameter which can be used to study the effect of fluid properties applicable to various fluids from Newtonian fluids, such as water, to non-New...

  8. Numerical solution of viscous and viscoelastic fluids flow through the branching channel by finite volume scheme

    Science.gov (United States)

    Keslerová, Radka; Trdlička, David

    2015-09-01

    This work deals with the numerical modelling of steady flows of incompressible viscous and viscoelastic fluids through the three dimensional channel with T-junction. The fundamental system of equations is the system of generalized Navier-Stokes equations for incompressible fluids. This system is based on the system of balance laws of mass and momentum for incompressible fluids. Two different mathematical models for the stress tensor are used for simulation of Newtonian and Oldroyd-B fluids flow. Numerical solution of the described models is based on cetral finite volume method using explicit Runge-Kutta time integration.

  9. Actual Romanian research in post-newtonian dynamics

    Science.gov (United States)

    Mioc, V.; Stavinschi, M.

    2007-05-01

    We survey the recent Romanian results in the study of the two-body problem in post-Newtonian fields. Such a field is characterized, in general, by a potential of the form U(q)=|q|^{-1}+ something (small, but not compulsorily). We distinguish some classes of post-Newtonian models: relativistic (Schwarzschild, Fock, Einstein PN, Reissner-Nordström, Schwarzschild - de Sitter, etc.) and nonrelativistic (Manev, Mücket-Treder, Seeliger, gravito-elastic, etc.). Generalized models (the zonal-satellite problem, quasihomogeneous fields), as well as special cases (anisotropic Manev-type and Schwarzschild-type models, Popovici or Popovici-Manev photogravitational problem), were also tackled. The methods used in such studies are various: analytical (using mainly the theory of perturbations, but also other theories: functions of complex variable, variational calculus, etc.), geometric (qualitative approach of the theory of dynamical systems), and numerical (especially using the Poincaré-section technique). The areas of interest and the general results obtained focus on: exact or approximate analytical solutions; characteristics of local flows (especially at limit situations: collision and escape); quasiperiodic and periodic orbits; equilibria; symmetries; chaoticity; geometric description of the global flow (and physical interpretation of the phase-space structure). We emphasize some special features, which cannot be met within the Newtonian framework: black-hole effect, oscillatory collisions, radial librations, bounded orbits for nonnegative energy, existence of unstable circular motion (or unstable rest), symmetric periodic orbits within anisotropic models, etc.

  10. EMHD micro-pumping of a non-conducting shear-thinning fluid under EDL phenomena

    International Nuclear Information System (INIS)

    Gaikwad, Harshad; Borole, Chetan; Basu, Dipankar N.; Mondal, Pranab K.

    2016-01-01

    The Electro-Magneto-Hydrodynamic (EMHD) pumping of a binary fluid system constituted by one non-conducting shear-thinning fluid (top layer) by exploiting the transverse momentum exchange through the interfacial viscous shearing effect from a conducting Newtonian fluid layer (bottom layer) in a microfluidic channel is investigated. An externally applied electric field drives the conducting fluid layer under the influence of an applied magnetic field as well. The study reveals that the volume transport of shear-thinning fluid gets augmented for low magnetic field strength, higher electrical double layer (EDL) effect, low viscosity ratio and moderate potential ratio. It is also established that the volumetric flow rate reduces significantly for the higher magnetic field strength. (author)

  11. On the analytic solution of the steady flow of a fourth grade fluid

    International Nuclear Information System (INIS)

    Sajid, M.; Hayat, T.; Asghar, S.

    2006-01-01

    The steady flow of a fourth grade fluid is a problem belonging to non-Newtonian fluid mechanics and deserves to be more widely studied than it has been to date. In the non-linear regime the literature is scarce. We develop a formulation suitable for solution of hydrodynamic equation containing non-linear rheological effects of fourth grade fluids. The homotopy analysis method (HAM) is used to investigate the flow of a fourth grade fluid past a porous plate. Explicit analytic solution is given. The non-linear effects on the velocity distribution is shown and discussed. Comparison of the present analysis is also made with the existing results in the literature

  12. Time in Newtonian physics and special relativity

    International Nuclear Information System (INIS)

    Kichenassamy, S.

    1980-01-01

    The Newtonian point of view is presented as is the relativist one over time: concepts of guide-marks, clocks and setting to time. One of the consequences of Einstein's theory, the dilation of durations, is developed in particular [fr

  13. Finite element approximation of flow of fluids with shear-rate- and pressure-dependent viscosity

    Czech Academy of Sciences Publication Activity Database

    Hirn, A.; Lanzendörfer, Martin; Stebel, Jan

    2012-01-01

    Roč. 32, č. 4 (2012), s. 1604-1634 ISSN 0272-4979 R&D Projects: GA ČR GA201/09/0917; GA AV ČR IAA100300802; GA MŠk LC06052 Institutional research plan: CEZ:AV0Z10300504; CEZ:AV0Z10190503 Keywords : non-Newtonian fluid * shear-rate- and pressure-dependent viscosity * finite element method * error analysis Subject RIV: BK - Fluid Dynamics Impact factor: 1.326, year: 2012

  14. Spray Formation of Herschel-Bulkley Fluids using Impinging Jets

    Science.gov (United States)

    Rodrigues, Neil; Gao, Jian; Chen, Jun; Sojka, Paul E.

    2015-11-01

    The impinging jet spray formation of two non-Newtonian, shear-thinning, Herschel-Bulkley fluids was investigated in this work. The water-based gelled solutions used were 1.0 wt.-% agar and 1.0 wt.-% kappa carrageenan. A rotational rheometer and a capillary viscometer were used to measure the strain-rate dependency of viscosity and the Herschel-Bulkley Extended (HBE) rheological model was used to characterize the shear-thinning behavior. A generalized HBE jet Reynolds number Rej , gen - HBE was used as the primary parameter to characterize the spray formation. A like-on-like impinging jet doublet was used to produce atomization. Shadowgraphs were captured in the plane of the sheet formed by the two jets using a CCD camera with an Nd:YAG laser beam providing the back-illumination. Typical behavior for impinging jet atomization using Newtonian liquids was not generally observed due to the non-Newtonian, viscous properties of the agar and kappa carrageenan gels. Instead various spray patterns were observed depending on Rej , gen - HBE. Spray characteristics of maximum instability wavelength and sheet breakup length were extracted from the shadowgraphs. Multi-University Research Initiative Grant Number W911NF-08-1-0171.

  15. Non-Newtonian Flow Characteristics of Heavy Oil in the Bohai Bay Oilfield: Experimental and Simulation Studies

    Directory of Open Access Journals (Sweden)

    Xiankang Xin

    2017-10-01

    Full Text Available In this paper, physical experiments and numerical simulations were applied to systematically investigate the non-Newtonian flow characteristics of heavy oil in porous media. Rheological experiments were carried out to determine the rheology of heavy oil. Threshold pressure gradient (TPG measurement experiments performed by a new micro-flow method and flow experiments were conducted to study the effect of viscosity, permeability and mobility on the flow characteristics of heavy oil. An in-house developed novel simulator considering the non-Newtonian flow was designed based on the experimental investigations. The results from the physical experiments indicated that heavy oil was a Bingham fluid with non-Newtonian flow characteristics, and its viscosity-temperature relationship conformed to the Arrhenius equation. Its viscosity decreased with an increase in temperature and a decrease in asphaltene content. The TPG measurement experiments was impacted by the flow rate, and its critical flow rate was 0.003 mL/min. The TPG decreased as the viscosity decreased or the permeability increased and had a power-law relationship with mobility. In addition, the critical viscosity had a range of 42–54 mPa∙s, above which the TPG existed for a given permeability. The validation of the designed simulator was positive and acceptable when compared to the simulation results run in ECLIPSE V2013.1 and Computer Modelling Group (CMG V2012 software as well as when compared to the results obtained during physical experiments. The difference between 0.0005 and 0.0750 MPa/m in the TPG showed a decrease of 11.55% in the oil recovery based on the simulation results, which demonstrated the largely adverse impact the TPG had on heavy oil production.

  16. Dynamics of Newtonian annular jets

    International Nuclear Information System (INIS)

    Paul, D.D.

    1978-12-01

    The main objectives of this investigation are to identify the significant parameters affecting the dynamics of Newtonian annular jets, and to develop theoretical models for jet break-up and collapse. This study has been motivated by recent developments in laser-fusion reactor designs; one proposed cavity design involves the use of an annular lithium jet to protect the cavity wall from the pellet debris emanating from the microexplosion

  17. Parameterized post-Newtonian cosmology

    International Nuclear Information System (INIS)

    Sanghai, Viraj A A; Clifton, Timothy

    2017-01-01

    Einstein’s theory of gravity has been extensively tested on solar system scales, and for isolated astrophysical systems, using the perturbative framework known as the parameterized post-Newtonian (PPN) formalism. This framework is designed for use in the weak-field and slow-motion limit of gravity, and can be used to constrain a large class of metric theories of gravity with data collected from the aforementioned systems. Given the potential of future surveys to probe cosmological scales to high precision, it is a topic of much contemporary interest to construct a similar framework to link Einstein’s theory of gravity and its alternatives to observations on cosmological scales. Our approach to this problem is to adapt and extend the existing PPN formalism for use in cosmology. We derive a set of equations that use the same parameters to consistently model both weak fields and cosmology. This allows us to parameterize a large class of modified theories of gravity and dark energy models on cosmological scales, using just four functions of time. These four functions can be directly linked to the background expansion of the universe, first-order cosmological perturbations, and the weak-field limit of the theory. They also reduce to the standard PPN parameters on solar system scales. We illustrate how dark energy models and scalar-tensor and vector-tensor theories of gravity fit into this framework, which we refer to as ‘parameterized post-Newtonian cosmology’ (PPNC). (paper)

  18. Parameterized post-Newtonian cosmology

    Science.gov (United States)

    Sanghai, Viraj A. A.; Clifton, Timothy

    2017-03-01

    Einstein’s theory of gravity has been extensively tested on solar system scales, and for isolated astrophysical systems, using the perturbative framework known as the parameterized post-Newtonian (PPN) formalism. This framework is designed for use in the weak-field and slow-motion limit of gravity, and can be used to constrain a large class of metric theories of gravity with data collected from the aforementioned systems. Given the potential of future surveys to probe cosmological scales to high precision, it is a topic of much contemporary interest to construct a similar framework to link Einstein’s theory of gravity and its alternatives to observations on cosmological scales. Our approach to this problem is to adapt and extend the existing PPN formalism for use in cosmology. We derive a set of equations that use the same parameters to consistently model both weak fields and cosmology. This allows us to parameterize a large class of modified theories of gravity and dark energy models on cosmological scales, using just four functions of time. These four functions can be directly linked to the background expansion of the universe, first-order cosmological perturbations, and the weak-field limit of the theory. They also reduce to the standard PPN parameters on solar system scales. We illustrate how dark energy models and scalar-tensor and vector-tensor theories of gravity fit into this framework, which we refer to as ‘parameterized post-Newtonian cosmology’ (PPNC).

  19. Application of volume of fluid method for simulation of a droplet impacting a fiber

    Directory of Open Access Journals (Sweden)

    M. Khalili

    2016-06-01

    Full Text Available In the present work, impact of a Newtonian drop on horizontal thin fibers with circular cross section is simulated in 2D views. The numerical simulations of the phenomena are carried out using volume of fluid (VOF method for tracking the free surface motion. Impacting of a Newtonian droplet on a circular thin fiber (350μm radius investigated numerically. The main focus of this simulation is to acquire threshold radius and velocity of a drop which is entirely captured by the fiber. The model agrees well with the experiments and demonstrates the threshold radius decreased generally with the increase of impact velocity. In other words, for velocity larger than threshold velocity of capture perhaps only a small portion of fluid is stuck on the solid and the rest of the drop is ejected for impact velocity smaller than critical velocity the drop is totally captured. This threshold velocity has been determined when the impact is centered.

  20. Effective fluid description of the dark universe

    Directory of Open Access Journals (Sweden)

    M. Cadoni

    2018-01-01

    Full Text Available We propose an effective anisotropic fluid description for a generic infrared-modified theory of gravity. In our framework, the additional component of the acceleration, commonly attributed to dark matter, is explained as a radial pressure generated by the reaction of the dark energy fluid to the presence of baryonic matter. Using quite general assumptions, and a microscopic description of the fluid in terms of a Bose–Einstein condensate of gravitons, we find the static, spherically symmetric solution for the metric in terms of the Misner–Sharp mass function and the fluid pressure. At galactic scales, we correctly reproduce the leading MOND-like log⁡(r and subleading (1/rlog⁡(r terms in the weak-field expansion of the potential. Our description also predicts a tiny (of order 10−6 for a typical spiral galaxy Machian modification of the Newtonian potential at galactic scales, which is controlled by the cosmological acceleration.

  1. On preconditioning incompressible non-Newtonian flow problems

    NARCIS (Netherlands)

    He, X.; Neytcheva, M.; Vuik, C.

    2013-01-01

    This paper deals with fast and reliable numerical solution methods for the incompressible non-Newtonian Navier-Stokes equations. To handle the nonlinearity of the governing equations, the Picard and Newton methods are used to linearize these coupled partial differential equations. For space

  2. Biorheological Model on Flow of Herschel-Bulkley Fluid through a Tapered Arterial Stenosis with Dilatation

    Directory of Open Access Journals (Sweden)

    S. Priyadharshini

    2015-01-01

    Full Text Available An analysis of blood flow through a tapered artery with stenosis and dilatation has been carried out where the blood is treated as incompressible Herschel-Bulkley fluid. A comparison between numerical values and analytical values of pressure gradient at the midpoint of stenotic region shows that the analytical expression for pressure gradient works well for the values of yield stress till 2.4. The wall shear stress and flow resistance increase significantly with axial distance and the increase is more in the case of converging tapered artery. A comparison study of velocity profiles, wall shear stress, and flow resistance for Newtonian, power law, Bingham-plastic, and Herschel-Bulkley fluids shows that the variation is greater for Herschel-Bulkley fluid than the other fluids. The obtained velocity profiles have been compared with the experimental data and it is observed that blood behaves like a Herschel-Bulkley fluid rather than power law, Bingham, and Newtonian fluids. It is observed that, in the case of a tapered stenosed tube, the streamline pattern follows a convex pattern when we move from r/R=0 to r/R=1 and it follows a concave pattern when we move from r/R=0 to r/R=-1. Further, it is of opposite behaviour in the case of a tapered dilatation tube which forms new information that is, for the first time, added to the literature.

  3. Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries

    Directory of Open Access Journals (Sweden)

    Blanchet Luc

    2006-06-01

    Full Text Available The article reviews the current status of a theoretical approach to the problem of the emission of gravitational waves by isolated systems in the context of general relativity. Part A of the article deals with general post-Newtonian sources. The exterior field of the source is investigated by means of a combination of analytic post-Minkowskian and multipolar approximations. The physical observables in the far-zone of the source are described by a specific set of radiative multipole moments. By matching the exterior solution to the metric of the post-Newtonian source in the near-zone we obtain the explicit expressions of the source multipole moments. The relationships between the radiative and source moments involve many non-linear multipole interactions, among them those associated with the tails (and tails-of-tails of gravitational waves. Part B of the article is devoted to the application to compact binary systems. We present the equations of binary motion, and the associated Lagrangian and Hamiltonian, at the third post-Newtonian (3PN order beyond the Newtonian acceleration. The gravitational-wave energy flux, taking consistently into account the relativistic corrections in the binary moments as well as the various tail effects, is derived through 3.5PN order with respect to the quadrupole formalism. The binary's orbital phase, whose prior knowledge is crucial for searching and analyzing the signals from inspiralling compact binaries, is deduced from an energy balance argument.

  4. On the mass of rotating stars in Newtonian gravity and GR

    International Nuclear Information System (INIS)

    Reina, Borja; Vera, Raül

    2016-01-01

    We show how the correction to the calculation of the mass in the original relativistic model of a rotating star by Hartle (1967 Astrophys. J. 150 1005–29), found recently by Reina and Vera (2015 Class. Quantum Grav. 32 155008), appears in the Newtonian limit, and that the correcting term is indeed present, albeit hidden, in the original Newtonian approach by Chandrasekhar (1933 Mon. Not. Roy. Astr. Soc. 93 390–406). (note)

  5. Parametrized post-Newtonian approximation and Rastall's gravitational field equations

    International Nuclear Information System (INIS)

    Smalley, L.L.

    1978-01-01

    The parametrized post-Newtonian (PPN) approximation is generalized to accomodate Rastall's modification of Einstein's theory of gravity, which allows nonzero divergence of the energy-momentum tensor. Rastall's theory is then shown to have consistent field equations, gauge conditions, and the correct Newtonian limit of the equations of motion. The PPN parameters are obtained and shown to agree experimentally with those for the Einstein theory. In light of the nonzero divergence condition, integral conservation laws are investigated and shown to yield conserved energy-momentum and angular-momentum. We conclude that the above generalization of metric theories, within the PPN framework, is a natural extension of the concept of metric theories

  6. Post-Newtonian N-body simulations

    Science.gov (United States)

    Aarseth, Sverre J.

    2007-06-01

    We report on the first fully consistent conventional cluster simulation which includes terms up to the third-order post-Newtonian approximation. Numerical problems for treating extremely energetic binaries orbiting a single massive object are circumvented by employing the special `wheel-spoke' regularization method of Zare which has not been used in large-N simulations before. Idealized models containing N = 1 × 105 particles of mass 1Msolar with a central black hole (BH) of 300Msolar have been studied on GRAPE-type computers. An initial half-mass radius of rh ~= 0.1 pc is sufficiently small to yield examples of relativistic coalescence. This is achieved by significant binary shrinkage within a density cusp environment, followed by the generation of extremely high eccentricities which are induced by Kozai cycles and/or resonant relaxation. More realistic models with white dwarfs and 10 times larger half-mass radii also show evidence of general relativity effects before disruption. An experimentation with the post-Newtonian terms suggests that reducing the time-scales for activating the different orders progressively may be justified for obtaining qualitatively correct solutions without aiming for precise predictions of the final gravitational radiation wave form. The results obtained suggest that the standard loss-cone arguments underestimate the swallowing rate in globular clusters containing a central BH.

  7. Linear Rayleigh-Taylor instability in an accelerated Newtonian fluid with finite width

    Science.gov (United States)

    Piriz, S. A.; Piriz, A. R.; Tahir, N. A.

    2018-04-01

    The linear theory of Rayleigh-Taylor instability is developed for the case of a viscous fluid layer accelerated by a semi-infinite viscous fluid, considering that the top interface is a free surface. Effects of the surface tensions at both interfaces are taken into account. When viscous effects dominate on surface tensions, an interplay of two mechanisms determines opposite behaviors of the instability growth rate with the thickness of the heavy layer for an Atwood number AT=1 and for sufficiently small values of AT. In the former case, viscosity is a less effective stabilizing mechanism for the thinnest layers. However, the finite thickness of the heavy layer enhances its viscous effects that, in general, prevail on the viscous effects of the semi-infinite medium.

  8. Comparing scalar-tensor gravity and f(R)-gravity in the Newtonian limit

    International Nuclear Information System (INIS)

    Capozziello, S.; Stabile, A.; Troisi, A.

    2010-01-01

    Recently, a strong debate has been pursued about the Newtonian limit (i.e. small velocity and weak field) of fourth order gravity models. According to some authors, the Newtonian limit of f(R)-gravity is equivalent to the one of Brans-Dicke gravity with ω BD =0, so that the PPN parameters of these models turn out to be ill-defined. In this Letter, we carefully discuss this point considering that fourth order gravity models are dynamically equivalent to the O'Hanlon Lagrangian. This is a special case of scalar-tensor gravity characterized only by self-interaction potential and that, in the Newtonian limit, this implies a non-standard behavior that cannot be compared with the usual PPN limit of General Relativity. The result turns out to be completely different from the one of Brans-Dicke theory and in particular suggests that it is misleading to consider the PPN parameters of this theory with ω BD =0 in order to characterize the homologous quantities of f(R)-gravity. Finally the solutions at Newtonian level, obtained in the Jordan frame for an f(R)-gravity, reinterpreted as a scalar-tensor theory, are linked to those in the Einstein frame.

  9. The influence of the non-Newtonian properties of blood on blood-hammer through the posterior cerebral artery.

    Science.gov (United States)

    Tazraei, Pedram; Riasi, Alireza; Takabi, Behrouz

    2015-06-01

    This work investigates a two dimensional numerical analysis of blood hammer through the posterior cerebral artery. The non-Newtonian and usual Newtonian blood models are compared in the case of blood hammer through the posterior cerebral artery to quantify the differences between the models. In this way, a validated CFD simulation is used to study non-Newtonian shear-thinning effects of blood. The governing equations for the modeling of two-dimensional transient flow are solved using a combination of characteristics and central finite difference methods, respectively for the hyperbolic and parabolic parts. Herein, the non-Newtonian viscosity characteristic of blood is incorporated by using the Carreau model. To convert the nonlinear terms available in the characteristics equation into the linear ones, the Newton-Kantorovich method is implemented. The verification and validation of the numerical results are carried out in detail. Hemodynamic characteristics of blood hammer through the posterior cerebral artery are derived with both the Newtonian and non-Newtonian models, and the results are meticulously compared and discussed. The results show that when blood hammer occurs, the non-Newtonian properties greatly influence the velocity and shear stress profiles. At the early stages of blood hammer, there is a 64% difference between magnitudes of wall shear stress in these two models, and the magnitude of the wall shear stress for the shear-thinning blood flow is lower than the Newtonian one. Copyright © 2015 Elsevier Inc. All rights reserved.

  10. Study of microvascular non-Newtonian blood flow modulated by electroosmosis.

    Science.gov (United States)

    Tripathi, Dharmendra; Yadav, Ashu; Anwar Bég, O; Kumar, Rakesh

    2018-05-01

    An analytical study of microvascular non-Newtonian blood flow is conducted incorporating the electro-osmosis phenomenon. Blood is considered as a Bingham rheological aqueous ionic solution. An externally applied static axial electrical field is imposed on the system. The Poisson-Boltzmann equation for electrical potential distribution is implemented to accommodate the electrical double layer in the microvascular regime. With long wavelength, lubrication and Debye-Hückel approximations, the boundary value problem is rendered non-dimensional. Analytical solutions are derived for the axial velocity, volumetric flow rate, pressure gradient, volumetric flow rate, averaged volumetric flow rate along one time period, pressure rise along one wavelength and stream function. A plug swidth is featured in the solutions. Via symbolic software (Mathematica), graphical plots are generated for the influence of Bingham plug flow width parameter, electrical Debye length and Helmholtz-Smoluchowski velocity (maximum electro-osmotic velocity) on the key hydrodynamic variables. This study reveals that blood flow rate accelerates with decreasing the plug width (i.e. viscoplastic nature of fluids) and also with increasing the Debye length parameter. Copyright © 2018 Elsevier Inc. All rights reserved.

  11. Three dimensional peristaltic flow of hyperbolic tangent fluid in non-uniform channel having flexible walls

    Directory of Open Access Journals (Sweden)

    M. Ali Abbas

    2016-03-01

    Full Text Available In this present analysis, three dimensional peristaltic flow of hyperbolic tangent fluid in a non-uniform channel has been investigated. We have considered that the pressure is uniform over the whole cross section and the interial effects have been neglected. For this purpose we consider laminar flow under the assumptions of long wavelength (λ→∞ and creeping flow (Re→0 approximations. The attained highly nonlinear equations are solved with the help of Homotopy perturbation method. The influence of various physical parameters of interest is demonstrated graphically for wall tension, mass characterization, damping nature of the wall, wall rigidity, wall elastance, aspect ratio and the Weissenberg number. In this present investigation we found that the magnitude of the velocity is maximum in the center of the channel whereas it is minimum near the walls. Stream lines are also drawn to discuss the trapping mechanism for all the physical parameters. Comparison has also been presented between Newtonian and non-Newtonian fluid.

  12. Symposium on the Foundations of Newtonian Scholarship

    CERN Document Server

    Nauenberg, Michael; The foundations of Newtonian scholarship

    2000-01-01

    Newtonian scholarship has taken great steps forward in the last half-century.The recent completion of critical editions of Newton's mathematical papers and of his scientific correspondence, as well as the publication of the first volume of his optical papers and of variant readings of the Principia in the original Latin, have made most of Newton's scientific work generally available for study and analysis for the first time. This has provided a better understanding of Newton's Principia and Optics especially regarding their origin and interpretation, much of which has remained obscure for several centuries. Some of the new developments and insights are presented in this book by several of the scholars who have made these primary sources accessible, and by others who are using them to elucidate Newton's work. Most of the papers included were presented at the Symposium on the Foundations of Newtonian Scholarship, held at the Royal Society in London in March 1997.

  13. Leading quantum correction to the Newtonian potential

    International Nuclear Information System (INIS)

    Donoghue, J.F.

    1994-01-01

    I argue that the leading quantum corrections, in powers of the energy or inverse powers of the distance, may be computed in quantum gravity through knowledge of only the low-energy structure of the theory. As an example, I calculate the leading quantum corrections to the Newtonian gravitational potential

  14. Tidal interaction of black holes and Newtonian viscous bodies

    International Nuclear Information System (INIS)

    Poisson, Eric

    2009-01-01

    The tidal interaction of a (rotating or nonrotating) black hole with nearby bodies produces changes in its mass, angular momentum, and surface area. Similarly, tidal forces acting on a Newtonian, viscous body do work on the body, change its angular momentum, and part of the transferred gravitational energy is dissipated into heat. The equations that describe the rate of change of the black-hole mass, angular momentum, and surface area as a result of the tidal interaction are compared with the equations that describe how the tidal forces do work, torque, and produce heat in the Newtonian body. The equations are strikingly similar, and unexpectedly, the correspondence between the Newtonian-body and black-hole results is revealed to hold in near-quantitative detail. The correspondence involves the combination k 2 τ of 'Love quantities' that incorporate the details of the body's internal structure; k 2 is the tidal Love number, and τ is the viscosity-produced delay between the action of the tidal forces and the body's reaction. The combination k 2 τ is of order GM/c 3 for a black hole of mass M; it does not vanish, in spite of the fact that k 2 is known to vanish individually for a nonrotating black hole.

  15. 3D Suspended Polymeric Microfluidics (SPMF3 with Flow Orthogonal to Bending (FOB for Fluid Analysis through Kinematic Viscosity

    Directory of Open Access Journals (Sweden)

    Mostapha Marzban

    2017-10-01

    Full Text Available Measuring of fluid properties such as dynamic viscosity and density has tremendous potential for various applications from physical to biological to chemical sensing. However, it is almost impossible to affect only one of these properties, as dynamic viscosity and density are coupled. Hence, this paper proposes kinematic viscosity as a comprehensive parameter which can be used to study the effect of fluid properties applicable to various fluids from Newtonian fluids, such as water, to non-Newtonian fluids, such as blood. This paper also proposes an ideal microplatform, namely polymeric suspended microfluidics (SPMF3, with flow plane orthogonal to the bending plane of the structure, along with tested results of various fluids covering a wide range of engineering applications. Kinematic viscosity, also called momentum diffusivity, considers changes in both fluid intermolecular forces and molecular inertia that define dynamic viscosity and fluid density, respectively. In this study a 3D suspended polymeric microfluidic system (SPMF3 was employed to detect changes in fluid parameters such as dynamic viscosity and density during fluid processes. Using this innovative design along with theoretical and experimental results, it is shown that, in fluids, the variations of fluid density and dynamic viscosity are not easily comprehensible due to their interconnectivity. Since any change in a fluid will affect both density and dynamic viscosity, measuring both of them is necessary to identify the fluid or process status. Finally, changes in fluid properties were analyzed using simulation and experiments. The experimental results with salt-DI water solution and milk with different fat concentrations as a colloidal fluid show that kinematic viscosity is a comprehensive parameter that can identify the fluids in a unique way using the proposed microplatform.

  16. Unconfined Unsteady Laminar Flow of a Power-Law Fluid across a Square Cylinder

    Directory of Open Access Journals (Sweden)

    Asterios Pantokratoras

    2016-11-01

    Full Text Available The flow of a non-Newtonian, power-law fluid, directed normally to a horizontal cylinder with square cross-section (two-dimensional flow is considered in the present paper. The problem is investigated numerically with a very large calculation domain in order that the flow could be considered unconfined. The investigation covers the power-law index from 0.1 up to 2 and the Reynolds number ranges from 60 to 160. Over this range of Reynolds numbers the flow is unsteady. It is found that the drag coefficient and the Strouhal number are higher in a confined flow compared to those of an unconfined flow. In addition some flow characteristics are lost in a confined flow. Complete results for the drag coefficient and Strouhal number in the entire shear-thinning and shear-thickening region have been produced. In shear-thinning fluids chaotic structures exist which diminish at higher values of power-law index. This study represents the first investigation of unsteady, non-Newtonian power-law flow past a square cylinder in an unconfined field.

  17. Fluid flow solidification simulation of molten alloys

    International Nuclear Information System (INIS)

    Kaschnitz, E.

    1997-01-01

    In an effort to minimize costs and to obtain optimum designs, computer simulation of shape casting processes is more and more used as a development tool. Accurate predictions are possible by means of three dimensional fluid flow and solidification modelling. The bases of the model are the transient laminar Navier-Stokes-equations for a Newtonian fluid including the tracking of the free surface. They are describing the melt flow pattern during the mold filling sequence. Simultaneously, the temperature development in the alloy and mold is calculated using Fourier's heat transfer equation. At OEGI, a commercial software package (MAGMAsoft) with a finite difference equation solver is used for improvement of casting processes. Different examples of industrial applications will be shown. (author)

  18. Transport Coefficients of Fluids

    CERN Document Server

    Eu, Byung Chan

    2006-01-01

    Until recently the formal statistical mechanical approach offered no practicable method for computing the transport coefficients of liquids, and so most practitioners had to resort to empirical fitting formulas. This has now changed, as demonstrated in this innovative monograph. The author presents and applies new methods based on statistical mechanics for calculating the transport coefficients of simple and complex liquids over wide ranges of density and temperature. These molecular theories enable the transport coefficients to be calculated in terms of equilibrium thermodynamic properties, and the results are shown to account satisfactorily for experimental observations, including even the non-Newtonian behavior of fluids far from equilibrium.

  19. Achieving effective confinement through utilization of non-Newtonian fluid mixture as stemming structure

    Directory of Open Access Journals (Sweden)

    Luís Felipe Gomes Marinho

    Full Text Available Abstract The economics of a mining operation is directly influenced by blasting outcomes, where blasting aims to comminute the rock mass in order to attain smaller grain sizes to be loaded and hauled at a minimum cost for its first processing stage. In order to promote adequate rock breakage, the stemming structure needs to provide proper confinement for the borehole charged with explosives, reflecting the energy released during the detonation in form of shock waves and gases to act throughout the in situ rock mass, enlarging its failures and fractures, and also creating new ones. To build up a stemming column, literature recommends the usage of dry granular materials instead of elements with plastic behavior. However, a study was performed using Gypsum plaster as stemming; a kind of material that exhibits solid-like behavior when it is dry. Following this theory, this test verified improvements regarding confinement effectiveness and energy propagation throughout the rock mass when a non-Newtonian mixture (NNM was applied as stemming; a material that shows a solid-like behavior when is under shear stress. When the stemming arrangement was composed of NNM, it was able to reduce energy and gas losses to the atmosphere, because of the liquid's property of filling voids into the borehole. The NNM yielded high results due to its better confinement effectiveness, a reduction of air overpressure, and an increase of the strain propagation and ground vibration throughout the rock.

  20. Fractional magnetohydrodynamics Oldroyd-B fluid over an oscillating plate

    Directory of Open Access Journals (Sweden)

    Jamil Muhammad

    2013-01-01

    Full Text Available This paper presents some new exact solutions corresponding to the oscillating flows of a MHD Oldroyd-B fluid with fractional derivatives. The fractional calculus approach in the governing equations is used. The exact solutions for the oscillating motions of a fractional MHD Oldroyd-B fluid due to sine and cosine oscillations of an infinite plate are established with the help of discrete Laplace transform. The expressions for velocity field and the associated shear stress that have been obtained, presented in series form in terms of Fox H functions, satisfy all imposed initial and boundary conditions. Similar solutions for ordinary MHD Oldroyd-B, fractional and ordinary MHD Maxwell, fractional and ordinary MHD Second grade and MHD Newtonian fluid as well as those for hydrodynamic fluids are obtained as special cases of general solutions. Finally, the obtained solutions are graphically analyzed through various parameters of interest.

  1. Data on mixing of viscous fluids by helical screw impellers in cylindrical vessels

    Directory of Open Access Journals (Sweden)

    Houari Ameur

    2016-09-01

    Full Text Available In this article, the data assembled regarding the mixing of Newtonian and shear thinning fluids by screw impellers in a cylindrical tank is disclosed. The data summarizing some information on the efficiency of such impellers are obtained via 3D calculations of velocities and viscous dissipation in the whole vessel volume. The data presented herein may be useful for those who want to outline the mixing characteristics in terms of fluid circulation and power consumption for this kind of impellers, therefore, avoiding a great effort for achieving a high number of experiments. Keyword: Mixing, Helical screw agitator, Power consumption, Fluid circulation, Cylindrical tanks

  2. On the Newtonian limit of emergent NC gravity and long-distance corrections

    International Nuclear Information System (INIS)

    Steinacker, Harold

    2009-01-01

    We show how Newtonian gravity emerges on 4-dimensional non-commutative spacetime branes in Yang-Mills matrix models. Large matter clusters such as galaxies are embedded in large-scale harmonic deformations of the space-time brane, which screen gravity for long distances. On shorter scales, the local matter distribution reproduces Newtonian gravity via local deformations of the brane and its metric. The harmonic 'gravity bag' acts as a halo with effective positive energy density. This leads in particular to a significant enhancement of the orbital velocities around galaxies at large distances compared with the Newtonian case, before dropping to zero as the geometry merges with a Milne-like cosmology. Besides these 'harmonic' solutions, there is another class of solutions which is more similar to Einstein gravity. Thus the IKKT model provides an accessible candidate for a quantum theory of gravity.

  3. Characterization of commercial magnetorheological fluids at high shear rate: influence of the gap

    Science.gov (United States)

    Golinelli, Nicola; Spaggiari, Andrea

    2018-07-01

    This paper reports the experimental tests on the behaviour of a commercial MR fluid at high shear rates and the effect of the gap. Three gaps were considered at multiple magnetic fields and shear rates. From an extended set of almost two hundred experimental flow curves, a set of parameters for the apparent viscosity are retrieved by using the Ostwald de Waele model for non-Newtonian fluids. It is possible to simplify the parameter correlation by making the following considerations: the consistency of the model depends only on the magnetic field, the flow index depends on the fluid type and the gap shows an important effect only at null or very low magnetic fields. This lead to a simple and useful model, especially in the design phase of a MR based product. During the off state, with no applied field, it is possible to use a standard viscous model. During the active state, with high magnetic field, a strong non-Newtonian nature becomes prevalent over the viscous one even at very high shear rate; the magnetic field dominates the apparent viscosity change, while the gap does not play any relevant role on the system behaviour. This simple assumption allows the designer to dimension the gap only considering the non-active state, as in standard viscous systems, and taking into account only the magnetic effect in the active state, where the gap does not change the proposed fluid model.

  4. Viscoelastic capillary flow: the case of whole blood

    Directory of Open Access Journals (Sweden)

    David Rabaud

    2016-07-01

    Full Text Available The dynamics of spontaneous capillary flow of Newtonian fluids is well-known and can be predicted by the Lucas-Washburn-Rideal (LWR law. However a wide variety of viscoelastic fluids such as alginate, xanthan and blood, does not exhibit the same Newtonian behavior.In this work we consider the Herschel-Bulkley (HB rheological model and Navier-Stokes equation to derive a generic expression that predicts the capillary flow of non-Newtonian fluids. The Herschel-Bulkley rheological model encompasses a wide variety of fluids, including the Power-law fluids (also called Ostwald fluids, the Bingham fluids and the Newtonian fluids. It will be shown that the proposed equation reduces to the Lucas-Washburn-Rideal law for Newtonian fluids and to the Weissenberg-Rabinowitsch-Mooney (WRM law for power-law fluids. Although HB model cannot reduce to Casson’s law, which is often used to model whole blood rheology, HB model can fit the whole blood rheology with the same accuracy.Our generalized expression for the capillary flow of non-Newtonian fluid was used to accurately fit capillary flow of whole blood. The capillary filling of a cylindrical microchannel by whole blood was monitored. The blood first exhibited a Newtonian behavior, then after 7 cm low shear stress and rouleaux formation made LWR fails to fit the data: the blood could not be considered as Newtonian anymore. This non-Newtonian behavior was successfully fit by the proposed equation.

  5. Against Laplacian Reduction of Newtonian Mass to Spatiotemporal Quantities

    Science.gov (United States)

    Martens, Niels C. M.

    2018-03-01

    Laplace wondered about the minimal choice of initial variables and parameters corresponding to a well-posed initial value problem. Discussions of Laplace's problem in the literature have focused on choosing between spatiotemporal variables relative to absolute space (i.e. substantivalism) or merely relative to other material bodies (i.e. relationalism) and between absolute masses (i.e. absolutism) or merely mass ratios (i.e. comparativism). This paper extends these discussions of Laplace's problem, in the context of Newtonian Gravity, by asking whether mass needs to be included in the initial state at all, or whether a purely spatiotemporal initial state suffices. It is argued that mass indeed needs to be included; removing mass from the initial state drastically reduces the predictive and explanatory power of Newtonian Gravity.

  6. Newtonian potential and geodesic completeness in infinite derivative gravity

    Science.gov (United States)

    Edholm, James; Conroy, Aindriú

    2017-08-01

    Recent study has shown that a nonsingular oscillating potential—a feature of infinite derivative gravity theories—matches current experimental data better than the standard General Relativity potential. In this work, we show that this nonsingular oscillating potential can be given by a wider class of theories which allows the defocusing of null rays and therefore geodesic completeness. We consolidate the conditions whereby null geodesic congruences may be made past complete, via the Raychaudhuri equation, with the requirement of a nonsingular Newtonian potential in an infinite derivative gravity theory. In doing so, we examine a class of Newtonian potentials characterized by an additional degree of freedom in the scalar propagator, which returns the familiar potential of General Relativity at large distances.

  7. A Mathematical Model for Swallowing of Concentrated Fluids in Oesophagus

    Directory of Open Access Journals (Sweden)

    S. K. Pandey

    2011-01-01

    Full Text Available This model investigates particularly the impact of an integral and a non-integral number of waves on the swallowing of food stuff such as jelly, tomato puree, soup, concentrated fruits juices and honey transported peristaltically through the oesophagus. The fluid is considered as a Casson fluid. Emphasis is on the study of the dependence of local pressure distribution on space and time. Mechanical efficiency, reflux limit and trapping are also discussed. The effect of Casson fluid vis-à-vis Newtonian fluid is investigated analytically and numerically too. The result is physically interpreted as that the oesophagus makes more efforts to swallow fluids with higher concentration. It is observed that the pressure is uniformly distributed when an integral number of waves is there in the oesophagus; but it is non-uniform when a non-integral number of waves is present therein. It is further observed that as the plug flow region widens, the pressure difference increases, which indicates that the averaged flow rate will reduce for a Casson fluid. It is also concluded that Casson fluids are more prone to reflux.

  8. Evaluation of the Use of a Bedleveler to Improve Navigability of Atchafalaya River Bar Channel Fluid Mud

    Science.gov (United States)

    2017-08-01

    dredged (new work), clay , and even small pieces of rock but are used much less often in sand. The number of passes required depends entirely on the...the vibrating fork sensor decreases as the density of the fluid mud increases, and the amplitude of vibrations decrease with increasing viscosity ...density and viscosity . In general, the tuning-fork method of measuring density and viscosity is restricted to Newtonian fluids, which continue to flow

  9. Large distance modification of Newtonian potential and structure formation in universe

    Science.gov (United States)

    Hameeda, Mir; Upadhyay, Sudhaker; Faizal, Mir; Ali, Ahmed F.; Pourhassan, Behnam

    2018-03-01

    In this paper, we study the effects of super-light brane world perturbative modes on structure formation in our universe. As these modes modify the large distance behavior of Newtonian potential, they effect the clustering of a system of galaxies. So, we explicitly calculate the clustering of galaxies interacting through such a modified Newtonian potential. We use a suitable approximation for analyzing this system of galaxies, and discuss the validity of such approximations. We observe that such corrections also modify the virial theorem for such a system of galaxies.

  10. Bubble Formation in Yield Stress Fluids Using Flow-Focusing and T-Junction Devices.

    Science.gov (United States)

    Laborie, Benoit; Rouyer, Florence; Angelescu, Dan E; Lorenceau, Elise

    2015-05-22

    We study the production of bubbles inside yield stress fluids (YSFs) in axisymmetric T-junction and flow-focusing devices. Taking advantage of yield stress over capillary stress, we exhibit a robust break-up mechanism reminiscent of the geometrical operating regime in 2D flow-focusing devices for Newtonian fluids. We report that when the gas is pressure driven, the dynamics is unsteady due to hydrodynamic feedback and YSF deposition on the walls of the channels. However, the present study also identifies pathways for potential steady-state production of bubbly YSFs at large scale.

  11. A Paradox of Newtonian Gravitation and Laplace's Solution

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 21; Issue 5. A Paradox of Newtonian Gravitation and Laplace's Solution. General Article Volume ... A physical phenomenonthat can justify Laplace's suggestion isalso mentioned briefly. This article also posesan interesting mathematical problem that can ...

  12. Shape sensitivity analysis of time-dependent flows of incompressible non-Newtonian fluids

    Czech Academy of Sciences Publication Activity Database

    Sokolowski, J.; Stebel, Jan

    2011-01-01

    Roč. 40, č. 4 (2011), s. 1077-1097 ISSN 0324-8569 R&D Projects: GA ČR GA201/09/0917 Institutional research plan: CEZ:AV0Z10190503 Keywords : shape optimization * shape gradient * incompressible viscous fluid Subject RIV: BA - General Mathematics Impact factor: 0.300, year: 2010

  13. Effects of transpiration on unsteady MHD flow of an upper convected Maxwell (UCM) fluid passing through a stretching surface in the presence of a first order chemical reaction

    International Nuclear Information System (INIS)

    Mukhopadhyay, Swati; Arif, M. Golam; Pk M Wazed Ali

    2013-01-01

    The aim of this article is to present the effects of transpiration on the unsteady two-dimensional boundary layer flow of non-Newtonian fluid passing through a stretching sheet in the presence of a first order constructive/destructive chemical reaction. The upper-convected Maxwell (UCM) model is used here to characterize the non-Newtonian behavior of the fluid. Using similarity solutions, the governing nonlinear partial differential equations are transformed into ordinary ones and are then solved numerically by the shooting method. The flow fields and mass transfer are significantly influenced by the governing parameters. The fluid velocity initially decreases as the unsteadiness parameter increases and the concentration decreases significantly due to the increase in the unsteadiness. The effect of increasing values of transpiration (suction) and the Maxwell parameter is to suppress the velocity field; however, the concentration is enhanced as transpiration (suction) and the Maxwell parameter increase. Also, it is found that the fluid velocity decreases as the magnetic parameter increases; however, the concentration increases in this case. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

  14. Experimental Studies on the Lorentz Symmetry in Post-Newtonian Gravity with Pulsars

    Directory of Open Access Journals (Sweden)

    Lijing Shao

    2016-12-01

    Full Text Available Local Lorentz invariance (LLI is one of the most important fundamental symmetries in modern physics. While the possibility of LLI violation (LLIv was studied extensively in flat spacetime, its counterpart in gravitational interaction also deserves significant examination from experiments. In this contribution, I review several recent studies of LLI in post-Newtonian gravity, using powerful tools of pulsar timing. It shows that precision pulsar timing experiments hold a unique position to probe LLIv in post-Newtonian gravity.

  15. Self-Similar Unsteady Flow of a Sisko Fluid in a Cylindrical Tube Undergoing Translation

    Directory of Open Access Journals (Sweden)

    M. Khan

    2015-01-01

    Full Text Available The governing nonlinear equation for unidirectional flow of a Sisko fluid in a cylindrical tube due to translation of the tube wall is modelled in cylindrical polar coordinates. The exact steady-state solution for the nonlinear problem is obtained. The reduction of the nonlinear initial value problem is carried out by using a similarity transformation. The partial differential equation is transformed into an ordinary differential equation, which is integrated numerically taking into account the influence of the exponent n and the material parameter b of the Sisko fluid. The initial approximation for the fluid velocity on the axis of the cylinder is obtained by matching inner and outer expansions for the fluid velocity. A comparison of the velocity, vorticity, and shear stress of Newtonian and Sisko fluids is presented.

  16. Injection of colloidal size particles of Fe0 in porous media with shearthinning fluids as a method to emplace a permeable reactive zone

    International Nuclear Information System (INIS)

    Cantrell, K.J.; Kaplan, D.I.; Gilmore, T.J.

    1997-01-01

    Previous work has demonstrated the feasibility of injecting suspensions of micron-size zero-valent (FeO) particles into porous media as a method to emplace a permeable reactive zone. Further studies were conducted to evaluate the effects of several shearthinning fluids on enhancing the injectability of micron-size FeO particles into porous media. In contrast to Newtonian fluids, whose viscosities are constant with shear rate, certain non-Newtonian fluids are shearthinning, that is, the viscosity of these fluids decreases with increasing shear rate. The primary benefit of using these fluids for this application is that they increase the viscosity of the aqueous phase without adversely decreasing the hydraulic conductivity. A suspension formulated with a shearthinning fluid will maintain a relatively high viscosity in solution near the FeO particles (where the shear stress is low) relative to locations near the surfaces of the porous media, where the shear stress is high. The increased viscosity decreases the rate of gravitational settling of the dense FeO colloids (7.6 9/cm3) while maintaining a relatively high hydraulic conductivity that permits pumping the colloid suspensions into porous media at greater flowrates and distances. Aqueous solutions of three polymers at different concentrations were investigated. It was determined that, the use of shear thinning fluids greatly increases the injectability of the colloidal FeO suspensions in porous media

  17. On Dual Phase-Space Relativity, the Machian Principle and Modified Newtonian Dynamics

    CERN Document Server

    Castro, C

    2004-01-01

    We investigate the consequences of the Mach's principle of inertia within the context of the Dual Phase Space Relativity which is compatible with the Eddington-Dirac large numbers coincidences and may provide with a physical reason behind the observed anomalous Pioneer acceleration and a solution to the riddle of the cosmological constant problem ( Nottale ). The cosmological implications of Non-Archimedean Geometry by assigning an upper impassible scale in Nature and the cosmological variations of the fundamental constants are also discussed. We study the corrections to Newtonian dynamics resulting from the Dual Phase Space Relativity by analyzing the behavior of a test particle in a modified Schwarzschild geometry (due to the the effects of the maximal acceleration) that leads in the weak-field approximation to essential modifications of the Newtonian dynamics and to violations of the equivalence principle. Finally we follow another avenue and find modified Newtonian dynamics induced by the Yang's Noncommut...

  18. Aspects of the motion of extended bodies in the post-Newtonian approximation to general relativity

    Science.gov (United States)

    Racine, Etienne

    We give a surface integral derivation of post-1-Newtonian translational equations of motion for a system of arbitrarily structured bodies, including the coupling to all the bodies' mass and current multipole moments. The explicit form of these translational equations of motion has not been previously derived. The derivation requires only that the post-1-Newtonian vacuum field equations are satisfied in weak-field regions between the bodies; the bodies' internal gravity can be arbitrarily strong. In particular black holes are not excluded. The derivation extends previous results due to Damour, Soffel and Xu (DSX) for weakly self-gravitating bodies in which the post-1- Newtonian field equations are satisfied everywhere. We also give a surface integral derivation of the leading-order evolution equations for the spin and energy of a relativistic body interacting with other bodies in the post-Newtonian expansion. As part of the computational method, new explicit expansions of general solutions of post-2-Newtonian vacuum field equations are derived. These expansions can serve as foundation for future work in a number of directions, including for example conserved quantities at post- 2-Newtonian order, definitions of angular momentum and studies of gauge invariance of tidal heating. As an astrophysical application of the translational equations of motion, we study gravitomagnetic resonant tidal excitations of r -modes in neutron star binary coalescence. We show that the effect of the resonance on the phase of the binary can be parametrized by a single number. We compute this number explicitly and discuss the detectability of this effect from its imprint on the gravitational wave signal emitted by the binary.

  19. Determination of the Köthe-Toeplitz Duals over the Non-Newtonian Complex Field

    Directory of Open Access Journals (Sweden)

    Uğur Kadak

    2014-01-01

    Full Text Available The important point to note is that the non-Newtonian calculus is a self-contained system independent of any other system of calculus. Therefore the reader may be surprised to learn that there is a uniform relationship between the corresponding operators of this calculus and the classical calculus. Several basic concepts based on non-Newtonian calculus are presented by Grossman (1983, Grossman and Katz (1978, and Grossman (1979. Following Grossman and Katz, in the present paper, we introduce the sets of bounded, convergent, null series and p-bounded variation of sequences over the complex field C* and prove that these are complete. We propose a quite concrete approach based on the notion of Köthe-Toeplitz duals with respect to the non-Newtonian calculus. Finally, we derive some inclusion relationships between Köthe space and solidness.

  20. Minimal gravitational coupling in the Newtonian theory and the covariant Schroedinger equation

    International Nuclear Information System (INIS)

    Duval, C.; Kuenzle, H.P.

    1983-02-01

    The role of the Bargmann group (11-dimensional extended Galilei group) in non relativistic gravitation theory is investigated. The generalized Newtonian gravitation theory (Newton-Cartan theory) achieves the status of a gauge theory about as much as General Relativity and couples minimally to a complex scalar field leading to a fourdimensionally covariant Schroedinger equation. Matter current and stress-energy tensor follow correctly from the Lagrangian. This theory on curved Newtonian space-time is also shown to be a limit of the Einstein-Klein-Gordon theory

  1. Minimal gravitational coupling in the Newtonian theory and the covariant Schroedinger equation

    International Nuclear Information System (INIS)

    Duval, C.; Kuenzle, H.P.

    1984-01-01

    The role of the Bargmann group (11-dimensional extended Galilei group) in nonrelativistic gravitation theory is investigated. The generalized Newtonian gravitation theory (Newton-Cartan theory) achieves the status of a gauge theory about as much as general relativity and couples minimally to a complex scalar field leading to a four-dimensionally covariant Schroedinger equation. Matter current and stress-energy tensor follow correctly from the Lagrangian. This theory on curved Newtonian space-time is also shown to be a limit of the Einstein-Klein-Gordon theory. (author)

  2. Notes on the post-Newtonian limit of the massive Brans-Dicke theory

    International Nuclear Information System (INIS)

    Roshan, Mahmood; Shojai, Fatimah

    2011-01-01

    We consider the post-Newtonian limit of the massive Brans-Dicke theory and make some notes about the post-Newtonian limit of the case ω = 0. This case is dynamically equivalent to the metric f(R) theory. It is known that this theory can be compatible with the solar system tests if the Chameleon mechanism occurs. Also, it is known that this mechanism is because of the nonlinearity in the field equations produced by the largeness of the local curvature relative to the background curvature. Thus, the linearization of the field equations breaks down. On the other hand, we know that the Chameleon mechanism exists when a coupling between the matter and the scalar field exists. In the Jordan frame of the Brans-Dicke theory, we have no such coupling. But in the Einstein frame, this theory behaves like a Chameleon scalar field. By confining ourselves to the case ω = 0, we show that 'Chameleon-like' behaviour can exist also in the Jordan frame, but it has an important difference compared with the Chameleon mechanism. Also we show that the conditions which lead to the existence of a 'Chameleon-like' mechanism are consistent with the conditions in the post-Newtonian limit which correspond to a heavy scalar field at the cosmological scale and a small effective cosmological constant. Thus, one can linearize field equations to the post-Newtonian order, and this linearization has no contradiction with the existence of 'Chameleon-like' behaviour.

  3. Parametric analysis and design of a screw extruder for slightly non-Newtonian (pseudoplastic materials

    Directory of Open Access Journals (Sweden)

    J.I. Orisaleye

    2018-04-01

    Full Text Available Extruders have found application in the food, polymer and pharmaceutical industries. Rheological characteristics of materials are important in the specification of design parameters of screw extruders. Biopolymers, which consist of proteins, nucleic acids and polysaccharides, are shear-thinning (pseudoplastic within normal operating ranges. However, analytical models to predict and design screw extruders for non-Newtonian pseudoplastic materials are rare. In this study, an analytical model suitable to design a screw extruder for slightly non-Newtonian materials was developed. The model was used to predict the performance of the screw extruder while processing materials with power law indices slightly deviating from unity (the Newtonian case. Using non-dimensional analysis, the effects of design and operational parameters were investigated. Expressions to determine the optimum channel depth and helix angle were also derived. The model is capable of predicting the performance of the screw extruder within the range of power law indices considered (1/2⩽n⩽1. The power law index influences the choice of optimum channel depth and helix angle of the screw extruder. Keywords: Screw extruder, Slightly non-Newtonian, Shear-thinning, Pseudoplastic, Biopolymer, Power law

  4. Taylor-Couette fluid flow with force oscillation in the inner-cylinder using the immersed boundary method

    Energy Technology Data Exchange (ETDEWEB)

    Borges, Jonatas Emmanuel; Lourenco, Marcos Antonio de Souza; Padilla, Elie Luis Martinez; Silveira Neto, Aristeu da [Federal University of Uberlandia , MG (Brazil)], e-mails: lourenco@mecanica.ufu.br, epadilla@mecanica.ufu.br, aristeus@mecanica.ufu.br; Leibsohn, Andre Martins [CENPES/Petrobras, Rio de Janeiro, RJ (Brazil)], e-mail: aleibsohn@petrobras.com

    2010-07-01

    As new challenges arise in the exploration of deep and ultra-deep water oil fields by PETROBRAS more knowledge and research are needed, so that tools could be developed to assist in the critical operations and make things practicable. In the context of the drilling process, the complexity of the fluid flow inside the riser is associated with the nature of the non-Newtonian flow, immersed solid particles, variable eccentricity and the superimposed traveling azimuthal waves on the inflow and outflow boundaries of the Taylor vortices. This work presents the numerical three-dimensional results of the following simplified fluid flows: Taylor-Couette, Taylor-Couette with varying imposed eccentricity and Taylor-Couette with forced oscillation in the inner cylinder. Using the Navier-Stokes equations, a finite volume method discretization with second order accuracy in both time and space was utilized to simulate the Newtonian, single-phase incompressible fluid flow in the three cases. The circular walls of the inner and outer cylinders are represented by the immersed boundary method, with the direct multi-forcing model. The determined results allow to evidence the flow structures in the three cases in a very qualitative way, even so in the presence of the inner cylinder oscillation. (author)

  5. General relativistic continuum mechanics and the post-Newtonian equations of motion

    International Nuclear Information System (INIS)

    Morrill, T.H.

    1991-01-01

    Aspects are examined of general relativistic continuum mechanics. Perfectly elastic materials are dealt with but not exclusively. The derivation of their equations of motion is emphasized, in the post-Newtonian approximation. A reformulation is presented based on the tetrad formalism, of Carter and Quintana's theory of general relativistic elastic continua. A field Lagrangian is derived describing perfect material media; show that the usual covariant conservations law for perfectly elastic media is fully equivalent to the Euler-Lagrange equations describing these same media; and further show that the equations of motion for such materials follow directly from Einstein's field equations. In addition, a version of this principle shows that the local mass density in curved space-time partially depends on the amount and distribution of mass energy in the entire universe and is related to the mass density that would occur if space-time were flat. The total Lagrangian was also expanded in an EIH (Einstein, Infeld, Hoffmann) series to obtain a total post-Newtonian Lagrangian. The results agree with those found by solving Einstein's equations for the metric coefficients and by deriving the post-Newtonian equations of motion from the covariant conservation law

  6. A numerical model for dynamic crustal-scale fluid flow

    Science.gov (United States)

    Sachau, Till; Bons, Paul; Gomez-Rivas, Enrique; Koehn, Daniel

    2015-04-01

    Fluid flow in the crust is often envisaged and modeled as continuous, yet minimal flow, which occurs over large geological times. This is a suitable approximation for flow as long as it is solely controlled by the matrix permeability of rocks, which in turn is controlled by viscous compaction of the pore space. However, strong evidence (hydrothermal veins and ore deposits) exists that a significant part of fluid flow in the crust occurs strongly localized in both space and time, controlled by the opening and sealing of hydrofractures. We developed, tested and applied a novel computer code, which considers this dynamic behavior and couples it with steady, Darcian flow controlled by the matrix permeability. In this dual-porosity model, fractures open depending on the fluid pressure relative to the solid pressure. Fractures form when matrix permeability is insufficient to accommodate fluid flow resulting from compaction, decompression (Staude et al. 2009) or metamorphic dehydration reactions (Weisheit et al. 2013). Open fractures can close when the contained fluid either seeps into the matrix or escapes by fracture propagation: mobile hydrofractures (Bons, 2001). In the model, closing and sealing of fractures is controlled by a time-dependent viscous law, which is based on the effective stress and on either Newtonian or non-Newtonian viscosity. Our simulations indicate that the bulk of crustal fluid flow in the middle to lower upper crust is intermittent, highly self-organized, and occurs as mobile hydrofractures. This is due to the low matrix porosity and permeability, combined with a low matrix viscosity and, hence, fast sealing of fractures. Stable fracture networks, generated by fluid overpressure, are restricted to the uppermost crust. Semi-stable fracture networks can develop in an intermediate zone, if a critical overpressure is reached. Flow rates in mobile hydrofractures exceed those in the matrix porosity and fracture networks by orders of magnitude

  7. The Newtonian force experienced by a point mass near a finite cylindrical source

    International Nuclear Information System (INIS)

    Selvaggi, Jerry P; Salon, Sheppard; Chari, M V K

    2008-01-01

    The Newtonian gravitational force experienced by a point mass located at some external point from a thick-walled, hollow and uniform finite circular cylindrical body was recently solved by Lockerbie, Veryaskin and Xu (1993 Class. Quantum Grav. 10 2419). Their method of attack relied on the introduction of the circular cylindrical free-space Green function representation for the inverse distance which appears in the formulation of the Newtonian potential function. This ultimately leads Lockerbie et al to a final expression for the Newtonian potential function which is expressed as a double summation of even-ordered Legendre polynomials. However, the kernel of the cylindrical free-space Green function which is represented by an infinite integral of the product of two Bessel functions and a decaying exponential can be analytically evaluated in terms of a toroidal function. This leads to a simplification in the mathematical analysis developed by Lockerbie et al. Also, each term in the infinite series solution for the Newtonian potential function can be expressed in closed form in terms of elementary functions. The authors develop the Newtonian potential function by employing toroidal functions of zeroth order or Legendre functions of half-integral degree, Q m-1/2 (β)(Bouwkamp and de Bruijn 1947 J. Appl. Phys.18 562, Cohl et al 2001 Phys. Rev.A 64 052509-1, Selvaggi et al 2004 IEEE Trans. Magn.40 3278). These functions are monotonically decreasing and converge rapidly (Moon and Spencer 1961 Field Theory for Engineers (New Jersey: Van Nostrand Company) pp 368-76, Cohl and Tohline 1999 Astrophys. J.527 86). The introduction of the toroidal harmonic expansion leads to an infinite series solution for which each term can be expressed as an elementary function. This enables one to easily compute the axial and radial forces experienced by an internal or an external point mass

  8. Analytical and numerical modelling of thermoviscous shocks in their interactions in nonlinear fluids including dissipation

    DEFF Research Database (Denmark)

    Rasmussen, Anders Rønne; Sørensen, Mads Peter; Gaididei, Yuri Borisovich

    2010-01-01

    A wave equation, that governs finite amplitude acoustic disturbances in a thermoviscous Newtonian fluid, and includes nonlinear terms up to second order, is proposed. The equation preserves the Hamiltonian structure of the fundamental fluid dynamical equations in the non dissipative limit. An exact...... thermoviscous shock solution is derived. This solution is, in an overall sense, equivalent to the Taylor shock solution of the Burgers equation. However, in contrast to the Burgers equation, the model equation considered here is capable to describe waves propagating in opposite directions. Studies of head...

  9. Starting solutions for the flow of second grade fluids in a rectangular channel due to an oscillating shear stress

    Science.gov (United States)

    Vieru, Dumitru; Fetecau, Corina; Rana, Mehwish

    2012-05-01

    The unsteady motion of a second grade fluid between two parallel side walls perpendicular to a plate is studied by means of the Fourier sine and cosine transforms. Initially, the fluid is at rest and at time t = 0+, the plate applies an oscillating shear to the fluid. The solutions that have been obtained, presented under integral and series form and written as a sum between steady time-periodic and transient solutions can be easily reduced to the similar solutions for Newtonian fluids performing the same motion. They describe the motion of the fluid some time after its initiation. After that time, when the transient solutions disappear, the motion of the fluid is described by the steady time-periodic solutions that are independent of the initial conditions. In the absence of side walls, more exactly when the distance between walls tends to infinity, all solutions reduce to those corresponding to the motion over an infinite plate. As it was to be expected, the steady time-periodic solutions corresponding to sine and cosine oscillations of the shear stress on the boundary differ by a phase shift. Finally, the influence of side walls on the fluid motion, the required time to reach the steady periodic flow, as well as the distance between walls for which the velocity of the fluid in the middle of the channel is unaffected by their presence are established by numerical calculus and graphical illustrations. As expected, the time needed to reach the steady periodic flows is lower in the presence of side walls. It is lower for Newtonian fluids in comparison with second grade fluids and greater for sine oscillations in comparison to the cosine oscillations of the boundary shear.

  10. Pulsatile flow of viscous and viscoelastic fluids in constricted tubes

    Energy Technology Data Exchange (ETDEWEB)

    Javadzadegan, A.; Esmaeili, M.; Majidi, S. [University of Tehran, Tehran (Iran, Islamic Republic of); Fakhimghanbarzadeh, B. [Sharif University of Technology, Tehran (Iran, Islamic Republic of)

    2009-09-15

    The unsteady flow of blood through stenosed artery, driven by an oscillatory pressure gradient, is studied. An appropriate shape of the time-dependent stenoses which are overlapped in the realm of the formation of arterial narrowing is constructed mathematically. A mathematical model is developed by treating blood as a non-Newtonian fluid characterized by the Oldroyd-B and Cross models. A numerical scheme has been used to solve the unsteady nonlinear Navier- stokes equations in cylindrical coordinate system governing flow, assuming axial symmetry under laminar flow condition so that the problem effectively becomes two-dimensional. Finite difference technique was used to investigate the effects of parameters such as pulsatility, non-Newtonian properties and the flow time on the velocity components, the rate of flow, and the wall shear stress through their graphical representations quantitatively at the end of the paper in order to validate the applicability of the present improved mathematical model under consideration

  11. Pulsatile flow of viscous and viscoelastic fluids in constricted tubes

    International Nuclear Information System (INIS)

    Javadzadegan, A.; Esmaeili, M.; Majidi, S.; Fakhimghanbarzadeh, B.

    2009-01-01

    The unsteady flow of blood through stenosed artery, driven by an oscillatory pressure gradient, is studied. An appropriate shape of the time-dependent stenoses which are overlapped in the realm of the formation of arterial narrowing is constructed mathematically. A mathematical model is developed by treating blood as a non-Newtonian fluid characterized by the Oldroyd-B and Cross models. A numerical scheme has been used to solve the unsteady nonlinear Navier- stokes equations in cylindrical coordinate system governing flow, assuming axial symmetry under laminar flow condition so that the problem effectively becomes two-dimensional. Finite difference technique was used to investigate the effects of parameters such as pulsatility, non-Newtonian properties and the flow time on the velocity components, the rate of flow, and the wall shear stress through their graphical representations quantitatively at the end of the paper in order to validate the applicability of the present improved mathematical model under consideration

  12. Lorentz-like covariant equations of non-relativistic fluids

    International Nuclear Information System (INIS)

    Montigny, M de; Khanna, F C; Santana, A E

    2003-01-01

    We use a geometrical formalism of Galilean invariance to build various hydrodynamics models. It consists in embedding the Newtonian spacetime into a non-Euclidean 4 + 1 space and provides thereby a procedure that unifies models otherwise apparently unrelated. After expressing the Navier-Stokes equation within this framework, we show that slight modifications of its Lagrangian allow us to recover the Chaplygin equation of state as well as models of superfluids for liquid helium (with both its irrotational and rotational components). Other fluid equations are also expressed in a covariant form

  13. Double-layer optical fiber coating analysis in MHD flow of an elastico-viscous fluid using wet-on-wet coating process

    Directory of Open Access Journals (Sweden)

    Zeeshan Khan

    Full Text Available Modern optical fibers require a double-layer coating on the glass fiber in order to provide protection from signal attenuation and mechanical damage. The most important plastic resins used in wires and optical fibers are plastic polyvinyl chloride (PVC and low and high density polyethylene (LDPE/HDPE, nylon and Polysulfone. One of the most important things which affect the final product after processing is the design of the coating die. In the present study, double-layer optical fiber coating is performed using melt polymer satisfying Oldroyd 8-constant fluid model in a pressure type die with the effect of magneto-hydrodynamic (MHD. Wet-on-wet coating process is applied for double-layer optical fiber coating. The coating process in the coating die is modeled as a simple two-layer Couette flow of two immiscible fluids in an annulus with an assigned pressure gradient. Based on the assumptions of fully developed laminar and MHD flow, the Oldroyd 8-constant model of non-Newtonian fluid of two immiscible resin layers is modeled. The governing nonlinear equations are solved analytically by the new technique of Optimal Homotopy Asymptotic Method (OHAM. The convergence of the series solution is established. The results are also verified by the Adomian Decomposition Method (ADM. The effect of important parameters such as magnetic parameter Mi, the dilatant constant α, the Pseodoplastic constant β, the radii ratio δ, the pressure gradient Ω, the speed of fiber optics V, and the viscosity ratio κ on the velocity profiles, thickness of coated fiber optics, volume flow rate, and shear stress on the fiber optics are investigated. At the end the result of the present work is also compared with the experimental results already available in the literature by taking non-Newtonian parameters tends to zero. Keywords: Non-Newtonian fluid, Oldroyd 8-constant fluid, MHD flow, Double-layer fiber coating, OHAM, ADM, Wet-on-wet coating process

  14. Was Newton right? A search for non-Newtonian behavior of weak-field gravity

    Directory of Open Access Journals (Sweden)

    Boynton Paul

    2014-06-01

    Full Text Available Empirical tests of Einstein’s metric theory of gravitation, even in the non-relativistic, weak-field limit, could play an important role in judging theory-driven extensions of the current Standard Model of fundamental interactions. Guided by Galileo's work and his own experiments, Newton formulated a theory of gravity in which the force of attraction between two bodies is independent of composition and proportional to the inertia of each, thereby transparently satisfying Galileo's empirically informed conjecture regarding the Universality of Free Fall. Similarly, Einstein honored the manifest success of Newton’s theory by assuring that the linearized equations of GTR matched the Newtonian formalism under “classical” conditions. Each of these steps, however, was explicitly an approximation raised to the status of principle. Perhaps, at some level, Newtonian gravity does not accurately describe the physical interaction between uncharged, unmagnetized, macroscopic bits of ordinary matter. What if Newton were wrong? Detecting any significant deviation from Newtonian behavior, no matter how small, could provide new insights and possibly reveal new physics. In the context of physics as an empirical science, for us this yet unanswered question constitutes sufficient motivation to attempt precision measurements of the kind described here. In this paper we report the current status of a project to search for violation of the Newtonian inverse square law of gravity.

  15. Exact Descriptions of General Relativity Derived from Newtonian Mechanics within Curved Geometries

    Science.gov (United States)

    Savickas, David

    2015-04-01

    General relativity and Newtonian mechanics are shown to be exactly related when Newton's second law is written in a curved geometry by using the physical components of a vector as is defined in tensor calculus. By replacing length within the momentum's velocity by the vector metric in a curved geometry the second law can then be shown to be exactly identical to the geodesic equation of motion occurring in general relativity. When time's vector direction is constant, as similarly occurs in Newtonian mechanics, this equation can be reduced to a curved three-dimensional equation of motion that yields the the Schwarzschild equations of motion for an isolated particle. They can be used to describe gravitational behavior for any array of masses for which the Newtonian gravitational potential is known, and is shown to describe a mass particle's behavior in the gravitational field of a thin mass-rod. This use of Newton's laws allows relativistic behavior to be described in a physically comprehensible manner. D. Savickas, Int. J. Mod. Phys. D 23 1430018, (2014).

  16. Astrophysical fluid dynamics

    Science.gov (United States)

    Ogilvie, Gordon I.

    2016-06-01

    > These lecture notes and example problems are based on a course given at the University of Cambridge in Part III of the Mathematical Tripos. Fluid dynamics is involved in a very wide range of astrophysical phenomena, such as the formation and internal dynamics of stars and giant planets, the workings of jets and accretion discs around stars and black holes and the dynamics of the expanding Universe. Effects that can be important in astrophysical fluids include compressibility, self-gravitation and the dynamical influence of the magnetic field that is `frozen in' to a highly conducting plasma. The basic models introduced and applied in this course are Newtonian gas dynamics and magnetohydrodynamics (MHD) for an ideal compressible fluid. The mathematical structure of the governing equations and the associated conservation laws are explored in some detail because of their importance for both analytical and numerical methods of solution, as well as for physical interpretation. Linear and nonlinear waves, including shocks and other discontinuities, are discussed. The spherical blast wave resulting from a supernova, and involving a strong shock, is a classic problem that can be solved analytically. Steady solutions with spherical or axial symmetry reveal the physics of winds and jets from stars and discs. The linearized equations determine the oscillation modes of astrophysical bodies, as well as their stability and their response to tidal forcing.

  17. Effect of wall compliance on peristaltic transport of a Newtonian fluid in an asymmetric channel

    Directory of Open Access Journals (Sweden)

    Mohamed H. Haroun

    2006-01-01

    Full Text Available Peristaltic transport of an incompressible viscous fluid in an asymmetric compliant channel is studied. The channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitudes and phases. The fluid-solid interaction problem is investigated by considering equations of motion of both the fluid and the deformable boundaries. The driving mechanism of the muscle is represented by assuming the channel walls to be compliant. The phenomenon of the “mean flow reversal” is discussed. The effect of wave amplitude ratio, width of the channel, phase difference, wall elastance, wall tension, and wall damping on mean-velocity and reversal flow has been investigated. The results reveal that the reversal flow occurs near the boundaries which is not possible in the elastic symmetric channel case.

  18. Turbulent Flow of Saudi Non-Newtonian Crude Oils in a Pipeline Écoulement turbulent de bruts non-newtoniens séoudiens dans une canalisation

    Directory of Open Access Journals (Sweden)

    Hemeidia A. M.

    2006-11-01

    Full Text Available Rheological properties of Saudi Arab-Light, Arab-Berri and Arab-Heavy crude oils were measured with Brookfield Viscometer (LVT Model at temperatures 10, 15, 20, 25, 38, 55 and 70°C. Saudi Arab-Light and Arab-Heavy exhibit non-Newtonian behavior at temperature less than or equal to 20°C, while Saudi Arab-Berri behaves as a non-Newtonian fluid at all temperatures. The main reason for this rheological behavior can be attributed to the thermal and shear histories; the relative amounts of wax and asphaltene content in Saudi crude oils as well. Therefore, Statistical Analysis (t-test was used to check the variability of the change in rheological behavior of Saudi non-Newtonian crude oils at a confidence level of 95%. The evaluation ensured that, all non-Newtonian data were statistically not different and were correlated with power-law model. Under turbulent flow conditions the pipeline design calculations were carried out through a computer program. Les propriétés rhéologiques des bruts séoudiens Arab-Light, Arab-Berri et Arab-Heavy ont été mesurées à l'aide d'un viscomètre Brookfield (modèle LVT à des températures de 10, 15, 20, 25, 38, 55 et 70°C. Les Saudi Arab-Light et Arab-Heavy présentent un comportement non newtonien à des températures égales ou inférieures à 20°C, tandis que le Saudi Arab-Berri se comporte comme un fluide non newtonien à toutes les températures. Ce comportement rhéologique est principalement dû aux historiques thermiques et de cisaillement, de même qu'aux quantités relatives de paraffine et à la teneur en asphaltène des bruts séoudiens. Une analyse statistique (essai t a donc été menée pour vérifier la variabilité des changements de comportement rhéologique des bruts séoudiens non newtoniens à un degré de fiabilité de 95%. Il en est ressorti que toutes les données non newtoniennes étaient statistiquement non différentes et étaient en corrélation avec le modèle de la loi des

  19. Test of modified Newtonian dynamics with recent Boomerang data

    International Nuclear Information System (INIS)

    Slosar, Anze; Melchiorri, Alessandro; Silk, Joseph I.

    2005-01-01

    Purely baryonic dark matter dominated models like modified Newtonian dynamics (MOND) based on modification of Newtonian gravity have been successful in reproducing some dynamical properties of galaxies. More recently, a relativistic formulation of MOND proposed by Bekenstein seems to agree with cosmological large scale structure formation. In this work, we revise the agreement of MOND with observations in light of the new results on the cosmic microwave anisotropies provided by the 2003 flight of Boomerang. The measurements of the height of the third acoustic peak, provided by several small scale CMB experiments have reached enough sensitivity to severely constrain models without cold dark matter. Assuming that acoustic peak structure in the CMB is unchanged and that local measurements of the Hubble constant can be applied, we find that the cold dark matter is strongly favored with Bayesian probability ratio of about one in two hundred

  20. ALE finite volume method for free-surface Bingham plastic fluids with general curvilinear coordinates

    International Nuclear Information System (INIS)

    Nagai, Katsuaki; Ushijima, Satoru

    2010-01-01

    A numerical prediction method has been proposed to predict Bingham plastic fluids with free-surface in a two-dimensional container. Since the linear relationships between stress tensors and strain rate tensors are not assumed for non-Newtonian fluids, the liquid motions are described with Cauchy momentum equations rather than Navier-Stokes equations. The profile of a liquid surface is represented with the two-dimensional curvilinear coordinates which are represented in each computational step on the basis of the arbitrary Lagrangian-Eulerian (ALE) method. Since the volumes of the fluid cells are transiently changed in the physical space, the geometric conservation law is applied to the finite volume discretizations. As a result, it has been shown that the present method enables us to predict reasonably the Bingham plastic fluids with free-surface in a container.

  1. ALE finite volume method for free-surface Bingham plastic fluids with general curvilinear coordinates

    Science.gov (United States)

    Nagai, Katsuaki; Ushijima, Satoru

    2010-06-01

    A numerical prediction method has been proposed to predict Bingham plastic fluids with free-surface in a two-dimensional container. Since the linear relationships between stress tensors and strain rate tensors are not assumed for non-Newtonian fluids, the liquid motions are described with Cauchy momentum equations rather than Navier-Stokes equations. The profile of a liquid surface is represented with the two-dimensional curvilinear coordinates which are represented in each computational step on the basis of the arbitrary Lagrangian-Eulerian (ALE) method. Since the volumes of the fluid cells are transiently changed in the physical space, the geometric conservation law is applied to the finite volume discretizations. As a result, it has been shown that the present method enables us to predict reasonably the Bingham plastic fluids with free-surface in a container.

  2. Notes on the post-Newtonian limit of the massive Brans-Dicke theory

    Energy Technology Data Exchange (ETDEWEB)

    Roshan, Mahmood; Shojai, Fatimah, E-mail: fshojai@ut.ac.ir [Department of Physics, University of Tehran, Tehran (Iran, Islamic Republic of)

    2011-07-21

    We consider the post-Newtonian limit of the massive Brans-Dicke theory and make some notes about the post-Newtonian limit of the case {omega} = 0. This case is dynamically equivalent to the metric f(R) theory. It is known that this theory can be compatible with the solar system tests if the Chameleon mechanism occurs. Also, it is known that this mechanism is because of the nonlinearity in the field equations produced by the largeness of the local curvature relative to the background curvature. Thus, the linearization of the field equations breaks down. On the other hand, we know that the Chameleon mechanism exists when a coupling between the matter and the scalar field exists. In the Jordan frame of the Brans-Dicke theory, we have no such coupling. But in the Einstein frame, this theory behaves like a Chameleon scalar field. By confining ourselves to the case {omega} = 0, we show that 'Chameleon-like' behaviour can exist also in the Jordan frame, but it has an important difference compared with the Chameleon mechanism. Also we show that the conditions which lead to the existence of a 'Chameleon-like' mechanism are consistent with the conditions in the post-Newtonian limit which correspond to a heavy scalar field at the cosmological scale and a small effective cosmological constant. Thus, one can linearize field equations to the post-Newtonian order, and this linearization has no contradiction with the existence of 'Chameleon-like' behaviour.

  3. Fluid flow for chemical and process engineers

    CERN Document Server

    Holland, F

    1995-01-01

    This major new edition of a popular undergraduate text covers topics of interest to chemical engineers taking courses on fluid flow. These topics include non-Newtonian flow, gas-liquid two-phase flow, pumping and mixing. It expands on the explanations of principles given in the first edition and is more self-contained. Two strong features of the first edition were the extensive derivation of equations and worked examples to illustrate calculation procedures. These have been retained. A new extended introductory chapter has been provided to give the student a thorough basis to understand the methods covered in subsequent chapters.

  4. Substitute fluid examinations for liquid manure

    Directory of Open Access Journals (Sweden)

    Schrader Kevin

    2017-01-01

    Full Text Available For the farming industry it is essential to use liquid manure as natural fertilizer. Through new agricultural regulation 2015 in Germany the industry must develop new liquid manure spreader systems because the ammonia and methane emission are limited. In a research project the University of Applied Sciences Zwickau and some other industry partners will develop such a new innovative liquid manure spreader. The new liquid manure spreader should use pulsating air to distribute the liquid manure exactly. The pulsating air, which flows through the pipelines, should be analysed at a test station. For examinations at this test station it is important to find another substitute fluid because liquid manure smells strong, is not transparent and is also not homogeneous enough for scientific investigations. Furthermore it is important to ensure that the substitute fluid is, like liquid manure, a non-Newtonian fluid. The substitute fluid must be a shear-thinning substance - this means the viscosity decrease at higher shear rate. Many different samples like soap-water-farragoes, jelly-water-farragoes, agar-water-farragoes, soap-ethanol-farragoes and more are, for the project, examined in regard of their physical properties to find the best substitute fluid. The samples are examined at the rotational viscometer for viscosity at various shear rates and then compared with the viscosity values of liquid manure.

  5. Substitute fluid examinations for liquid manure

    Science.gov (United States)

    Schrader, Kevin; Riedel, Marco; Eichert, Helmut

    For the farming industry it is essential to use liquid manure as natural fertilizer. Through new agricultural regulation 2015 in Germany the industry must develop new liquid manure spreader systems because the ammonia and methane emission are limited. In a research project the University of Applied Sciences Zwickau and some other industry partners will develop such a new innovative liquid manure spreader. The new liquid manure spreader should use pulsating air to distribute the liquid manure exactly. The pulsating air, which flows through the pipelines, should be analysed at a test station. For examinations at this test station it is important to find another substitute fluid because liquid manure smells strong, is not transparent and is also not homogeneous enough for scientific investigations. Furthermore it is important to ensure that the substitute fluid is, like liquid manure, a non-Newtonian fluid. The substitute fluid must be a shear-thinning substance - this means the viscosity decrease at higher shear rate. Many different samples like soap-water-farragoes, jelly-water-farragoes, agar-water-farragoes, soap-ethanol-farragoes and more are, for the project, examined in regard of their physical properties to find the best substitute fluid. The samples are examined at the rotational viscometer for viscosity at various shear rates and then compared with the viscosity values of liquid manure.

  6. Head-on infall of two compact objects: Third post-Newtonian energy flux

    International Nuclear Information System (INIS)

    Mishra, Chandra Kant; Iyer, Bala R.

    2010-01-01

    Head-on infall of two compact objects with arbitrary mass ratio is investigated using the multipolar post-Minkowskian approximation method. At the third post-Newtonian order the energy flux, in addition to the instantaneous contributions, also includes hereditary contributions consisting of the gravitational-wave tails, tails-of-tails, and the tail-squared terms. The results are given both for infall from infinity and also for infall from a finite distance. These analytical expressions should be useful for the comparison with the high accuracy numerical relativity results within the limit in which post-Newtonian approximations are valid.

  7. Numerical Modeling of Mixing of Chemically Reacting, Non-Newtonian Slurry for Tank Waste Retrieval

    International Nuclear Information System (INIS)

    Yuen, David A.; Onishi, Yasuo; Rustad, James R.; Michener, Thomas E.; Felmy, Andrew R.; Ten, Arkady A.; Hier, Catherine A.

    2000-01-01

    Many highly radioactive wastes will be retrieved by installing mixer pumps that inject high-speed jets to stir up the sludge, saltcake, and supernatant liquid in the tank, blending them into a slurry. This slurry will then be pumped out of the tank into a waste treatment facility. Our objectives are to investigate interactions-chemical reactions, waste rheology, and slurry mixing-occurring during the retrieval operation and to provide a scientific basis for the waste retrieval decision-making process. Specific objectives are to: (1) Evaluate numerical modeling of chemically active, non-Newtonian tank waste mixing, coupled with chemical reactions and realistic rheology; (2) Conduct numerical modeling analysis of local and global mixing of non-Newtonian and Newtonian slurries; and (3) Provide the bases to develop a scientifically justifiable, decision-making support tool for the tank waste retrieval operation

  8. Maintenance fluid therapy and fluid creep impose more significant fluid, sodium, and chloride burdens than resuscitation fluids in critically ill patients: a retrospective study in a tertiary mixed ICU population.

    Science.gov (United States)

    Van Regenmortel, Niels; Verbrugghe, Walter; Roelant, Ella; Van den Wyngaert, Tim; Jorens, Philippe G

    2018-04-01

    Research on intravenous fluid therapy and its side effects, volume, sodium, and chloride overload, has focused almost exclusively on the resuscitation setting. We aimed to quantify all fluid sources in the ICU and assess fluid creep, the hidden and unintentional volume administered as a vehicle for medication or electrolytes. We precisely recorded the volume, sodium, and chloride burdens imposed by every fluid source administered to 14,654 patients during the cumulative 103,098 days they resided in our 45-bed tertiary ICU and simulated the impact of important strategic fluid choices on patients' chloride burdens. In septic patients, we assessed the impact of the different fluid sources on cumulative fluid balance, an established marker of morbidity. Maintenance and replacement fluids accounted for 24.7% of the mean daily total fluid volume, thereby far exceeding resuscitation fluids (6.5%) and were the most important sources of sodium and chloride. Fluid creep represented a striking 32.6% of the mean daily total fluid volume [median 645 mL (IQR 308-1039 mL)]. Chloride levels can be more effectively reduced by adopting a hypotonic maintenance strategy [a daily difference in chloride burden of 30.8 mmol (95% CI 30.5-31.1)] than a balanced resuscitation strategy [daily difference 3.0 mmol (95% CI 2.9-3.1)]. In septic patients, non-resuscitation fluids had a larger absolute impact on cumulative fluid balance than did resuscitation fluids. Inadvertent daily volume, sodium, and chloride loading should be avoided when prescribing maintenance fluids in view of the vast amounts of fluid creep. This is especially important when adopting an isotonic maintenance strategy.

  9. A Finite Element Method for Free-Surface Flows of Incompressible Fluids in Three Dimensions, Part II: Dynamic Wetting Lines

    Energy Technology Data Exchange (ETDEWEB)

    Baer, T.A.; Cairncross, R.A.; Rao, R.R.; Sackinger, P.A.; Schunk, P.R.

    1999-01-29

    To date, few researchers have solved three-dimensional free-surface problems with dynamic wetting lines. This paper extends the free-surface finite element method described in a companion paper [Cairncross, R.A., P.R. Schunk, T.A. Baer, P.A. Sackinger, R.R. Rao, "A finite element method for free surface flows of incompressible fluid in three dimensions, Part I: Boundary-Fitted mesh motion.", to be published (1998)] to handle dynamic wetting. A generalization of the technique used in two dimensional modeling to circumvent double-valued velocities at the wetting line, the so-called kinematic paradox, is presented for a wetting line in three dimensions. This approach requires the fluid velocity normal to the contact line to be zero, the fluid velocity tangent to the contact line to be equal to the tangential component of web velocity, and the fluid velocity into the web to be zero. In addition, slip is allowed in a narrow strip along the substrate surface near the dynamic contact line. For realistic wetting-line motion, a contact angle which varies with wetting speed is required because contact lines in three dimensions typically advance or recede a different rates depending upon location and/or have both advancing and receding portions. The theory is applied to capillary rise of static fluid in a corner, the initial motion of a Newtonian droplet down an inclined plane, and extrusion of a Newtonian fluid from a nozzle onto a moving substrate. The extrusion results are compared to experimental visualization. Subject Categories

  10. Improving the sensitivity of future GW observatories in the 1-10 Hz band: Newtonian and seismic noise

    NARCIS (Netherlands)

    Beker, M.G.; Cella, G.; DeSalvo, R.; Doets, M.; Grote, H.; Harms, J.; Hennes, E.; Mandic, V.; Rabeling, D.S.; van den Brand, J.F.J.; van Leeuwen, C.M.

    2011-01-01

    The next generation gravitational wave interferometric detectors will likely be underground detectors to extend the GW detection frequency band to frequencies below the Newtonian noise limit. Newtonian noise originates from the continuous motion of the Earth's crust driven by human activity, tidal

  11. Giant intracranial aneurysm embolization with a yield stress fluid material: insights from CFD analysis.

    Science.gov (United States)

    Wang, Weixiong; Graziano, Francesca; Russo, Vittorio; Ulm, Arthur J; De Kee, Daniel; Khismatullin, Damir B

    2013-01-01

    The endovascular treatment of intracranial aneurysms remains a challenge, especially when the aneurysm is large in size and has irregular, non-spherical geometry. In this paper, we use computational fluid dynamics to simulate blood flow in a vertebro-basilar junction giant aneurysm for the following three cases: (1) an empty aneurysm, (2) an aneurysm filled with platinum coils, and (3) an aneurysm filled with a yield stress fluid material. In the computational model, blood and the coil-filled region are treated as a non-Newtonian fluid and an isotropic porous medium, respectively. The results show that yield stress fluids can be used for aneurysm embolization provided the yield stress value is 20 Pa or higher. Specifically, flow recirculation in the aneurysm and the size of the inflow jet impingement zone on the aneurysm wall are substantially reduced by yield stress fluid treatment. Overall, this study opens up the possibility of using yield stress fluids for effective embolization of large-volume intracranial aneurysms.

  12. N-MODY: A Code for Collisionless N-body Simulations in Modified Newtonian Dynamics

    Science.gov (United States)

    Londrillo, Pasquale; Nipoti, Carlo

    2011-02-01

    N-MODY is a parallel particle-mesh code for collisionless N-body simulations in modified Newtonian dynamics (MOND). N-MODY is based on a numerical potential solver in spherical coordinates that solves the non-linear MOND field equation, and is ideally suited to simulate isolated stellar systems. N-MODY can be used also to compute the MOND potential of arbitrary static density distributions. A few applications of N-MODY indicate that some astrophysically relevant dynamical processes are profoundly different in MOND and in Newtonian gravity with dark matter.

  13. Analysis of the laminar Newtonian fluid flow through a thin fracture modelled as a fluid-saturated sparsely packed porous medium

    Energy Technology Data Exchange (ETDEWEB)

    Pazanin, Igor [Zagreb Univ. (Croatia). Dept. of Mathematics; Siddheshwar, Pradeep G. [Bangalore Univ., Bengaluru (India). Dept. of Mathematics

    2017-06-01

    In this article we investigate the fluid flow through a thin fracture modelled as a fluid-saturated porous medium. We assume that the fracture has constrictions and that the flow is governed by the prescribed pressure drop between the edges of the fracture. The problem is described by the Darcy-Lapwood-Brinkman model acknowledging the Brinkman extension of the Darcy law as well as the flow inertia. Using asymptotic analysis with respect to the thickness of the fracture, we derive the explicit higher-order approximation for the velocity distribution. We make an error analysis to comment on the order of accuracy of the method used and also to provide rigorous justification for the model.

  14. LISA observations of supermassive black holes: Parameter estimation using full post-Newtonian inspiral waveforms

    International Nuclear Information System (INIS)

    Trias, Miquel; Sintes, Alicia M.

    2008-01-01

    We study parameter estimation of supermassive black hole binary systems in the final stage of inspiral using the full post-Newtonian gravitational waveforms. We restrict our analysis to systems in circular orbit with negligible spins, in the mass range 10 8 M · -10 5 M · , and compare the results with those arising from the commonly used restricted post-Newtonian approximation. The conclusions of this work are particularly important with regard to the astrophysical reach of future Laser Interferometer Space Antenna measurements. Our analysis clearly shows that modeling the inspiral with the full post-Newtonian waveform, not only extends the reach to higher mass systems, but also improves in general the parameter estimation. In particular, there are remarkable improvements in angular resolution and distance measurement for systems with a total mass higher than 5x10 6 M · , as well as a large improvement in the mass determination

  15. First general solutions for unidirectional motions of rate type fluids over an infinite plate

    Directory of Open Access Journals (Sweden)

    Constantin Fetecau

    2015-09-01

    Full Text Available Based on a simple but important remark regarding the governing equation for the non-trivial shear stress corresponding to the motion of a fluid over an infinite plate, exact solutions are established for the motion of Oldroyd-B fluids due to the plate that applies an arbitrary time-dependent shear stress to the fluid. These solutions, that allow us to provide the first exact solutions for motions of rate type fluids produced by an infinite plate that applies constant, constantly accelerating or oscillating shears stresses to the fluid, can easily be reduced to the similar solutions for Maxwell, second grade or Newtonian fluids performing the same motion. Furthermore, the obtained solutions are used to develop general solutions for the motion induced by a moving plate and to correct or recover as special cases different known results from the existing literature. Consequently, the motion problem of such fluids over an infinite plate that is moving in its plane or applies a shear stress to the fluid is completely solved.

  16. Analysis of Eyring-Powell Fluid in Helical Screw Rheometer

    Directory of Open Access Journals (Sweden)

    A. M. Siddiqui

    2014-01-01

    Full Text Available This paper aims to study the flow of an incompressible, isothermal Eyring-Powell fluid in a helical screw rheometer. The complicated geometry of the helical screw rheometer is simplified by “unwrapping or flattening” the channel, lands, and the outside rotating barrel, assuming the width of the channel is larger as compared to the depth. The developed second order nonlinear differential equations are solved by using Adomian decomposition method. Analytical expressions are obtained for the velocity profiles, shear stresses, shear at wall, force exerted on fluid, volume flow rates, and average velocity. The effect of non-Newtonian parameters, pressure gradients, and flight angle on the velocity profiles is noticed with the help of graphical representation. The observation confirmed the vital role of involved parameters during the extrusion process.

  17. Flapping motion and force generation in a viscoelastic fluid

    Science.gov (United States)

    Normand, Thibaud; Lauga, Eric

    2008-12-01

    In a variety of biological situations, swimming cells have to move through complex fluids. Similarly, mucociliary clearance involves the transport of polymeric fluids by beating cilia. Here, we consider the extent to which complex fluids could be exploited for force generation on small scales. We consider a prototypical reciprocal motion (i.e., identical under time-reversal symmetry): the periodic flapping of a tethered semi-infinite plane. In the Newtonian limit, such motion cannot be used for force generation according to Purcell’s scallop theorem. In a polymeric fluid (Oldroyd-B, and its generalization), we show that this is not the case and calculate explicitly the forces on the flapper for small-amplitude sinusoidal motion. Three setups are considered: a flapper near a wall, a flapper in a wedge, and a two-dimensional scalloplike flapper. In all cases, we show that at quadratic order in the oscillation amplitude, the tethered flapping motion induces net forces, but no average flow. Our results demonstrate therefore that the scallop theorem is not valid in polymeric fluids. The reciprocal component of the movement of biological appendages such as cilia can thus generate nontrivial forces in polymeric fluid such as mucus, and normal-stress differences can be exploited as a pure viscoelastic force generation and propulsion method.

  18. Microrheological observations of the onset of non-Newtonian behavior in suspensions

    Energy Technology Data Exchange (ETDEWEB)

    Mondy, L A; Graham, A L; Gottlieb, M

    1988-01-01

    As the column fraction of solids increases above about 0.30, suspensions of non-Brownian, uniform spheres in Newtonian liquids begin to exhibit shear-thinning, normal stresses, and other non- Newtonian behavior. Here, we report on observations obtained from falling-ball and capillary rheometry at these high volume fractions. Specifically, we find that measured viscosity values are dependent on the size-scale of the viscometer (cylinder diameter, D, and falling- ball diameter, d) relative to the diameter of the suspended spheres d/sub s/. We report the dependence of the measured viscosity on the ratios d/d/sub s/, D/d, and D/d/sub s/, as well as critical values of these ratios above which the apparent viscosity is constant. 5 refs., 3 figs., 1 tab.

  19. Variational description of multifluid hydrodynamics: Uncharged fluids

    Science.gov (United States)

    Prix, Reinhard

    2004-02-01

    We present a formalism for Newtonian multifluid hydrodynamics derived from an unconstrained variational principle. This approach provides a natural way of obtaining the general equations of motion for a wide range of hydrodynamic systems containing an arbitrary number of interacting fluids and superfluids. In addition to spatial variations we use “time shifts” in the variational principle, which allows us to describe dissipative processes with entropy creation, such as chemical reactions, friction or the effects of external non-conservative forces. The resulting framework incorporates the generalization of the entrainment effect originally discussed in the case of the mixture of two superfluids by Andreev and Bashkin. In addition to the conservation of energy and momentum, we derive the generalized conservation laws of vorticity and helicity, and the special case of Ertel’s theorem for the single perfect fluid. We explicitly discuss the application of this framework to thermally conducting fluids, superfluids, and superfluid neutron star matter. The equations governing thermally conducting fluids are found to be more general than the standard description, as the effect of entrainment usually seems to be overlooked in this context. In the case of superfluid 4He we recover the Landau-Khalatnikov equations of the two-fluid model via a translation to the “orthodox” framework of superfluidity, which is based on a rather awkward choice of variables. Our two-fluid model for superfluid neutron star matter allows for dissipation via mutual friction and also “transfusion” via β reactions between the neutron fluid and the proton-electron fluid.

  20. Finite approximations in fluid mechanics

    International Nuclear Information System (INIS)

    Hirschel, E.H.

    1986-01-01

    This book contains twenty papers on work which was conducted between 1983 and 1985 in the Priority Research Program ''Finite Approximations in Fluid Mechanics'' of the German Research Society (Deutsche Forschungsgemeinschaft). Scientists from numerical mathematics, fluid mechanics, and aerodynamics present their research on boundary-element methods, factorization methods, higher-order panel methods, multigrid methods for elliptical and parabolic problems, two-step schemes for the Euler equations, etc. Applications are made to channel flows, gas dynamical problems, large eddy simulation of turbulence, non-Newtonian flow, turbomachine flow, zonal solutions for viscous flow problems, etc. The contents include: multigrid methods for problems from fluid dynamics, development of a 2D-Transonic Potential Flow Solver; a boundary element spectral method for nonstationary viscous flows in 3 dimensions; navier-stokes computations of two-dimensional laminar flows in a channel with a backward facing step; calculations and experimental investigations of the laminar unsteady flow in a pipe expansion; calculation of the flow-field caused by shock wave and deflagration interaction; a multi-level discretization and solution method for potential flow problems in three dimensions; solutions of the conservation equations with the approximate factorization method; inviscid and viscous flow through rotating meridional contours; zonal solutions for viscous flow problems

  1. Development of a Model Foamy Viscous Fluid

    Directory of Open Access Journals (Sweden)

    Vial C.

    2013-08-01

    Full Text Available The objective is to develop a model viscous foamy fluid, i.e. below the very wet limit, the rheological and stability properties of which can be tuned. First, the method used for the preparation of foamy fluids is detailed, including process and formulation. Then, experimental results highlight that stable foamy fluids with a monomodal bubble size distribution can be prepared with a void fraction between 25% and 50% (v/v. Their viscoelastic properties under flow and low-strain oscillatory conditions are shown to result from the interplay between the formulation of the continuous phase, void fraction and bubble size. Their apparent viscosity can be described using the Cross equation and zero-shear Newtonian viscosity may be predicted by a Mooney equation up to a void fraction about 40%. The Cox-Merz and the Laun’s rules apply when the capillary number Ca is lower than 0.1. The upper limit of the zero-shear plateau region decreases when void fraction increases or bubble size decreases. In the shear-thinning region, shear stress varies with Ca1/2, as in wet foams with immobile surfaces. Finally, foamy fluids can be sheared up to Ca about 0.1 without impairing their microstructure. Their stability at rest achieves several hours and increases with void fraction due to compact packing constraints. These constitute, therefore, versatile model fluids to investigate the behaviour of foamy fluids below the very wet limit in process conditions.

  2. Impact of induced magnetic field on synovial fluid with peristaltic flow in an asymmetric channel

    Science.gov (United States)

    Afsar Khan, Ambreen; Farooq, Arfa; Vafai, Kambiz

    2018-01-01

    In this paper, we have worked for the impact of induced magnetic field on peristaltic motion of a non-Newtonian, incompressible, synovial fluid in an asymmetric channel. We have solved the problem for two models, Model-1 which behaves as shear thinning fluid and Model-2 which behaves as shear thickening fluid. The problem is solved by using modified Adomian Decomposition method. It has seen that two models behave quite opposite to each other for some parameters. The impact of various parameters on u, dp/dx, Δp and induced magnetic field bx have been studied graphically. The significant findings of this study is that the size of the trapped bolus and the pressure gradient increases by increasing M for both models.

  3. Fluids and vortex from constrained fluctuations around C-metric black holes

    Science.gov (United States)

    Hao, Xin; Wu, Bin; Zhao, Liu

    2017-08-01

    By foliating the four-dimensional C-metric black hole spacetime, we consider a kind of initial-value-like formulation of the vacuum Einstein's equation, the holographic initial data is a double consisting of the induced metric and the Brown-York energy momentum tensor on an arbitrary initial hypersurface. Then by perturbing the initial data that generates the background spacetime, it is shown that, in an appropriate limit, the fluctuation modes are governed by the continuity equation and the compressible Navier-Stokes equation which describe the momentum transport in non-relativistic viscous fluid on a flat Newtonian space. It turns out that the flat space fluid behaves as a pure vortex and the viscosity to entropy ratio is subjected to the black hole acceleration.

  4. A New Method to Simulate Free Surface Flows for Viscoelastic Fluid

    Directory of Open Access Journals (Sweden)

    Yu Cao

    2015-01-01

    Full Text Available Free surface flows arise in a variety of engineering applications. To predict the dynamic characteristics of such problems, specific numerical methods are required to accurately capture the shape of free surface. This paper proposed a new method which combined the Arbitrary Lagrangian-Eulerian (ALE technique with the Finite Volume Method (FVM to simulate the time-dependent viscoelastic free surface flows. Based on an open source CFD toolbox called OpenFOAM, we designed an ALE-FVM free surface simulation platform. In the meantime, the die-swell flow had been investigated with our proposed platform to make a further analysis of free surface phenomenon. The results validated the correctness and effectiveness of the proposed method for free surface simulation in both Newtonian fluid and viscoelastic fluid.

  5. Post-Newtonian Reference Frames For Advanced Theory Of The Lunar Motion And For A New Generation Of Lunar Laser Ranging

    International Nuclear Information System (INIS)

    Xie, Y.; Kopeikon, S.

    2010-01-01

    We overview a set of post-Newtonian reference frames for a comprehensive study of the orbital dynamics and rotational motion of Moon and Earth by means of lunar laser ranging (LLR). We employ a scalar-tensor theory of gravity depending on two post-Newtonian parameters, and , and utilize the relativistic resolutions on reference frames adopted by the International Astronomical Union (IAU) in 2000. We assume that the solar system is isolated and space-time is asymptotically flat at infinity. The primary reference frame covers the entire space-time, has its origin at the solar-system barycenter (SSB) and spatial axes stretching up to infinity. The SSB frame is not rotating with respect to a set of distant quasars that are forming the International Celestial Reference Frame (ICRF). The secondary reference frame has its origin at the Earth-Moon barycenter (EMB). The EMB frame is locally-inertial and is not rotating dynamically in the sense that equation of motion of a test particle moving with respect to the EMB frame, does not contain the Coriolis and centripetal forces. Two other local frames geocentric (GRF) and selenocentric (SRF) have their origins at the center of mass of Earth and Moon respectively and do not rotate dynamically. Each local frame is subject to the geodetic precession both with respect to other local frames and with respect to the ICRF because of their relative motion with respect to each other. Theoretical advantage of the dynamically non-rotating local frames is in a more simple mathematical description. Each local frame can be aligned with the axes of ICRF after applying the matrix of the relativistic precession. The set of one global and three local frames is introduced in order to fully decouple the relative motion of Moon with respect to Earth from the orbital motion of the Earth-Moon barycenter as well as to connect the coordinate description of the lunar motion, an observer on Earth, and a retro-reflector on Moon to directly measurable

  6. Post-Newtonian reference frames for advanced theory of the lunar motion and for a new generation of Lunar laser ranging

    International Nuclear Information System (INIS)

    Xie, Yi.; Kopeikin, S.

    2010-01-01

    We overview a set of post-Newtonian reference frames for a comprehensive study of the orbital dynamics and rotational motion of Moon and Earth by means of lunar laser ranging. We employ a scalar-tensor theory of gravity depending on two post-Newtonian parameters, and utilize the relativistic resolutions on reference frames adopted by the International Astronomical Union in 2000. We assume that the solar system is isolated and space-time is asymptotically flat at infinity. The primary reference frame covers the entire space-time, has its origin at the solar-system barycenter and spatial axes stretching up to infinity. The solar-system barycenter frame is not rotating with respect to a set of distant quasars that are forming the International Celestial Reference Frame. The secondary reference frame has its origin at the Earth-Moon barycenter. The Earth-Moon barycenter frame is locally-inertial and is not rotating dynamically in the sense that equation of motion of a test particle moving with respect to the Earth-Moon barycenter frame, does not contain the Coriolis and centripetal forces. Two other local frames-geocentric and seleno centric-have their origins at the center of mass of Earth and Moon respectively and do not rotate dynamically. Each local frame is subject to the geodetic precession both with respect to other local frames and with respect to the International Celestial Reference Frame because of their relative motion with respect to each other. Theoretical advantage of the dynamically non-rotating local frames is in a more simple mathematical description. Each local frame can be aligned with the axes of International Celestial Reference Frame after applying the matrix of the relativistic precession. The set of one global and three local frames is introduced in order to fully decouple the relative motion of Moon with respect to Earth from the orbital motion of the Earth-Moon barycenter as well as to connect the coordinate description of the lunar motion

  7. Magnetic particle translation as a surrogate measure for synovial fluid mechanics.

    Science.gov (United States)

    Shah, Yash Y; Maldonado-Camargo, Lorena; Patel, Neal S; Biedrzycki, Adam H; Yarmola, Elena G; Dobson, Jon; Rinaldi, Carlos; Allen, Kyle D

    2017-07-26

    The mechanics of synovial fluid vary with disease progression, but are difficult to quantify quickly in a clinical setting due to small sample volumes. In this study, a novel technique to measure synovial fluid mechanics using magnetic nanoparticles is introduced. Briefly, microspheres embedded with superparamagnetic iron oxide nanoparticles, termed magnetic particles, are distributed through a 100μL synovial fluid sample. Then, a permanent magnet inside a protective sheath is inserted into the synovial fluid sample. Magnetic particles translate toward the permanent magnet and the percentage of magnetic particles collected by the magnet in a given time can be related to synovial fluid viscosity. To validate this relationship, magnetic particle translation was demonstrated in three phases. First, magnetic particle translation was assessed in glycerol solutions with known viscosities, demonstrating that as fluid viscosity increased, magnetic particle translation decreased. Next, the relationship between magnetic particle translation and synovial fluid viscosity was assessed using bovine synovial fluid that was progressively degenerated via ultrasonication. Here, particle collection in a given amount of time increased as fluid degenerated, demonstrating that the relationship between particle collection and fluid mechanics holds in non-Newtonian synovial fluid. Finally, magnetic particle translation was used to assess differences between healthy and OA affected joints in equine synovial fluid. Here, particle collection in a given time was higher in OA joints relative to healthy horses (pfluid mechanics in limited volumes of synovial fluid sample. Copyright © 2017 Elsevier Ltd. All rights reserved.

  8. Modified Newtonian dynamics and the Coma cluster

    International Nuclear Information System (INIS)

    The, L.S.; White, S.D.M.

    1988-01-01

    The consistency of Milgrom's theory of modified Newtonian dynamics is checked against optical and X-ray data for the Coma cluster of galaxies. It is found that viable models for the cluster containing no dark matter can be constructed. They require an extensive gaseous atmosphere through which galaxies move on near-radial orbits. The gas temperature is predicted to have a shallow minimum near the cluster center; this structure may conflict with the best X-ray spectra of the cluster. 18 references

  9. Orbit classification in an equal-mass non-spinning binary black hole pseudo-Newtonian system

    Science.gov (United States)

    Zotos, Euaggelos E.; Dubeibe, F. L.; González, Guillermo A.

    2018-04-01

    The dynamics of a test particle in a non-spinning binary black hole system of equal masses is numerically investigated. The binary system is modeled in the context of the pseudo-Newtonian circular restricted three-body problem, such that the primaries are separated by a fixed distance and move in a circular orbit around each other. In particular, the Paczyński-Wiita potential is used for describing the gravitational field of the two non-Newtonian primaries. The orbital properties of the test particle are determined through the classification of the initial conditions of the orbits, using several values of the Jacobi constant, in the Hill's regions of possible motion. The initial conditions are classified into three main categories: (i) bounded, (ii) escaping and (iii) displaying close encounters. Using the smaller alignment index (SALI) chaos indicator, we further classify bounded orbits into regular, sticky or chaotic. To gain a complete view of the dynamics of the system, we define grids of initial conditions on different types of two-dimensional planes. The orbital structure of the configuration plane, along with the corresponding distributions of the escape and collision/close encounter times, allow us to observe the transition from the classical Newtonian to the pseudo-Newtonian regime. Our numerical results reveal a strong dependence of the properties of the considered basins with the Jacobi constant as well as with the Schwarzschild radius of the black holes.

  10. Parametrized tests of post-Newtonian theory using Advanced LIGO and Einstein Telescope

    International Nuclear Information System (INIS)

    Mishra, Chandra Kant; Arun, K. G.; Iyer, Bala R.; Sathyaprakash, B. S.

    2010-01-01

    General relativity has very specific predictions for the gravitational waveforms from inspiralling compact binaries obtained using the post-Newtonian (PN) approximation. We investigate the extent to which the measurement of the PN coefficients, possible with the second generation gravitational-wave detectors such as the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) and the third generation gravitational-wave detectors such as the Einstein Telescope (ET), could be used to test post-Newtonian theory and to put bounds on a subclass of parametrized-post-Einstein theories which differ from general relativity in a parametrized sense. We demonstrate this possibility by employing the best inspiralling waveform model for nonspinning compact binaries which is 3.5PN accurate in phase and 3PN in amplitude. Within the class of theories considered, Advanced LIGO can test the theory at 1.5PN and thus the leading tail term. Future observations of stellar mass black hole binaries by ET can test the consistency between the various PN coefficients in the gravitational-wave phasing over the mass range of 11-44M · . The choice of the lower frequency cutoff is important for testing post-Newtonian theory using the ET. The bias in the test arising from the assumption of nonspinning binaries is indicated.

  11. An experimental investigation of the dielectric properties of electrorheological fluids

    International Nuclear Information System (INIS)

    Sun, Y; Thomas, M; Masounave, J

    2009-01-01

    A home-made electrorheological (ER) fluid, known as ETSERF, has been created with suspension-based powders dispersed in silicone oil. Because of the special structure of their particles, ETSERF suspensions present a complex behavior. In the absence of an electric field, the ETSERF fluid manifests a near-Newtonian behavior, but when an electric field is applied, it exhibits a pseudoplastic behavior with yield stress. The ER effect under DC electric fields has been experimentally investigated using both hydrous and anhydrous ER fluids. The ER properties are strongly dependent on the dielectric properties of ETSERF suspensions, and hydrous ER fluids have a high dielectric constant and a high relaxation frequency which show a strong electrorheological effect. The relationship between the electrorheological effect and the permittivity of ER fluids has also been extensively studied. Experimental results show that the interfacial polarization plays an important role in the electrorheological phenomenon. The ageing of ETSERF fluids was also studied and it was found that the dielectric properties (mainly the dielectric loss tangent) and ER properties are strongly related to the duration of ageing. A fresh ETSERF suspension exhibits high relaxation frequency and high dielectric constant. These results are mainly explained by the effect of interfacial polarizations

  12. Exact solution of an electroosmotic flow for generalized Burgers fluid in cylindrical domain

    Directory of Open Access Journals (Sweden)

    Masood Khan

    Full Text Available The present paper reports a theoretical study of the dynamics of an electroosmotic flow (EOF in cylindrical domain. The Cauchy momentum equation is first simplified by incorporating the electrostatic body force in the electric double layer and the generalized Burgers fluid constitutive model. The electric potential distribution is given by the linearized Poisson–Boltzmann equation. After solving the linearized Poisson–Boltzmann equation, the Cauchy momentum equation with electrostatic body force is solved analytically by using the temporal Fourier and finite Hankel transforms. The effects of important involved parameters are examined and presented graphically. The results obtained reveal that the magnitude of velocity increases with increase of the Debye–Huckel and electrokinetic parameters. Further, it is shown that the results presented for generalized Burgers fluid are quite general so that results for the Burgers, Oldroyd-B, Maxwell and Newtonian fluids can be obtained as limiting cases. Keywords: Generalized Burgers fluid, Electroosmotic flow, Fourier and Hankel transform

  13. Five decades of tackling models for stiff fluid dynamics problems a scientific autobiography

    CERN Document Server

    Zeytounian, Radyadour Kh

    2014-01-01

    Rationality - as opposed to 'ad-hoc' - and asymptotics - to emphasize the fact that perturbative methods are at the core of the theory - are the two main concepts associated with the Rational Asymptotic Modeling (RAM) approach in fluid dynamics when the goal is to specifically provide useful models accessible to numerical simulation via high-speed computing. This approach has contributed to a fresh understanding of Newtonian fluid flow problems and has opened up new avenues for tackling real fluid flow phenomena, which are known to lead to very difficult mathematical and numerical problems irrespective of turbulence. With the present scientific autobiography the author guides the reader through his somewhat non-traditional career; first discovering fluid mechanics, and then devoting more than fifty years to intense work in the field. Using both personal and general historical contexts, this account will be of benefit to anyone interested in the early and contemporary developments of an important branch of the...

  14. Unsteady Mixed Convection Boundary Layer from a Circular Cylinder in a Micropolar Fluid

    Directory of Open Access Journals (Sweden)

    Anati Ali

    2010-01-01

    Full Text Available Most industrial fluids such as polymers, liquid crystals, and colloids contain suspensions of rigid particles that undergo rotation. However, the classical Navier-Stokes theory normally associated with Newtonian fluids is inadequate to describe such fluids as it does not take into account the effects of these microstructures. In this paper, the unsteady mixed convection boundary layer flow of a micropolar fluid past an isothermal horizontal circular cylinder is numerically studied, where the unsteadiness is due to an impulsive motion of the free stream. Both the assisting (heated cylinder and opposing cases (cooled cylinder are considered. Thus, both small and large time solutions as well as the occurrence of flow separation, followed by the flow reversal are studied. The flow along the entire surface of a cylinder is solved numerically using the Keller-box scheme. The obtained results are compared with the ones from the open literature, and it is shown that the agreement is very good.

  15. Physics of Life: A Model for Non-Newtonian Properties of Living Systems

    Science.gov (United States)

    Zak, Michail

    2010-01-01

    This innovation proposes the reconciliation of the evolution of life with the second law of thermodynamics via the introduction of the First Principle for modeling behavior of living systems. The structure of the model is quantum-inspired: it acquires the topology of the Madelung equation in which the quantum potential is replaced with the information potential. As a result, the model captures the most fundamental property of life: the progressive evolution; i.e. the ability to evolve from disorder to order without any external interference. The mathematical structure of the model can be obtained from the Newtonian equations of motion (representing the motor dynamics) coupled with the corresponding Liouville equation (representing the mental dynamics) via information forces. All these specific non-Newtonian properties equip the model with the levels of complexity that matches the complexity of life, and that makes the model applicable for description of behaviors of ecological, social, and economical systems. Rather than addressing the six aspects of life (organization, metabolism, growth, adaptation, response to stimuli, and reproduction), this work focuses only on biosignature ; i.e. the mechanical invariants of life, and in particular, the geometry and kinematics of behavior of living things. Living things obey the First Principles of Newtonian mechanics. One main objective of this model is to extend the First Principles of classical physics to include phenomenological behavior on living systems; to develop a new mathematical formalism within the framework of classical dynamics that would allow one to capture the specific properties of natural or artificial living systems such as formation of the collective mind based upon abstract images of the selves and non-selves; exploitation of this collective mind for communications and predictions of future expected characteristics of evolution; and for making decisions and implementing the corresponding corrections if

  16. The significance of Newtonian cosmology

    International Nuclear Information System (INIS)

    Galletto, D.; Barberis, B.

    1984-01-01

    Starting from the hypotheses that the physical space is Euclidean, that the Universe is infinite and homogeneous and that with regard to our galaxy its behaviour is isotropic, without resorting to Newton's law of gravitation we deduce Hubble's law, the law of motion of a typical galaxy, the equation of evolution of the Universe, that the force at a distance exerted between any two galaxies is expressed by Newton's law of gravitation, etc. Adding the hypothesis that the velocity of light is independent of its source, we obtain that the metric of spacetime is necessarily given by the Einstein-de Sitter metric, that the tensorial form of the equations of Newtonian cosmology is given by Einstein's gravitational equations, etc. (Auth.)

  17. Steady flow and heat transfer analysis of Phan-Thein-Tanner fluid in double-layer optical fiber coating analysis with Slip Conditions.

    Science.gov (United States)

    Khan, Zeeshan; Shah, Rehan Ali; Islam, Saeed; Jan, Bilal; Imran, Muhammad; Tahir, Farisa

    2016-10-06

    Modern optical fibers require double-layer coating on the glass fiber to provide protection from signal attenuation and mechanical damage. The most important plastic resins used in wires and optical fibers are plastic polyvinyl chloride (PVC) and low-high density polyethylene (LDPE/HDPE), nylon and Polysulfone. In this paper, double-layer optical fiber coating is performed using melt polymer satisfying PTT fluid model in a pressure type die using wet-on-wet coating process. The assumption of fully developed flow of Phan-Thien-Tanner (PTT) fluid model, two-layer liquid flows of an immiscible fluid is modeled in an annular die, where the fiber is dragged at a higher speed. The equations characterizing the flow and heat transfer phenomena are solved exactly and the effects of emerging parameters (Deborah and slip parameters, characteristic velocity, radii ratio and Brinkman numbers on the axial velocity, flow rate, thickness of coated fiber optics, and temperature distribution) are reported in graphs. It is shown that an increase in the non-Newtonian parameters increase the velocity in the absence or presence of slip parameters which coincides with related work. The comparison is done with experimental work by taking λ → 0 (non-Newtonian parameter).

  18. Unsteady MHD free convection flow of casson fluid over an inclined vertical plate embedded in a porous media

    Science.gov (United States)

    Manideep, P.; Raju, R. Srinivasa; Rao, T. Siva Nageswar; Reddy, G. Jithender

    2018-05-01

    This paper deals, an unsteady magnetohydrodynamic heat transfer natural convection flow of non-Newtonian Casson fluid over an inclined vertical plate embedded in a porous media with the presence of boundary conditions such as oscillating velocity, constant wall temperature. The governing dimensionless boundary layer partial differential equations are reduced to simultaneous algebraic linear equation for velocity, temperature of Casson fluid through finite element method. Those equations are solved by Thomas algorithm after imposing the boundary conditions through MATLAB for analyzing the behavior of Casson fluid velocity and temperature with various physical parameters. Also analyzed the local skin-friction and rate of heat transfer. Compared the present results with earlier reported studies, the results are comprehensively authenticated and robust FEM.

  19. Non-Newtonian plastic flow of a Ni-Si-B metallic glass at low stresses

    International Nuclear Information System (INIS)

    Csach, K.; Fursova, Y.V.; Khonik, V.A.; Ocelik, V.

    1998-01-01

    The problem of the rheological behavior of metallic glasses (MGs) is quite important both from theoretical and practical viewpoints. Early experiments carried out on MGs at temperatures T > 300 K using low shear stress levels revealed plastic flow to be Newtonian while measurements at relative high shear stresses (more than 200 to 400 MPa, depending on temperature, thermal prehistory of samples and chemical composition) indicated a non-linear behavior with 1 < m < 12. Numerous investigations performed later both on as-cast and relaxed MGs of various chemical compositions using a number of testing methods (tensile creep, tensile and bend stress relaxation) showed that a transition from Newtonian behavior at low stresses to a non-linear flow at high stresses was observed. At present, such a situation is considered to be generally accepted. The authors performed precise creep measurements of a Ni-Si-B metallic glass. The results obtained indicate that plastic flow in this case at low tensile stress (12 le σ le 307 MPa) is clearly non-Newtonian and, consequently, the viscosity is stress dependent

  20. Dynamics of continua and particles from general covariance of Newtonian gravitation theory

    International Nuclear Information System (INIS)

    Duval, C.; Kunzle, H.P.

    1976-07-01

    The principle of general covariance, which states that the total action functional in General Relativity is independent of coordinate transformations, is shown to be also applicable to the four-dimensional geometric theory of Newtonian gravitation. It leads to the correct conservation (or balance) equations of continuum mechanics as well as the equations of motion of test particles in a gravitational field. The degeneracy of the ''metric'' of Newtonian space-time forces to introduce a ''gauge field'' which fixes the connection and leads to a conserved current, the mass flow. The particle equations are also derived from an invariant Hamiltonian structure on the extended Galilei group and a minimal interaction principle. One not only finds the same equations of motion but even the same gauge fields

  1. Evaluation of magnetorheological fluid augmented fabric as a fragment barrier material

    International Nuclear Information System (INIS)

    Son, Kwon Joong; Fahrenthold, Eric P

    2012-01-01

    The augmentation of high strength fabrics with non-Newtonian fluids has been suggested as a means for improving the ballistic performance of fragment barrier materials widely used in fan blade containment, body armor, orbital debris shielding, and other applications. Magnetorheological (MR) fluids have attracted particular interest, in view of their controllability and proven effectiveness in a variety of damping applications. In a basic research investigation of the MR fluid augmented fabric barrier concept, the authors have fabricated MR fluid saturated Kevlar targets and measured the ballistic performance of these targets both with and without an applied magnetic field. The experimental results show that magnetization of the MR fluid does, when considered in isolation, improve the ability of the augmented fabric to absorb impact energy. However, the benefits of plastic and viscous energy dissipation in the magnetized semi-solid are more than offset by the detrimental effects of yarn lubrication associated with the fluid’s hydrocarbon carrier. An analytical model developed to assist in the interpretation of the experimental data suggests that frictional interaction of the yarns is significantly more effective than magnetorheological augmentation of the fabric in distributing projectile loads away from the point of impact. (paper)

  2. Spin and Madelung fluid

    International Nuclear Information System (INIS)

    Salesi, G.

    1995-07-01

    Starting from the Pauli current the decomposition of the non-relativistic local velocity has been obtained in two parts (in the ordinary tensorial language): one parallel and the other orthogonal to the impulse. The former is recognized to be the classical part, that is, the center-of-mass (CM) velocity, and the latter the quantum one, that is, the velocity of the motion in the CM frame (namely, the internal spin motion or Zitterbewegung). Inserting this complete, composite expression of the velocity into the kinetic energy term of the classical non-relativistic (i.e. Newtonian) Lagrangian, the author straightforwardly get the appearance of the so called quantum potential associates as it is known, to the Madelung fluid. In such a way, the quantum mechanical behaviour of particles appears to be strictly correlated to the existence of spin and Zitterbewegung

  3. Fractional Flow Theory Applicable to Non-Newtonian Behavior in EOR Processes

    NARCIS (Netherlands)

    Rossen, W.R.; Venkatraman, A.; Johns, R.T.; Kibodeaux, K.R.; Lai, H.; Moradi Tehrani, N.

    2011-01-01

    The method of characteristics, or fractional-flow theory, is extremely useful in understanding complex Enhanced Oil Recovery (EOR) processes and in calibrating simulators. One limitation has been its restriction to Newtonian rheology except in rectilinear flow. Its inability to deal with

  4. The flow of a non-Newtonian fluid induced due to the oscillations of a porous plate

    Directory of Open Access Journals (Sweden)

    S. Asghar

    2004-01-01

    Full Text Available An analytic solution of the flow of a third-grade fluid on a porous plate is constructed. The porous plate is executing oscillations in its own plane with superimposed injection or suction. An increasing or decreasing velocity amplitude of the oscillating porous plate is also examined. It is also shown that in case of third-grade fluid, a combination of suction/injection and decreasing/increasing velocity amplitude is possible as well. Several limiting situations with their implications are given and discussed.

  5. Effect of Carreau-Yasuda rheological parameters on subcritical Lapwood convection in horizontal porous cavity saturated by shear-thinning fluid

    Science.gov (United States)

    Khechiba, Khaled; Mamou, Mahmoud; Hachemi, Madjid; Delenda, Nassim; Rebhi, Redha

    2017-06-01

    The present study is focused on Lapwood convection in isotropic porous media saturated with non-Newtonian shear thinning fluid. The non-Newtonian rheological behavior of the fluid is modeled using the general viscosity model of Carreau-Yasuda. The convection configuration consists of a shallow porous cavity with a finite aspect ratio and subject to a vertical constant heat flux, whereas the vertical walls are maintained impermeable and adiabatic. An approximate analytical solution is developed on the basis of the parallel flow assumption, and numerical solutions are obtained by solving the full governing equations. The Darcy model with the Boussinesq approximation and energy transport equations are solved numerically using a finite difference method. The results are obtained in terms of the Nusselt number and the flow fields as functions of the governing parameters. A good agreement is obtained between the analytical approximation and the numerical solution of the full governing equations. The effects of the rheological parameters of the Carreau-Yasuda fluid and Rayleigh number on the onset of subcritical convection thresholds are demonstrated. Regardless of the aspect ratio of the enclosure and thermal boundary condition type, the subcritical convective flows are seen to occur below the onset of stationary convection. Correlations are proposed to estimate the subcritical Rayleigh number for the onset of finite amplitude convection as a function of the fluid rheological parameters. Linear stability of the convective motion, predicted by the parallel flow approximation, is studied, and the onset of Hopf bifurcation, from steady convective flow to oscillatory behavior, is found to depend strongly on the rheological parameters. In general, Hopf bifurcation is triggered earlier as the fluid becomes more and more shear-thinning.

  6. Harmonic oscillations of a circular cylinder moving with constant velocity in a quiescent fluid

    OpenAIRE

    Jan Novaes Recica; Luiz Antonio Alcântara Pereira; Miguel Hiroo Hirata

    2008-01-01

    The flow around an oscillating circular cylinder which moves with constant velocity in a quiescent Newtonian fluid with constant properties is analyzed. The influences of the frequency and amplitude oscillation on the aerodynamic loads and on the Strouhal number are presented. For the numerical simulation, a cloud of discrete Lamb vortices are utilized. For each time step of the simulation, a number of discrete vortices are placed close to the body surface; the intensity of theirs is determin...

  7. Non linear thermal radiation effect on Williamson fluid with particle-liquid suspension past a stretching surface

    Directory of Open Access Journals (Sweden)

    K. Ganesh Kumar

    Full Text Available A mathematical analysis of two-phase boundary layer flow and heat transfer of a Williamson fluid with fluid particle suspension over a stretching sheet has been carried out in this paper. The region of temperature jump and nonlinear thermal radiation is considered in the energy transfer process. The principal equations of boundary layer flow and temperature transmission are reformed to a set of non-linear ordinary differential equations under suitable similarity transformations. The transfigured equalities are solved numerically with the help of RKF-45 order method. The effect of influencing parameters on velocity and temperature transfer of fluid is examined and deliberated by plotted graphs and tabulated values. Significances of the mass concentration of dust particle parameter play a key role in controlling flow and thermal behavior of non-Newtonian fluids. Further, the temperature and concern boundary layer girth are declines for increasing values of Williamson parameter. Keywords: Two-phase flow, Williamson fluid, Nonlinear thermal radiation, Magnetic field, Temperature jump

  8. Exact Solutions for Unsteady Free Convection Flow of Casson Fluid over an Oscillating Vertical Plate with Constant Wall Temperature

    Directory of Open Access Journals (Sweden)

    Asma Khalid

    2015-01-01

    Full Text Available The unsteady free flow of a Casson fluid past an oscillating vertical plate with constant wall temperature has been studied. The Casson fluid model is used to distinguish the non-Newtonian fluid behaviour. The governing partial differential equations corresponding to the momentum and energy equations are transformed into linear ordinary differential equations by using nondimensional variables. Laplace transform method is used to find the exact solutions of these equations. Expressions for shear stress in terms of skin friction and the rate of heat transfer in terms of Nusselt number are also obtained. Numerical results of velocity and temperature profiles with various values of embedded flow parameters are shown graphically and their effects are discussed in detail.

  9. Instrumentation to Monitor Transient Periodic Developing Flow in Non-Newtonian Slurries

    Energy Technology Data Exchange (ETDEWEB)

    Bamberger, Judith A.; Enderlin, Carl W.

    2013-11-15

    Staff at Pacific Northwest National Laboratory have conducted mixing and mobilization experiments with non-Newtonian slurries that exhibit Bingham plastic and shear thinning behavior and shear strength. This paper describes measurement techniques applied to identify the interface between flowing and stationary regions of non-Newtonian slurries that are subjected to transient, periodic, developing flows. Techniques were developed to identify the boundary between the flowing and stationary regions, time to mix, characteristic velocities of the flow field produced by the symmetrically spaced nozzles, and the velocity of the upwell formed in the center of the tank by the intersection of flow from four symmetrically spaced nozzles that impinge upon the tank floor. Descriptions of the instruments and instrument performance are presented. These techniques were an effective approach to characterize mixing phenomena, determine mixing energy required to fully mobilize vessel contents and to determine mixing times for process evaluation.

  10. Experimental study and CFD simulation of rotational eccentric cylinder in a magnetorheological fluid

    Science.gov (United States)

    Omidbeygi, F.; Hashemabadi, S. H.

    2012-07-01

    In this study, a magnetorheological (MR) fluid is prepared using carbonyl iron filings and low viscosity lubricating oil. The effects of magnetic field and weight percentage of particles on the viscosity of the MR fluid have been measured using a rotational viscometer. The yield stress under an applied magnetic field was also obtained experimentally. In the absence of an applied magnetic field, the MR fluid behaves as a Newtonian fluid. When the magnetic field is applied, the MR fluid behaves like Bingham plastics with a magnetic field dependent yield stress. Afterward, the results compared with those of CFD simulation of two eccentric cylinders in the MR fluid. Results show that the influences of MR effects, caused by the applied magnetic field, on the model characteristics are significant and not negligible. The viscosity is enhanced by increasing of the magnetic field, eccentricity ratio and weight percentage of suspensions. The MR effects and increasing of weight percentage and eccentricity ratio also provide an enhancement in the yield stresses and required total torque for rotation of inner cylinder. Also the simulation results indicate a good representation of the experiment by the model.

  11. Flutter and divergence instability of supported piezoelectric nanotubes conveying fluid

    Science.gov (United States)

    Bahaadini, Reza; Hosseini, Mohammad; Jamali, Behnam

    2018-01-01

    In this paper, divergence and flutter instabilities of supported piezoelectric nanotubes containing flowing fluid are investigated. To take the size effects into account, the nonlocal elasticity theory is implemented in conjunction with the Euler-Bernoulli beam theory incorporating surface stress effects. The Knudsen number is applied to investigate the slip boundary conditions between the flow and wall of nanotube. The nonlocal governing equations of nanotube are obtained using Newtonian method, including the influence of piezoelectric voltage, surface effects, Knudsen number and nonlocal parameter. Applying Galerkin approach to transform resulting equations into a set of eigenvalue equations under the simple-simple (S-S) and clamped-clamped (C-C) boundary conditions. The effects of the piezoelectric voltage, surface effects, Knudsen number, nonlocal parameter and boundary conditions on the divergence and flutter boundaries of nanotubes are discussed. It is observed that the fluid-conveying nanotubes with both ends supported lose their stability by divergence first and then by flutter with increase in fluid velocity. Results indicate the importance of using piezoelectric voltage, nonlocal parameter and Knudsen number in decrease of critical flow velocities of system. Moreover, the surface effects have a significant role on the eigenfrequencies and critical fluid velocity.

  12. Student Misconceptions about Newtonian Mechanics: Origins and Solutions through Changes to Instruction

    Science.gov (United States)

    Adair, Aaron Michael

    In order for Physics Education Research (PER) to achieve its goals of significant learning gains with efficient methods, it is necessary to figure out what are the sorts of preexisting issues that students have prior to instruction and then to create teaching methods that are best able to overcome those problems. This makes it necessary to figure out what is the nature of student physics misconceptions---prior beliefs that are both at variance to Newtonian mechanics and also prevent a student from properly cognizing Newtonian concepts. To understand the prior beliefs of students, it is necessary to uncover their origins, which may allow instructors to take into account the sources for ideas of physics that are contrary to Newtonian mechanics understanding. That form of instruction must also induce the sorts of metacognitive processes that allow students to transition from their previous conceptions to Newtonian ones, let alone towards those of modern physics. In this paper, the notions of basic dynamics that are common among first-year college students are studied and compared with previous literature. In particular, an analysis of historical documents from antiquity up to the early modern period shows that these conceptions were rather widespread and consistent over thousands of years and in numerous cultural contexts. This is one of the only analyses in PER that considers the original languages of some of these texts, along with appropriate historical scholarship. Based on the consistent appearance of these misconceptions, a test and interview module was devised to help elucidate the feelings students have that may relate to fictitious forces. The test looked at one-dimensional motion and forces. The first part of the interview asked each student about their answers to the test questions, while the second part asked how students felt when undergoing three cases of constant acceleration in a car. We determined that students confabulated relative motion with the

  13. Review Of Applied Mathematical Models For Describing The Behaviour Of Aqueous Humor In Eye Structures

    Science.gov (United States)

    Dzierka, M.; Jurczak, P.

    2015-12-01

    In the paper, currently used methods for modeling the flow of the aqueous humor through eye structures are presented. Then a computational model based on rheological models of Newtonian and non-Newtonian fluids is proposed. The proposed model may be used for modeling the flow of the aqueous humor through the trabecular meshwork. The trabecular meshwork is modeled as an array of rectilinear parallel capillary tubes. The flow of Newtonian and non-Newtonian fluids is considered. As a results of discussion mathematical equations of permeability of porous media and velocity of fluid flow through porous media have been received.

  14. Steady Flow of a Second-Grade Fluid in an Annulus with Porous Walls

    Directory of Open Access Journals (Sweden)

    M. Emin Erdoğan

    2008-01-01

    Full Text Available An exact solution of an incompressible second-grade fluid for flow between two coaxial cylinders with porous walls is given. It is assumed that the inner cylinder is rotating with a constant angular velocity and the outer one is at rest. The solution is expressed in terms of the confluent hypergeometric functions and it is valid for all values of the cross-Reynolds number and the elastic number. The solutions for −2, +∞, and −∞ values of the cross-Reynolds number are obtained and a comparison with those of the Newtonian fluid is given. Furthermore, the torque exerted by the fluid on the inner cylinder is calculated. It is shown that the moment coefficient depends on the cross-Reynolds number, the elastic number, and the ratio of the radii of the cylinders. The variation of the moment coefficient with these numbers is discussed.

  15. Effects of electric field and Coriolis force on electrohydrodynamic stability of poorly conducting couple stress parallel fluid flow in a channel

    International Nuclear Information System (INIS)

    Shankar, B.M.; Rudraiah, N.

    2013-01-01

    The linear stability of electrohydrodynamic poorly conducting couple stress viscous parallel fluid flow in a channel is studied in the presence of a non-uniform transverse electric field and Coriolis force using energy method and supplemented with Galerkin Technique. The sufficient condition for stability is obtained for sufficiently small values of the Reynolds number, R e . From this condition we show that strengthening or weakening of the stability criterion is dictated by the values of the strength of electric field, the coefficient of couple stress fluid and independent of Taylor number. In particular, it is shown that the interaction of electric field with couple stress is more effective in stabilizing the poorly conducting couple stress fluid compared to that in an ordinary Newtonian viscous fluid. (author)

  16. Non-newtonian deformation of co-based metallic glass at low stresses

    NARCIS (Netherlands)

    Fursova, YV; Khonik, VA; Csach, K; Ocelik, Vaclav

    2000-01-01

    The results of precision measurements of creep in Co-based metallic glass are presented. It is shown that, in spite of generally accepted concepts, plastic flow at low stresses under intense structural relaxation conditions is of a non-Newtonian type. Consequences of this fact are considered. (C)

  17. Study of blades inclination influence of gate impeller with a non-Newtonian fluid of Bingham

    Directory of Open Access Journals (Sweden)

    Rahmani Lakhdar

    2016-01-01

    Full Text Available A large number of chemical operations, biochemical or petrochemical industry is very depending on the rheological fluids nature. In this work, we study the case of highly viscous of viscoplastic fluids in a classical system of agitation: a cylindrical tank with plate bottom without obstacles agitated by gate impeller agitator. We are interested to the laminar, incompressible and isothermal flows. We devote to a numerical approach carried out using an industrial code CFD Fluent 6.3.26 based on the method of finites volumes discretization of Navier - Stokes equations formulated in variables (U.V.P. The threshold of flow related to the viscoplastic behavior is modeled by a theoretical law of Bingham. The results obtained are used to compare between the five configurations suggested of power consumption. We study the influence of inertia by the variation of Reynolds number.

  18. The Transient Elliptic Flow of Power-Law Fluid in Fractal Porous Media

    Institute of Scientific and Technical Information of China (English)

    宋付权; 刘慈群

    2002-01-01

    The steady oil production and pressure distribution formulae of vertically fractured well for power-law non-Newtonian fluid were derived on the basis of the elliptic flow model in fractal reservoirs. The corresponding transient flow in fractal reservoirs was studied by numerical differentiation method: the influence of fractal index to transient pressure of vertically fractured well was analyzed. Finally the approximate analytical solution of transient flow was given by average mass conservation law. The study shows that using elliptic flow method to analyze the flow of vertically fractured well is a simple method.

  19. Constraint on the post-Newtonian parameter γ on galactic size scales

    International Nuclear Information System (INIS)

    Bolton, Adam S.; Rappaport, Saul; Burles, Scott

    2006-01-01

    We constrain the post-Newtonian gravity parameter γ on kiloparsec scales by comparing the masses of 15 elliptical lensing galaxies from the Sloan Lens ACS Survey as determined in two independent ways. The first method assumes only that Newtonian gravity is correct and is independent of γ, while the second uses gravitational lensing which depends on γ. More specifically, we combine Einstein radii and radial surface-brightness gradient measurements of the lens galaxies with empirical distributions for the mass concentration and velocity anisotropy of elliptical galaxies in the local universe to predict γ-dependent probability distributions for the lens-galaxy velocity dispersions. By comparing with observed velocity dispersions, we derive a maximum-likelihood value of γ=0.98±0.07 (68% confidence). This result is in excellent agreement with the prediction of general relativity that γ=1, which has previously been verified to this accuracy only on solar-system length scales

  20. Hereditary effects in eccentric compact binary inspirals to third post-Newtonian order

    Science.gov (United States)

    Loutrel, Nicholas; Yunes, Nicolás

    2017-02-01

    While there has been much success in understanding the orbital dynamics and gravitational wave emission of eccentric compact binaries in the post-Newtonian formalism, some problems still remain. The largest of these concerns hereditary effects: non-linear phenomena related to the scattering off of the background curved spacetime (tails) and to the generation of gravitational waves by gravitational waves (memory). Currently, these hereditary effects are only known numerically for arbitrary eccentricity through infinite sums of Bessel functions, with closed-form, analytic results only available in the small eccentricity limit. We here calculate, for the first time, closed-form, analytic expressions for all hereditary effects to third post-Newtonian order in binaries with arbitrary eccentricity. For the tails, we first asymptotically expand all Bessel functions in high eccentricity and find a superasymptotic series for each enhancement factor, accurate to better than 10-3 relative to post-Newtonian numerical calculations at all eccentricities. We further improve the small-eccentricity behavior of the superasymptotic series by generating hyperasymptotic expressions for each enhancement factor, typically accurate to better than 10-8 at all eccentricities. For the memory, we discuss its computation within the context of an osculating approximation of the binary’s orbit and the difficulties that arise. Our closed-form analytic expressions for the hereditary fluxes allow us to numerically compute orbital phases that are identical to those found using an infinite sum of Bessel functions to double numerical precision.

  1. Hereditary effects in eccentric compact binary inspirals to third post-Newtonian order

    International Nuclear Information System (INIS)

    Loutrel, Nicholas; Yunes, Nicolás

    2017-01-01

    While there has been much success in understanding the orbital dynamics and gravitational wave emission of eccentric compact binaries in the post-Newtonian formalism, some problems still remain. The largest of these concerns hereditary effects: non-linear phenomena related to the scattering off of the background curved spacetime (tails) and to the generation of gravitational waves by gravitational waves (memory). Currently, these hereditary effects are only known numerically for arbitrary eccentricity through infinite sums of Bessel functions, with closed-form, analytic results only available in the small eccentricity limit. We here calculate, for the first time, closed-form, analytic expressions for all hereditary effects to third post-Newtonian order in binaries with arbitrary eccentricity. For the tails, we first asymptotically expand all Bessel functions in high eccentricity and find a superasymptotic series for each enhancement factor, accurate to better than 10 −3 relative to post-Newtonian numerical calculations at all eccentricities. We further improve the small-eccentricity behavior of the superasymptotic series by generating hyperasymptotic expressions for each enhancement factor, typically accurate to better than 10 −8 at all eccentricities. For the memory, we discuss its computation within the context of an osculating approximation of the binary’s orbit and the difficulties that arise. Our closed-form analytic expressions for the hereditary fluxes allow us to numerically compute orbital phases that are identical to those found using an infinite sum of Bessel functions to double numerical precision. (paper)

  2. Initial value gravitational quadrupole radiation theorem

    International Nuclear Information System (INIS)

    Winicour, J.

    1987-01-01

    A rigorous version of the quadrupole radiation formula is derived using the characteristic initial value formulation of a general relativistic fluid space-time. Starting from initial data for a Newtonian fluid, an algorithm is presented that determines characteristic initial data for a one-parameter family of general relativistic fluid space-times. At the initial time, a one-parameter family of space-times with this initial data osculates the evolution of the Newtonian fluid and has leading order news function equal to the third time derivative of the transverse Newtonian quadrupole moment

  3. Towards a first design of a Newtonian-noise cancellation system for Advanced LIGO

    International Nuclear Information System (INIS)

    Coughlin, M; Mukund, N; Mitra, S; Harms, J; Driggers, J; Adhikari, R

    2016-01-01

    Newtonian gravitational noise from seismic fields is predicted to be a limiting noise source at low frequency for second generation gravitational-wave detectors. Mitigation of this noise will be achieved by Wiener filtering using arrays of seismometers deployed in the vicinity of all test masses. In this work, we present optimized configurations of seismometer arrays using a variety of simplified models of the seismic field based on seismic observations at LIGO Hanford. The model that best fits the seismic measurements leads to noise reduction limited predominantly by seismometer self-noise. A first simplified design of seismic arrays for Newtonian-noise cancellation at the LIGO sites is presented, which suggests that it will be sufficient to monitor surface displacement inside the buildings. (paper)

  4. Newtonian liquid jet impaction on a high-speed moving surface

    International Nuclear Information System (INIS)

    Keshavarz, B.; Green, S.I.; Davy, M.H.; Eadie, D.T.

    2011-01-01

    Highlights: ► We studied experimentally the interaction of a liquid jet with a moving surface. ► Decreasing the Reynolds number reduced the incidence of splash. ► The Weber number had a much smaller impact on splash than the Reynolds number. ► The jet impingement angle had only a small effect on the splash. ► Increasing the surface roughness substantially decreased the splash threshold. - Abstract: In the railroad industry a friction modifying agent may be applied to the rail or wheel in the form of a liquid jet. In this mode of application the interaction between the high-speed liquid jet and a fast moving surface is important. Seven different Newtonian liquids with widely varying shear viscosities were tested to isolate the effect of viscosity from other fluid properties. Tests were also done on five surfaces of different roughness heights to investigate the effects of surface roughness. High-speed video imaging was employed to scrutinize the interaction between the impacting jet and the moving surface. For all surfaces, decreasing the Reynolds number reduced the incidence of splash and consequently enhanced the transfer efficiency. At the elevated Weber numbers of the testing, the Weber number had a much smaller impact on splash than the Reynolds number. The ratio of the surface velocity to the jet velocity has only a small effect on the splash, whereas increasing the roughness-height-to-jet-diameter ratio substantially decreased the splash threshold.

  5. Analytical solution for pulsatile viscous flow in a straight elliptic annulus and application to the motion of the cerebrospinal fluid

    Science.gov (United States)

    Gupta, Sumeet; Poulikakos, Dimos; Kurtcuoglu, Vartan

    2008-09-01

    We present here the analytical solution of transient, laminar, viscous flow of an incompressible, Newtonian fluid driven by a harmonically oscillating pressure gradient in a straight elliptic annulus. The analytical formulation is based on the exact solution of the governing fluid flow equations known as Navier-Stokes equations. We validate the analytical solution using a finite-volume computational fluid dynamics approach. As the analytical solution includes Mathieu and modified Mathieu functions, we also present a stepwise procedure for their evaluation for large complex arguments typically associated with viscous flows. We further outline the procedure for evaluating the associated Fourier coefficients and their eigenvalues. We finally apply the analytical solution to investigate the cerebrospinal fluid flow in the human spinal cavity, which features a shape similar to an elliptic annulus.

  6. Two-fluid model for locomotion under self-confinement

    Science.gov (United States)

    Reigh, Shang Yik; Lauga, Eric

    2017-09-01

    The bacterium Helicobacter pylori causes ulcers in the stomach of humans by invading mucus layers protecting epithelial cells. It does so by chemically changing the rheological properties of the mucus from a high-viscosity gel to a low-viscosity solution in which it may self-propel. We develop a two-fluid model for this process of swimming under self-generated confinement. We solve exactly for the flow and the locomotion speed of a spherical swimmer located in a spherically symmetric system of two Newtonian fluids whose boundary moves with the swimmer. We also treat separately the special case of an immobile outer fluid. In all cases, we characterize the flow fields, their spatial decay, and the impact of both the viscosity ratio and the degree of confinement on the locomotion speed of the model swimmer. The spatial decay of the flow retains the same power-law decay as for locomotion in a single fluid but with a decreased magnitude. Independent of the assumption chosen to characterize the impact of confinement on the actuation applied by the swimmer, its locomotion speed always decreases with an increase in the degree of confinement. Our modeling results suggest that a low-viscosity region of at least six times the effective swimmer size is required to lead to swimming with speeds similar to locomotion in an infinite fluid, corresponding to a region of size above ≈25 μ m for Helicobacter pylori.

  7. Extrema principles of entrophy production and energy dissipation in fluid mechanics

    Science.gov (United States)

    Horne, W. Clifton; Karamcheti, Krishnamurty

    1988-01-01

    A survey is presented of several extrema principles of energy dissipation as applied to problems in fluid mechanics. An exact equation is derived for the dissipation function of a homogeneous, isotropic, Newtonian fluid, with terms associated with irreversible compression or expansion, wave radiation, and the square of the vorticity. By using entropy extrema principles, simple flows such as the incompressible channel flow and the cylindrical vortex are identified as minimal dissipative distributions. The principal notions of stability of parallel shear flows appears to be associated with a maximum dissipation condition. These different conditions are consistent with Prigogine's classification of thermodynamic states into categories of equilibrium, linear nonequilibrium, and nonlinear nonequilibrium thermodynamics; vortices and acoustic waves appear as examples of dissipative structures. The measurements of a typical periodic shear flow, the rectangular wall jet, show that direct measurements of the dissipative terms are possible.

  8. Simple Navier’s slip boundary condition for the non-Newtonian Lattice Boltzmann fluid dynamics solver

    DEFF Research Database (Denmark)

    Svec, Oldrich; Skoček, Jan

    2013-01-01

    The ability of the Lattice Boltzmann method, as the fluid dynamics solver, to properly simulate macroscopic Navier’s slip boundary condition is investigated. An approximate equation relating the Lattice Boltzmann variable slip boundary condition with the macroscopic Navier’s slip boundary condition...

  9. Effect of viscosity on tear drainage and ocular residence time.

    Science.gov (United States)

    Zhu, Heng; Chauhan, Anuj

    2008-08-01

    An increase in residence time of dry eye medications including artificial tears will likely enhance therapeutic benefits. The drainage rates and the residence time of eye drops depend on the viscosity of the instilled fluids. However, a quantitative understanding of the dependence of drainage rates and the residence time on viscosity is lacking. The current study aims to develop a mathematical model for the drainage of Newtonian fluids and also for power-law non-Newtonian fluids of different viscosities. This study is an extension of our previous study on the mathematical model of tear drainage. The tear drainage model is modified to describe the drainage of Newtonian fluids with viscosities higher than the tear viscosity and power-law non-Newtonian fluids with rheological parameters obtained from fitting experimental data in literature. The drainage rate through canaliculi was derived from the modified drainage model and was incorporated into a tear mass balance to calculate the transients of total solute quantity in ocular fluids and the bioavailability of instilled drugs. For Newtonian fluids, increasing the viscosity does not affect the drainage rate unless the viscosity exceeds a critical value of about 4.4 cp. The viscosity has a maximum impact on drainage rate around a value of about 100 cp. The trends are similar for shear thinning power law fluids. The transients of total solute quantity, and the residence time agrees at least qualitatively with experimental studies. A mathematical model has been developed for the drainage of Newtonian fluids and power-law fluids through canaliculi. The model can quantitatively explain different experimental observations on the effect of viscosity on the residence of instilled fluids on the ocular surface. The current study is helpful for understanding the mechanism of fluid drainage from the ocular surface and for improving the design of dry eye treatments.

  10. The Boundary Layer Flows of a Rivlin-Ericksen Fluid

    Science.gov (United States)

    Sadeghy, K.; Khabazi, N.; Taghavi, S. M.

    The present work deals with the two-dimensional incompressible, laminar, steady-state boundary layer equations. First, we determine a family of velocity distributions outside the boundary layer such that these problems may have similarity solutions. We study the Falkner-Skan flow of a viscoelastic fluid governed by second order model, as the Reynolds number Re→ ∞. We obtain an ordinary forth order differential equation to obtain the stream function, velocity profile and the stress. The stream function is then governed by a generalized Falkner-Skan equation. In comparison with Newtonian Falkner-Skan equation that has two coefficients this new one has four coefficients that two of them represent elastic properties of the fluid. The effects of the elastic parameter on the velocity filed have been discussed. As it is shown in the figure there is a good agreement between numerical results and previous special cases confirm the validity of the presented algorithm.

  11. Multiscale Behavior of Viscous Fluids Dynamics: Experimental Observations

    Science.gov (United States)

    Arciniega-Ceballos, Alejandra; Spina, Laura; Scheu, Bettina; Dingwell, Donald B.

    2016-04-01

    The dynamics of Newtonian fluids with viscosities of mafic to intermediate silicate melts (10-1000 Pa s) during slow decompression present multi-time scale processes. To observe these processes we have performed several experiments on silicon oil saturated with Argon gas for 72 hours, in a Plexiglas autoclave. The slow decompression, dropping from 10 MPa to ambient pressure, acting as the excitation mechanism, triggered several processes with their own distinct timescales. These processes generate complex non-stationary microseismic signals, which have been recorded with 7 high-dynamic piezoelectric sensors located along the conduit flanked by high-speed video recordings. The analysis in time and frequency of these time series and their correlation with the associated high-speed imaging enables the characterization of distinct phases and the extraction of the individual processes during the evolution of decompression of these viscous fluids. We have observed fluid-solid elastic interaction, degassing, fluid mass expansion and flow, bubble nucleation, growth, coalescence and collapse, foam building and vertical wagging. All these processes (in fine and coarse scales) are sequentially coupled in time, occur within specific pressure intervals, and exhibit a localized distribution along the conduit. Their coexistence and interactions constitute the stress field and driving forces that determine the dynamics of the conduit system. Our observations point to the great potential of this experimental approach in the understanding of volcanic conduit dynamics and volcanic seismicity.

  12. Turbulence characteristics and mixing performances of viscoelastic fluid flow in a serpentine microchannel

    International Nuclear Information System (INIS)

    Tatsumi, K; Takeda, Y; Nakabe, K; Suga, K

    2011-01-01

    Flow velocity measurement and visualization using particle image velocimetry and fluorescent dye were carried out for a viscoelastic fluid flow in a serpentine microchannel for the purpose to quantitatively evaluate the unsteady flow characteristics that is observed even under very low Reynolds number regime due to the combined effect of the viscoelastic fluid properties and the channel shape. Sucrose water solution (Newtonian fluid) and the polyacrylamide-sucrose water solution (viscoelastic fluid) were used as working fluids. The mixing performance markedly increased when the Reynolds number exceeded a certain value in the polyacrylamide solution case. The single-point, cross-sectional and two-dimensional velocity distributions showed that low frequency fluctuation was produced in the polyacrylamide solution case. Particularly large fluctuation in the channel spanwise direction was observed in the upstream area of the serpentine channel. On the other hand, the amplitude of the fluctuation decreased in the downstream region. The fluctuation in the upstream region is believed to be generated by the flow instability at the curved part of the channel, while the fluctuations in the downstream area were attributed to the local instability and the vortices provided from the upstream region.

  13. A Lagrangian PFEM approach for non-Newtonian viscoplastic materials

    OpenAIRE

    Larese, A.

    2017-01-01

    This paper presents the application of a stabilized mixed Particle Finite Element Method (PFEM) to the solution of viscoplastic non-Newtonian flows. The application of the proposed model to the deformation of granular non-cohesive material is analysed. A variable yield threshold modified Bingham model is presented, using a Mohr Coulomb resistance criterion. Since the granular material is expected to undergo severe deformation, a Lagrangian approach is preferred to a fixed mesh one. PFEM i...

  14. Experimental and computational fluid dynamic studies of mixing for complex oral health products

    Science.gov (United States)

    Garcia, Marti Cortada; Mazzei, Luca; Angeli, Panagiota

    2015-11-01

    Mixing high viscous non-Newtonian fluids is common in the consumer health industry. Sometimes this process is empirical and involves many pilot plants trials which are product specific. The first step to study the mixing process is to build on knowledge on the rheology of the fluids involved. In this research a systematic approach is used to validate the rheology of two liquids: glycerol and a gel formed by polyethylene glycol and carbopol. Initially, the constitutive equation is determined which relates the viscosity of the fluids with temperature, shear rate, and concentration. The key variable for the validation is the power required for mixing, which can be obtained both from CFD and experimentally using a stirred tank and impeller of well-defined geometries at different impeller speeds. A good agreement between the two values indicates a successful validation of the rheology and allows the CFD model to be used for the study of mixing in the complex vessel geometries and increased sizes encountered during scale up.

  15. The Start Of Ebullition In Quiescent, Yield-Stress Fluids

    International Nuclear Information System (INIS)

    Reed, G. R.; Sherwood, David J.; Saez, A. Eduardo

    2012-01-01

    Non-Newtonian rheology is typical for the high-level radioactive waste (HLW) slurries processed in the Hanford Tank Waste Treatment and Immobilization Plant (WTP). Hydrogen and other flammable gases are generated in the aqueous phase by radiolytic and chemical reactions. HLW slurries have a capacity for retaining gas characterized by the shear strength holding the bubbles still. The sizes and degassing characteristics of flammable gas bubbles in the HLW slurries expected to be processed by the WTP are important considerations for designing equipment and operating procedures. Slurries become increasingly susceptible to degassing as the bubble concentration increases. This susceptibility and the process of ebullitive bubble enlargement are described here. When disturbed, the fluid undergoes localized flow around neighboring bubbles which are dragged together and coalesce, producing an enlarged bubble. For the conditions considered in this work, bubble size increase is enough to displace the weight required to overcome the fluid shear strength and yield the surroundings. The buoyant bubble ascends and accumulates others within a zone of influence, enlarging by a few orders of magnitude. This process describes how the first bubbles appear on the surface of a 7 Pa shear strength fluid a few seconds after being jarred

  16. The Start Of Ebullition In Quiescent, Yield-Stress Fluids

    Energy Technology Data Exchange (ETDEWEB)

    Reed, G. R.; Sherwood, David J.; Saez, A. Eduardo

    2012-08-30

    Non-Newtonian rheology is typical for the high-level radioactive waste (HLW) slurries processed in the Hanford Tank Waste Treatment and Immobilization Plant (WTP). Hydrogen and other flammable gases are generated in the aqueous phase by radiolytic and chemical reactions. HLW slurries have a capacity for retaining gas characterized by the shear strength holding the bubbles still. The sizes and degassing characteristics of flammable gas bubbles in the HLW slurries expected to be processed by the WTP are important considerations for designing equipment and operating procedures. Slurries become increasingly susceptible to degassing as the bubble concentration increases. This susceptibility and the process of ebullitive bubble enlargement are described here. When disturbed, the fluid undergoes localized flow around neighboring bubbles which are dragged together and coalesce, producing an enlarged bubble. For the conditions considered in this work, bubble size increase is enough to displace the weight required to overcome the fluid shear strength and yield the surroundings. The buoyant bubble ascends and accumulates others within a zone of influence, enlarging by a few orders of magnitude. This process describes how the first bubbles appear on the surface of a 7 Pa shear strength fluid a few seconds after being jarred.

  17. Experimental study and CFD simulation of rotational eccentric cylinder in a magnetorheological fluid

    International Nuclear Information System (INIS)

    Omidbeygi, F.; Hashemabadi, S.H.

    2012-01-01

    In this study, a magnetorheological (MR) fluid is prepared using carbonyl iron filings and low viscosity lubricating oil. The effects of magnetic field and weight percentage of particles on the viscosity of the MR fluid have been measured using a rotational viscometer. The yield stress under an applied magnetic field was also obtained experimentally. In the absence of an applied magnetic field, the MR fluid behaves as a Newtonian fluid. When the magnetic field is applied, the MR fluid behaves like Bingham plastics with a magnetic field dependent yield stress. Afterward, the results compared with those of CFD simulation of two eccentric cylinders in the MR fluid. Results show that the influences of MR effects, caused by the applied magnetic field, on the model characteristics are significant and not negligible. The viscosity is enhanced by increasing of the magnetic field, eccentricity ratio and weight percentage of suspensions. The MR effects and increasing of weight percentage and eccentricity ratio also provide an enhancement in the yield stresses and required total torque for rotation of inner cylinder. Also the simulation results indicate a good representation of the experiment by the model. - Highlights: ► Preparation of a magnetorheological fluid with carbonyl iron particles in lubricating oil. ► Rheological measurement for influence of solid content and magnetic field intensity. ► Simulation of eccentric rotating cylinder in prepared MR fluid with CFD techniques.

  18. Newtonian-noise cancellation in large-scale interferometric GW detectors using seismic tiltmeters

    International Nuclear Information System (INIS)

    Harms, Jan; Venkateswara, Krishna

    2016-01-01

    The mitigation of terrestrial gravity noise, also known as Newtonian noise (NN), is one of the foremost challenges to improve low-frequency sensitivity of ground-based gravitational-wave detectors. At frequencies above 1 Hz, it is predicted that gravity noise from seismic surface Rayleigh waves is the dominant contribution to NN in surface detectors, and may still contribute significantly in future underground detectors. Noise cancellation based on a coherent estimate of NN using data from a seismometer array was proposed in the past. In this article, we propose an alternative scheme to cancel NN using a seismic tiltmeter. It is shown that even under pessimistic assumptions concerning the complexity of the seismic field, a single tiltmeter under each test mass of the detector is sufficient to achieve substantial noise cancellation. A technical tiltmeter design is presented to achieve the required sensitivity in the Newtonian-noise frequency band. (paper)

  19. Non-Gaussian initial conditions in ΛCDM: Newtonian, relativistic, and primordial contributions

    International Nuclear Information System (INIS)

    Bruni, Marco; Hidalgo, Juan Carlos; Meures, Nikolai; Wands, David

    2014-01-01

    The goal of the present paper is to set initial conditions for structure formation at nonlinear order, consistent with general relativity, while also allowing for primordial non-Gaussianity. We use the nonlinear continuity and Raychaudhuri equations, which together with the nonlinear energy constraint, determine the evolution of the matter density fluctuation in general relativity. We solve this equations at first and second order in a perturbative expansion, recovering and extending previous results derived in the matter-dominated limit and in the Newtonian regime. We present a second-order solution for the comoving density contrast in a ΛCDM universe, identifying nonlinear contributions coming from the Newtonian growing mode, primordial non-Gaussianity and intrinsic non-Gaussianity, due to the essential nonlinearity of the relativistic constraint equations. We discuss the application of these results to initial conditions in N-body simulations, showing that relativistic corrections mimic a non-zero nonlinear parameter f NL

  20. Time-dependent dynamical behavior of surface tension on rotating fluids under microgravity environment

    Science.gov (United States)

    Hung, R. J.; Tsao, Y. D.; Hong, B. B.; Leslie, F. W.

    1988-01-01

    Time dependent evolutions of the profile of free surface (bubble shapes) for a cylindrical container partially filled with a Newtonian fluid of constant density, rotating about its axis of symmetry, have been studied. Numerical computations of the dynamics of bubble shapes have been carried out with the following situations: (1) linear functions of spin-up and spin-down in low and microgravity environments, (2) step functions of spin-up and spin-down in a low gravity environment, and (3) sinusoidal function oscillation of gravity environment in high and low rotating cylinder speeds.