Compressible generalized Newtonian fluids
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
Asymmetric bubble collapse and jetting in generalized Newtonian fluids
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.
Numerical solution of pipe flow problems for generalized Newtonian fluids
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.)
Steady flow of non-Newtonian fluids - monotonicity methods in generalized orlicz spaces
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
Steady flow of non-Newtonian fluids - monotonicity methods in generalized orlicz spaces
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
Variational methods for problems from plasticity theory and for generalized Newtonian fluids
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.
Non-Newtonian fluid flow in 2D fracture networks
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.
Spreading of Non-Newtonian and Newtonian Fluids on a Solid Substrate under Pressure
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.
Boundary layer for non-newtonian fluids on curved surfaces
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
Revisiting Newtonian and Non-Newtonian Fluid Mechanics Using Computer Algebra
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,…
Conditions of equilibrium of a rotating ideal fluid in the parametrized post-Newtonian formalism
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
Pseudo-Newtonian Equations for Evolution of Particles and Fluids in Stationary Space-times
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.
Applying Tiab’s direct synthesis technique to dilatant non-Newtonian/Newtonian fluids
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.
Gass-Assisted Displacement of Non-Newtonian Fluids
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...
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
Bubble coalescence in a Newtonian fluid
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.
Dynamic characteristics of Non Newtonian fluid Squeeze film damper
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.
Force effects on rotor of squeeze film damper using Newtonian and non-Newtonian fluid
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.
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.
Conceptual Models of the Climate 2003 Program of Study: Non-Newtonian Geophysical Fluid Dynamics
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...
Characterization of the transition of regimes in a non-newtonian fluids in ducts
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
Non-Newtonian fluid structure interaction in flexible biomimetic microchannels
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.
Verification of vertically rotating flume using non-newtonian fluids
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.
Transport phenomena in Newtonian fluids a concise primer
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
Borehole guided waves in a non-Newtonian (Maxwell) fluid-saturated porous medium
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)
Relativistic generalization of the Newtonian force
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)
Hyperdiffusive Dynamics in Newtonian Nanoparticle Fluids
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.
Hyperdiffusive Dynamics in Newtonian Nanoparticle Fluids
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.
Calculation of the Pitot tube correction factor for Newtonian and non-Newtonian fluids.
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.
Flocking particles in a non-Newtonian shear thickening fluid
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.
On Laminar Flow of Non-Newtonian Fluids in Porous Media
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.
On Laminar Flow of Non-Newtonian Fluids in Porous Media
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.
Newtonian and post-Newtonian approximations are asymptotic to general relativity
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
Constraining Relativistic Generalizations of Modified Newtonian Dynamics with Gravitational Waves.
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.
Transverse thermopherotic MHD Oldroyd-B fluid with Newtonian heating
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.
Attractors of equations of non-Newtonian fluid dynamics
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
Dynamics of magnetic nano-flake vortices in Newtonian fluids
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.
Open mathematical problems regarding non-Newtonian fluids
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)
Front‐tracking simulations of bubbles rising in non‐Newtonian fluids
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...
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
Saffman-Taylor Instability for a non-Newtonian fluid
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).
Non-newtonian heat transfer on a plate heat exchanger with generalized configurations
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.)
Generalized Galilean algebras and Newtonian gravity
González, N.; Rubio, G.; Salgado, P.; Salgado, S.
2016-04-01
The non-relativistic versions of the generalized Poincaré algebras and generalized AdS-Lorentz algebras are obtained. These non-relativistic algebras are called, generalized Galilean algebras of type I and type II and denoted by GBn and GLn respectively. Using a generalized Inönü-Wigner contraction procedure we find that the generalized Galilean algebras of type I can be obtained from the generalized Galilean algebras type II. The S-expansion procedure allows us to find the GB5 algebra from the Newton Hooke algebra with central extension. The procedure developed in Ref. [1] allows us to show that the nonrelativistic limit of the five dimensional Einstein-Chern-Simons gravity is given by a modified version of the Poisson equation. The modification could be compatible with the effects of Dark Matter, which leads us to think that Dark Matter can be interpreted as a non-relativistic limit of Dark Energy.
Flow of a non-Newtonian fluid through channels with permeable wall
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)
Flows of Newtonian and Power-Law Fluids in Symmetrically Corrugated Cappilary Fissures and Tubes
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.
Flows of Newtonian and Power-Law Fluids in Symmetrically Corrugated Cappilary Fissures and Tubes
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.
A Symmetry Particle Method towards Implicit Non‐Newtonian Fluids
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.
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
Effect of non-Newtonian viscosity on the fluid-dynamic characteristics in stenotic vessels
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
Secondary flow in a curved artery model with Newtonian and non-Newtonian blood-analog fluids
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.
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…
Displacement of one Newtonian fluid by another: density effects in axial annular flow
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....
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.
Free surface flow of a suspension of rigid particles in a non-Newtonian fluid
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...
Non-Newtonian fluid flow in annular pipes and entropy generation ...
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.
Does general relativity theory possess the classical newtonian limit
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
On approximation of non-Newtonian fluid flow by the finite element method
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.
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.
Modeling of flow of particles in a non-Newtonian fluid using lattice Boltzmann method
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...
Hydrodynamically Coupled Brownian Dynamics simulations for flow on non-Newtonian fluids
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
Newtonian heating effects in three-dimensional flow of viscoelastic fluid
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)
Non-Newtonian fluids: Frictional pressure loss prediction for fully-developed flow in straight pipes
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.
Topics in the Foundations of General Relativity and Newtonian Gravitation Theory
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
EXPERIMENTAL BUBBLE FORMATION IN A LARGE SCALE SYSTEM FOR NEWTONIAN AND NONNEWTONIAN FLUIDS
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.
External gear pumps operating with non-Newtonian fluids: Modelling and experimental validation
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.
On a numerical strategy to compute gravity currents of non-Newtonian fluids
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
The turbulent mixing of non-Newtonian fluids
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.
Fundamentals of convection in non-Newtonian fluids
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
Unsteady free convection flow of a micropolar fluid with Newtonian heating: Closed form solution
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.
Diffusion in Poiseuille and Couette flows of binary mixtures of incompressible newtonian fluids
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
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.
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
Downhole Temperature Modeling for Non-Newtonian Fluids in ERD Wells
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.
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.
A new 3D immersed boundary method for non-Newtonian fluid-structure-interaction with application
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.
The rheology of non-suspended sediment transport mediated by a Newtonian fluid
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.
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.
Acoustic waveform of continuous bubbling in a non-Newtonian fluid.
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.
Two-phase flow modeling for low concentration spherical particle motion through a Newtonian fluid
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...
A Numerical Study of Mesh Adaptivity in Multiphase Flows with Non-Newtonian Fluids
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.
CFD-PBM Coupled Simulation of an Airlift Reactor with Non-Newtonian Fluid
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.
Nonisothermal flow of a non-Newtonian fluid with viscous heating between two parallel plates
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.)
CFD simulation of gas and non-Newtonian fluid two-phase flow in anaerobic digesters.
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.
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.
Non-Newtonian fluid flow in an axisymmetric channel with porous wall
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.
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
Physically based model for extracting dual permeability parameters using non-Newtonian fluids
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.
Acoustic geometry for general relativistic barotropic irrotational fluid flow
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.
Development of a new continuous process for mixing of complex non-Newtonian fluids
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.
Motion of Charged Suspended Particle in a Non-Newtonian Fluid between Two Long Parallel Plated
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
Motion of charged suspended particle in a non-Newtonian fluid between two long parallel plates
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.
Experimental model for non-Newtonian fluid viscosity estimation: Fit to mathematical expressions
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.
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.
Post-Newtonian parameter γ in generalized non-local gravity
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.
Aspects of the motion of extended bodies in the post-Newtonian approximation to general relativity
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.
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.
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.
On multiple solutions of non-Newtonian Carreau fluid flow over an inclined shrinking sheet
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.
Simulation of forced convection in non-Newtonian fluid through sandstones
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.
Electro-osmosis of non-Newtonian fluids in porous media using lattice Poisson-Boltzmann method.
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.
Diagnosis at a glance of biological non-Newtonian fluids with Film Interference Flow Imaging (FIFI)
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.
Dynamics of continua and particles from general covariance of Newtonian gravitation theory
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
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.
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.
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.
General relativistic continuum mechanics and the post-Newtonian equations of motion
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
Exact Descriptions of General Relativity Derived from Newtonian Mechanics within Curved Geometries
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).
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
Physics of non-Newtonian fluids and interdisciplinary relations (biology and criminology)
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.
Newtonian and pseudo-Newtonian Hill problem
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
Shapiro, S.L.; Teukolsky, S.A.
1987-01-01
The dynamical behavior of nonspherical systems in general relativity is analyzed, allowing for rotation and the emission of gravitational waves. An axisymmetric code for solving the Vlasov equation in the Newtonian limit based on a mean-field particle simulation scheme is constructed and tested by reproducing the known evolution of homogeneous spheroids with and without rotation, including the Lin-Kestel-Shu instability. Results for the collapse of homogeneous, nonequilbrium spheroids are described, and stability studies of homogeneous, equilibrium spheroids are summarized. Finally, the code is used to follow the evolution of inhomogeneous, centrally condensed spheroids, and the results are compared with those for homogeneous collapse. 22 references
Spinning fluids in general relativity
Ray, J. R.; Smalley, L. L.
1982-01-01
General relativity field equations are employed to examine a continuous medium with internal spin. A variational principle formerly applied in the special relativity case is extended to the general relativity case, using a tetrad to express the spin density and the four-velocity of the fluid. An energy-momentum tensor is subsequently defined for a spinning fluid. The equations of motion of the fluid are suggested to be useful in analytical studies of galaxies, for anisotropic Bianchi universes, and for turbulent eddies.
Shape optimization for non-Newtonian fluids in time-dependent domains
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
Shape sensitivity analysis of time-dependent flows of incompressible non-Newtonian fluids
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
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.
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.
Maharjan, Rijan; Brown, Eric
2017-12-01
We investigated the transient relaxation of a discontinuous shear thickening (DST) suspension of cornstarch in water. We performed two types of relaxation experiments starting from a steady shear in a parallel-plate rheometer, followed either by stopping the top plate rotation and measuring the transient torque relaxation or by removing the torque on the plate and measuring the transient rotation of the tool. We found that at low effective weight fraction ϕeffmodel. The regime where the relaxation was inconsistent with the generalized Newtonian model was the same where we found positive normal stress during relaxation, and in some cases we found an oscillatory response, suggestive of a solidlike structure consisting of a system-spanning contact network of particles. This regime also corresponds to the same packing fraction range where we consistently found discontinuous shear thickening in rate-controlled, steady-state measurements. The relaxation time in this range scales with the inverse of the critical shear rate at the onset of shear thickening, which may correspond to a contact relaxation time for nearby particles in the structure to flow away from each other. In this range, the relaxation time was the same in both stress- and rate-controlled relaxation experiments, indicating the relaxation time is more intrinsic than an effective viscosity in this range and is needed in addition to the steady-state viscosity function to describe transient flows. The discrepancy between the measured relaxation times and the generalized Newtonian prediction was found to be as large as four orders of magnitude, and extrapolations diverge in the limit as ϕeff→ϕc as the generalized Newtonian prediction approaches 0. This quantitative discrepancy indicates the relaxation is not controlled by the dissipative terms in the constitutive relation. At the highest weight fractions, the relaxation time scales were measured to be on the order of ˜1 s. The fact that this time scale is
The Effect of Surface Tension on the Gravity-driven Thin Film Flow of Newtonian and Power-law Fluids
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
The influence of pH on gas-liquid mass transfer in non-Newtonian fluids
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...
MHD free convection flow of a non-Newtonian power-law fluid over ...
... 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
Shape optimization for non-Newtonian fluids in time-dependent domains
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
Linear Rayleigh-Taylor instability in an accelerated Newtonian fluid with finite width
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.
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.
Entropy generation in non-Newtonian fluid flow in a slider bearing
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 ...
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.
Variational formulation for the Newtonian cosmology
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.
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
Leigh, Nathan W. C.; Wegsman, Shalma
2018-05-01
We present a formalism for constructing schematic diagrams to depict chaotic three-body interactions in Newtonian gravity. This is done by decomposing each interaction into a series of discrete transformations in energy- and angular momentum-space. Each time a transformation is applied, the system changes state as the particles re-distribute their energy and angular momenta. These diagrams have the virtue of containing all of the quantitative information needed to fully characterize most bound or unbound interactions through time and space, including the total duration of the interaction, the initial and final stable states in addition to every intervening temporary meta-stable state. As shown via an illustrative example for the bound case, prolonged excursions of one of the particles, which by far dominates the computational cost of the simulations, are reduced to a single discrete transformation in energy- and angular momentum-space, thereby potentially mitigating any computational expense. We further generalize our formalism to sequences of (unbound) three-body interactions, as occur in dense stellar environments during binary hardening. Finally, we provide a method for dynamically evolving entire populations of binaries via three-body scattering interactions, using a purely analytic formalism. In principle, the techniques presented here are adaptable to other three-body problems that conserve energy and angular momentum.
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.
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.
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
The influence of pH on gas-liquid mass transfer in non-Newtonian fluids
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.
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.
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
MASS TRANSFER COEFFICIENTS FOR A NON-NEWTONIAN FLUID AND WATER WITH AND WITHOUT ANTI-FOAM AGENTS
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.
MASS TRANSFER COEFFICIENTS FOR A NON-NEWTONIAN FLUID AND WATER WITH AND WITHOUT ANTI-FOAM AGENTS
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
Solitons as Newtonian particles
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
Flow modelling of a newtonian fluid by two regions- the region of pure fluid and porous region
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
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.
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.
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.
Entropy analysis of convective MHD flow of third grade non-Newtonian fluid over a stretching sheet
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.
Numerical solution of chemically reactive non-Newtonian fluid flow: Dual stratification
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.
Motion of a suspended charged particle in a NON-Newtonian fluid. Vol. 2
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.
Effect of wall compliance on peristaltic transport of a Newtonian fluid in an asymmetric channel
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.
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
Generating perfect fluid spheres in general relativity
Boonserm, Petarpa; Visser, Matt; Weinfurtner, Silke
2005-06-01
Ever since Karl Schwarzschild’s 1916 discovery of the spacetime geometry describing the interior of a particular idealized general relativistic star—a static spherically symmetric blob of fluid with position-independent density—the general relativity community has continued to devote considerable time and energy to understanding the general-relativistic static perfect fluid sphere. Over the last 90 years a tangle of specific perfect fluid spheres has been discovered, with most of these specific examples seemingly independent from each other. To bring some order to this collection, in this article we develop several new transformation theorems that map perfect fluid spheres into perfect fluid spheres. These transformation theorems sometimes lead to unexpected connections between previously known perfect fluid spheres, sometimes lead to new previously unknown perfect fluid spheres, and in general can be used to develop a systematic way of classifying the set of all perfect fluid spheres.
Generating perfect fluid spheres in general relativity
Boonserm, Petarpa; Visser, Matt; Weinfurtner, Silke
2005-01-01
Ever since Karl Schwarzschild's 1916 discovery of the spacetime geometry describing the interior of a particular idealized general relativistic star--a static spherically symmetric blob of fluid with position-independent density--the general relativity community has continued to devote considerable time and energy to understanding the general-relativistic static perfect fluid sphere. Over the last 90 years a tangle of specific perfect fluid spheres has been discovered, with most of these specific examples seemingly independent from each other. To bring some order to this collection, in this article we develop several new transformation theorems that map perfect fluid spheres into perfect fluid spheres. These transformation theorems sometimes lead to unexpected connections between previously known perfect fluid spheres, sometimes lead to new previously unknown perfect fluid spheres, and in general can be used to develop a systematic way of classifying the set of all perfect fluid spheres
Post-Newtonian reference ellipsoid for relativistic geodesy
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
Study of blades inclination influence of gate impeller with a non-Newtonian fluid of Bingham
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.
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.
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)
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.
Exact solution of an electroosmotic flow for generalized Burgers fluid in cylindrical domain
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
Tidal generation of gravitational waves from orbiting Newtonian stars. I. General formalism
Turner, M.
1977-01-01
A linearized formalism is presented for the calculation of the tidally produced gravitational radiation potential h/sup TT/ from binary systems with arbitrary orbits. The stars are Newtonian, isentropic, and nonrotating. Normal-mode analysis is used to calculate the tidally generated internal motions; the resulting radiation potential h/sup TT/ and its Fourier decomposition are calculated in the Newtonian limit of the multipole formalism. The tidal radiation potential is weaker than that produced by the orbital motion by a factor of order [(stellar radius)/(periastron distance)] 5 . If we assume that the time scale of the tidal perturbation is always much less than the damping time of the star, then if in addition the damping time is much less than the time between periastron passages, the radiation spectrum consists of the l=2 eigenfrequencies of the star near the fundamental l=2 eigenfrequency; if the reverse is true (damping time >> time between periastrons), the spectrum is similar to the orbital gravitational radiation specturm
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.
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.
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.
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
Extension of Generalized Fluid System Simulation Program's Fluid Property Database
Patel, Kishan
2011-01-01
This internship focused on the development of additional capabilities for the General Fluid Systems Simulation Program (GFSSP). GFSSP is a thermo-fluid code used to evaluate system performance by a finite volume-based network analysis method. The program was developed primarily to analyze the complex internal flow of propulsion systems and is capable of solving many problems related to thermodynamics and fluid mechanics. GFSSP is integrated with thermodynamic programs that provide fluid properties for sub-cooled, superheated, and saturation states. For fluids that are not included in the thermodynamic property program, look-up property tables can be provided. The look-up property tables of the current release version can only handle sub-cooled and superheated states. The primary purpose of the internship was to extend the look-up tables to handle saturated states. This involves a) generation of a property table using REFPROP, a thermodynamic property program that is widely used, and b) modifications of the Fortran source code to read in an additional property table containing saturation data for both saturated liquid and saturated vapor states. Also, a method was implemented to calculate the thermodynamic properties of user-fluids within the saturation region, given values of pressure and enthalpy. These additions required new code to be written, and older code had to be adjusted to accommodate the new capabilities. Ultimately, the changes will lead to the incorporation of this new capability in future versions of GFSSP. This paper describes the development and validation of the new capability.
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.
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.
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.
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.
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
Newtonian cosmology Newton would understand
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
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
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.
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.
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).
First general solutions for unidirectional motions of rate type fluids over an infinite plate
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.
Sojka, Paul E.; Rodrigues, Neil S.
2015-11-01
The current study investigates the drop characteristics of three Carboxymethylcellulose (CMC) sprays produced by the impingement of two liquid jets. The three water-based solutions used in this work (0.5 wt.-% CMC-7MF, 0.8 wt.-% CMC-7MF, and 1.4 wt.-% CMC-7MF) exhibited strong shear-thinning, non-Newtonian behavior - characterized by the Bird-Carreau rheological model. A generalized Bird-Carreau jet Reynolds number was used as the primary parameter to characterize the drop size and the drop velocity, which were measured using Phase Doppler Anemometry (PDA). PDA optical configuration enabled a drop size measurement range of approximately 2.3 to 116.2 μm. 50,000 drops were measured at each test condition to ensure statistical significance. The arithmetic mean diameter (D10) , Sauter mean diameter (D32) , and mass median diameter (MMD) were used as representative diameters to characterize drop size. The mean axial drop velocity Uz -mean along with its root-mean square Uz -rms were used to characterize drop velocity. Incredibly, measurements for all three CMC liquids and reference DI water sprays seemed to follow a single curve for D32 and MMD drop diameters in the high generalized Bird-Carreau jet Reynolds number range considered in this work (9.21E +03
Majumdar, Alok; Leclair, Andre; Moore, Ric; Schallhorn, Paul
2011-01-01
GFSSP stands for Generalized Fluid System Simulation Program. It is a general-purpose computer program to compute pressure, temperature and flow distribution in a flow network. GFSSP calculates pressure, temperature, and concentrations at nodes and calculates flow rates through branches. It was primarily developed to analyze Internal Flow Analysis of a Turbopump Transient Flow Analysis of a Propulsion System. GFSSP development started in 1994 with an objective to provide a generalized and easy to use flow analysis tool for thermo-fluid systems.
Negative wake behind bubbles in non-newtonian liquids
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...
Breuer, R.A.; Rudolph, E.
1982-01-01
The force between two well-separated bodies is calculated in a fully dynamic system of two extended bodies up to and including the second post-Newtonian approximation (PNA). The iteration procedure as formulated by Anderson and Decanio is used in a version whose divergences have been pushed to the third PNA. The following are shown: (i) The force law assumes the ''Newtonian form'' if a second approximation in 1/(separation of the bodies) is made; (ii) the mass terms appearing in the force law are the (Tolman) masses of the individual bodies expanded up the second PNA; the internal masses equal the (passive and active) gravitational masses of the bodies in order considered; they are all constants of the motion; (iii) the self-fields of the bodies vanish in the second PNA; hence there is no Nordvedt effect in the second PNA; (iv) the compactness of the bodies, i.e., (gravitational radius)/(body size), does not appear in the force law; only the relation between mass and the matter variables is changed in the PNA as compared with the corresponding Newtonian result. (author)
The flow of a non-Newtonian fluid induced due to the oscillations of a porous plate
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.
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...
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.
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.
A boundary integral method for two-dimensional (non)-Newtonian drops in slow viscous flow
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
Supercritical fluids technology. Pt. 1 General topics
Marongiu, B.; De Giorgi, M. R.; Porcedda, S.; Cadoni, E.
1998-01-01
Supercritical fluids technology is among the emerging 'clean' technologies, that allows the minimization in the use of chemical and thermic treatments and products irradiation, diminishing the quantity of liquid wastes to be treated. In this first article phase equilibria thermodynamics and fluid mechanics of transport phenomena are reviewed [it
Non Newtonian gravity creeping flow
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
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....
Lucchesi, David M; Peron, Roberto
2010-12-03
The pericenter shift of a binary system represents a suitable observable to test for possible deviations from the newtonian inverse-square law in favor of new weak interactions between macroscopic objects. We analyzed 13 years of tracking data of the LAGEOS satellites with GEODYN II software but with no models for general relativity. From the fit of LAGEOS II pericenter residuals we have been able to obtain a 99.8% agreement with the predictions of Einstein's theory. This result may be considered as a 99.8% measurement in the field of the Earth of the combination of the γ and β parameters of general relativity, and it may be used to constrain possible deviations from the inverse-square law in favor of new weak interactions parametrized by a Yukawa-like potential with strength α and range λ. We obtained |α| ≲ 1 × 10(-11), a huge improvement at a range of about 1 Earth radius.
Post-Newtonian gravitational bremsstrahlung
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
Post-Newtonian gravitational bremsstrahlung
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
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.
Experimental investigation of non-Newtonian droplet collisions : the role of extensional viscosity
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.
Comparative PIV and LDA studies of Newtonian and non-Newtonian flows in an agitated tank.
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.
Introduction to mathematical fluid dynamics
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.
Spinning fluids in general relativity: a variational formulation
Oliveira, H.P. de; Salim, J.M.
1990-01-01
In this paper we present a variational formulation for spinning fluids in General Relativity. In our model each volume element of the fluid has rigid microstructure. We deduce a symmetrical energy-moment tensor where there is an explicit contribution of kinetic spin energy to the total energy. (author)
Generalized dark energy interactions with multiple fluids
De Bruck, Carsten van; Mifsud, Jurgen [Consortium for Fundamental Physics, School of Mathematics and Statistics, University of Sheffield, Hounsfield Road, Sheffield S3 7RH (United Kingdom); Mimoso, José P.; Nunes, Nelson J., E-mail: c.vandebruck@sheffield.ac.uk, E-mail: jmifsud1@sheffield.ac.uk, E-mail: jpmimoso@fc.ul.pt, E-mail: njnunes@fc.ul.pt [Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências da Universidade de Lisboa, Campo Grande, PT1749-016 Lisboa (Portugal)
2016-11-01
In the search for an explanation for the current acceleration of the Universe, scalar fields are the most simple and useful tools to build models of dark energy. This field, however, must in principle couple with the rest of the world and not necessarily in the same way to different particles or fluids. We provide the most complete dynamical system analysis to date, consisting of a canonical scalar field conformally and disformally coupled to both dust and radiation. We perform a detailed study of the existence and stability conditions of the systems and comment on constraints imposed on the disformal coupling from Big-Bang Nucleosynthesis and given current limits on the variation of the fine-structure constant.
The Post-Newtonian Approximation for Relativistic Compact Binaries
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.
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
Structural Optimization of Non-Newtonian Rectifiers
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...
Intraoperative Fluids and Fluid Management for Ambulatory Dental Sedation and General Anesthesia.
Saraghi, Mana
2015-01-01
Intravenous fluids are administered in virtually every parenteral sedation and general anesthetic. The purpose of this article is to review the physiology of body-water distribution and fluid dynamics at the vascular endothelium, evaluation of fluid status, calculation of fluid requirements, and the clinical rationale for the use of various crystalloid and colloid solutions. In the setting of elective dental outpatient procedures with minor blood loss, isotonic balanced crystalloid solutions are the fluids of choice. Colloids, on the other hand, have no use in outpatient sedation or general anesthesia for dental or minor oral surgery procedures but may have several desirable properties in long and invasive maxillofacial surgical procedures where advanced hemodynamic monitoring may assess the adequacy of intravascular volume.
Generalized Fluid System Simulation Program (GFSSP) - Version 6
Majumdar, Alok; LeClair, Andre; Moore, Ric; Schallhorn, Paul
2015-01-01
The Generalized Fluid System Simulation Program (GFSSP) is a finite-volume based general-purpose computer program for analyzing steady state and time-dependent flow rates, pressures, temperatures, and concentrations in a complex flow network. The program is capable of modeling real fluids with phase changes, compressibility, mixture thermodynamics, conjugate heat transfer between solid and fluid, fluid transients, pumps, compressors, flow control valves and external body forces such as gravity and centrifugal. The thermo-fluid system to be analyzed is discretized into nodes, branches, and conductors. The scalar properties such as pressure, temperature, and concentrations are calculated at nodes. Mass flow rates and heat transfer rates are computed in branches and conductors. The graphical user interface allows users to build their models using the 'point, drag, and click' method; the users can also run their models and post-process the results in the same environment. The integrated fluid library supplies thermodynamic and thermo-physical properties of 36 fluids, and 24 different resistance/source options are provided for modeling momentum sources or sinks in the branches. Users can introduce new physics, non-linear and time-dependent boundary conditions through user-subroutine.
Pappas, George; Apostolatos, Theocharis A
2014-03-28
Recently, it was shown that slowly rotating neutron stars exhibit an interesting correlation between their moment of inertia I, their quadrupole moment Q, and their tidal deformation Love number λ (the I-Love-Q relations), independently of the equation of state of the compact object. In the present Letter a similar, more general, universality is shown to hold true for all rotating neutron stars within general relativity; the first four multipole moments of the neutron star are related in a way independent of the nuclear matter equation of state we assume. By exploiting this relation, we can describe quite accurately the geometry around a neutron star with fewer parameters, even if we don't know precisely the equation of state. Furthermore, this universal behavior displayed by neutron stars could promote them to a more promising class of candidates (next to black holes) for testing theories of gravity.
Hamiltonian formalism for perfect fluids in general relativity
Demaret, J.; Moncrief, V.
1980-01-01
Schutz's Hamiltonian theory of a relativistic perfect fluid, based on the velocity-potential version of classical perfect fluid hydrodynamics as formulated by Seliger and Whitham, is used to derive, in the framework of the Arnowitt, Deser, and Misner (ADM) method, a general partially reduced Hamiltonian for relativistic systems filled with a perfect fluid. The time coordinate is chosen, as in Lund's treatment of collapsing balls of dust, as minus the only velocity potential different from zero in the case of an irrotational and isentropic fluid. A ''semi-Dirac'' method can be applied to quantize astrophysical and cosmological models in the framework of this partially reduced formalism. If one chooses Taub's adapted comoving coordinate system, it is possible to derive a fully reduced ADM Hamiltonian, which is equal to minus the total baryon number of the fluid, generalizing a result previously obtained by Moncrief in the more particular framework of Taub's variational principle, valid for self-gravitating barotropic relativistic perfect fluids. An unconstrained Hamiltonian density is then explicitly derived for a fluid obeying the equation of state p=(gamma-1)rho (1 < or = γ < or = 2), which can adequately describe the phases of very high density attained in a catastrophic collapse or during the early stages of the Universe. This Hamiltonian density, shown to be equivalent to Moncrief's in the particular case of an isentropic fluid, can be simplified for fluid-filled class-A diagonal Bianchi-type cosmological models and appears as a suitable starting point for the study of the canonical quantization of these models
The Hamiltonian structure of general relativistic perfect fluids
Bao, D.; Houston Univ., TX; Marsden, J.; Walton, R.
1985-01-01
We show that the evolution equations for a perfect fluid coupled to general relativity in a general lapse and shift, are Hamiltonian relative to a certain Poisson structure. For the fluid variables, a Lie-Poisson structure associated to the dual of a semi-direct product Lie algebra is used, while the bracket for the gravitational variables has the usual canonical symplectic structure. The evolution is governed by a Hamiltonian which is equivalent to that obtained from a canonical analysis. The relationship of our Hamiltonian structure with other approaches in the literature, such as Clebsch potentials, Lagrangian to Eulerian transformations, and its use in clarifying linearization stability, are discussed. (orig.)
Generalized Fluid System Simulation Program, Version 5.0-Educational
Majumdar, A. K.
2011-01-01
The Generalized Fluid System Simulation Program (GFSSP) is a finite-volume based general-purpose computer program for analyzing steady state and time-dependent flow rates, pressures, temperatures, and concentrations in a complex flow network. The program is capable of modeling real fluids with phase changes, compressibility, mixture thermodynamics, conjugate heat transfer between solid and fluid, fluid transients, pumps, compressors and external body forces such as gravity and centrifugal. The thermofluid system to be analyzed is discretized into nodes, branches, and conductors. The scalar properties such as pressure, temperature, and concentrations are calculated at nodes. Mass flow rates and heat transfer rates are computed in branches and conductors. The graphical user interface allows users to build their models using the point, drag and click method; the users can also run their models and post-process the results in the same environment. The integrated fluid library supplies thermodynamic and thermo-physical properties of 36 fluids and 21 different resistance/source options are provided for modeling momentum sources or sinks in the branches. This Technical Memorandum illustrates the application and verification of the code through 12 demonstrated example problems.
Post-Newtonian celestial dynamics in cosmology: Field equations
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
Impinging jet spray formation using non-Newtonian liquids
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
Numerical analysis of non-Newtonian rheology effect on hydrocyclone flow field
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.
Generalized Roe's numerical scheme for a two-fluid model
Toumi, I.; Raymond, P.
1993-01-01
This paper is devoted to a mathematical and numerical study of a six equation two-fluid model. We will prove that the model is strictly hyperbolic due to the inclusion of the virtual mass force term in the phasic momentum equations. The two-fluid model is naturally written under a nonconservative form. To solve the nonlinear Riemann problem for this nonconservative hyperbolic system, a generalized Roe's approximate Riemann solver, is used, based on a linearization of the nonconservative terms. A Godunov type numerical scheme is built, using this approximate Riemann solver. 10 refs., 5 figs,
Studying mixing in Non-Newtonian blue maize flour suspensions using color analysis.
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.
Quasi-local mass in the covariant Newtonian spacetime
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
Generalized Fluid System Simulation Program, Version 6.0
Majumdar, A. K.; LeClair, A. C.; Moore, R.; Schallhorn, P. A.
2016-01-01
The Generalized Fluid System Simulation Program (GFSSP) is a general purpose computer program for analyzing steady state and time-dependent flow rates, pressures, temperatures, and concentrations in a complex flow network. The program is capable of modeling real fluids with phase changes, compressibility, mixture thermodynamics, conjugate heat transfer between solid and fluid, fluid transients, pumps, compressors, and external body forces such as gravity and centrifugal. The thermofluid system to be analyzed is discretized into nodes, branches, and conductors. The scalar properties such as pressure, temperature, and concentrations are calculated at nodes. Mass flow rates and heat transfer rates are computed in branches and conductors. The graphical user interface allows users to build their models using the 'point, drag, and click' method; the users can also run their models and post-process the results in the same environment. Two thermodynamic property programs (GASP/WASP and GASPAK) provide required thermodynamic and thermophysical properties for 36 fluids: helium, methane, neon, nitrogen, carbon monoxide, oxygen, argon, carbon dioxide, fluorine, hydrogen, parahydrogen, water, kerosene (RP-1), isobutene, butane, deuterium, ethane, ethylene, hydrogen sulfide, krypton, propane, xenon, R-11, R-12, R-22, R-32, R-123, R-124, R-125, R-134A, R-152A, nitrogen trifluoride, ammonia, hydrogen peroxide, and air. The program also provides the options of using any incompressible fluid with constant density and viscosity or ideal gas. The users can also supply property tables for fluids that are not in the library. Twenty-four different resistance/source options are provided for modeling momentum sources or sinks in the branches. These options include pipe flow, flow through a restriction, noncircular duct, pipe flow with entrance and/or exit losses, thin sharp orifice, thick orifice, square edge reduction, square edge expansion, rotating annular duct, rotating radial duct
Pseudo-Newtonian planar circular restricted 3-body problem
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.
Pseudo-Newtonian planar circular restricted 3-body problem
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.
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.
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.
Green's function for a generalized two-dimensional fluid.
Iwayama, Takahiro; Watanabe, Takeshi
2010-09-01
A Green's function for a generalized two-dimensional (2D) fluid in an unbounded domain (the so-called α turbulence system) is discussed. The generalized 2D fluid is characterized by a relationship between an advected quantity q and the stream function ψ : namely, q=-(-Δ){α/2}ψ . Here, α is a real number and q is referred to as the vorticity. In this study, the Green's function refers to the stream function produced by a delta-functional distribution of q , i.e., a point vortex with unit strength. The Green's function has the form G{(α)}(r)∝r{α-2} , except when α is an even number, where r is the distance from the point vortex. This functional form is known as the Riesz potential. When α is a positive even number, the logarithmic correction to the Riesz potential has the form G(r){(α)}∝r{α-2} ln r . In contrast, when α is a negative even number, G{(α)} is given by the higher-order Laplacian of the delta function. The transition of the small-scale behavior of q at α=2 , a well-known property of forced and dissipative α turbulence, is explained in terms of the Green's function. Moreover, the azimuthal velocity around the point vortex is derived from the Green's function. The functional form of the azimuthal velocity indicates that physically realizable systems for the generalized 2D fluid exist only when α≤3 . The Green's function and physically realizable systems for an anisotropic generalized 2D fluid are presented as an application of the present study.
Structural Optimization of non-Newtonian Microfluidics
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....
Structural Optimization of non-Newtonian Microfluidics
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...
Newtonian cosmology with a quantum bounce
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.)
Viumdal, Håkon; Mylvaganam, Saba
2017-01-01
In oil and gas and geothermal installations, open channels followed by sieves for removal of drill cuttings, are used to monitor the quality and quantity of the drilling fluids. Drilling fluid flow rate is difficult to measure due to the varying flow conditions (e.g., wavy, turbulent and irregular) and the presence of drilling cuttings and gas bubbles. Inclusion of a Venturi section in the open channel and an array of ultrasonic level sensors above it at locations in the vicinity of and above the Venturi constriction gives the varying levels of the drilling fluid in the channel. The time series of the levels from this array of ultrasonic level sensors are used to estimate the drilling fluid flow rate, which is compared with Coriolis meter measurements. Fuzzy logic, neural networks and support vector regression algorithms applied to the data from temporal and spatial ultrasonic level measurements of the drilling fluid in the open channel give estimates of its flow rate with sufficient reliability, repeatability and uncertainty, providing a novel soft sensing of an important process variable. Simulations, cross-validations and experimental results show that feedforward neural networks with the Bayesian regularization learning algorithm provide the best flow rate estimates. Finally, the benefits of using this soft sensing technique combined with Venturi constriction in open channels are discussed. PMID:29072595
Are Non-Newtonian Effects Important in Hemodynamic Simulations of Patients With Autogenous Fistula?
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.
Are Non-Newtonian Effects Important in Hemodynamic Simulations of Patients With Autogenous Fistula?
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
Expanding perfect fluid generalizations of the C metric
Wylleman, Lode; Beke, David
2010-01-01
Petrov type D gravitational fields, generated by a perfect fluid with spatially homogeneous energy density and with flow lines which form a nonshearing and nonrotating timelike congruence, are reexamined. It turns out that the anisotropic such spacetimes, which comprise the vacuum C metric as a limit case, can have nonzero expansion, contrary to the conclusion in the original investigation by Barnes [A. Barnes, Gen. Relativ. Gravit. 4, 105 (1973).]. Apart from the static members, this class consists of cosmological models with precisely one symmetry. The general line element is constructed and some important properties are discussed. It is also shown that purely electric Petrov type D vacuum spacetimes admit shear-free normal timelike congruences everywhere, even in the nonstatic regions. This result incited to deduce intrinsic, easily testable criteria regarding shear-free normality and staticity of Petrov type D spacetimes in general, which are added in an appendix.
On Numerical Methods in Non-Newtonian Flows
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)
Keivan Shayesteh
2015-02-01
Full Text Available In tubular reactors, there are different parameters which can affect the degree of conversion. The type of fluid motion and velocity profile of substances in the reactor are of most central measures. Different rheological models can be employed to study the behavior of fluids; power law model is one of the most commonly used models. In this study, the rheological behaviour of polymerization reaction of methyl methacrylate was examined. Due to the similarity function of tubular and batch reactors, the number of test tubes are used to prepare the solution. After preparation of the reactor solution, the n value of power law model was estimated within the span of 0.3492 to 0.9889 by curve fitting. Employing these rheological data, a reactor has been designed. Moreover, the effects of parameters such as reaction temperature, initiator wt%, the concentration of monomer and reactor’s radius on the degree of conversion have been studied. The obtained results in the research indicate a direct proportionality of conversion with the reaction temperature, initiator wt% and the concentration of monomer and also an inverse proportionality of conversion with reactor’s radius. Finally, the amount of conversion was obtained equal to 56.47% and according to its laboratory proportion which was 55.88% we have reached the conclusion that the modeling duly undertaken is applicable and valid.
Presenting Newtonian gravitation
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
Non-Newtonian Hele-Shaw Flow and the Saffman-Taylor Instability
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
Newtonian cosmology with a time-varying constant of gravitation
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)
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
Safdar, Rabia; Imran, M.; Khalique, Chaudry Masood
2018-06-01
Exact solutions for velocity field and tangential stress for rotational flow of a generalized Burgers' fluid within an infinite circular pipe are derived by using the methods of Laplace and finite Hankel transformations. Firstly we take the position of fluid at rest and then the fluid flow due to the rotation of the pipe around the axis of flow having time dependant angular velocity. The exact solutions are presented in terms of the generalized Ga,b,c (., t) -functions. The corresponding results can be freely specified for the same results of Burgers', Oldroyd B, Maxwell, second grade and Newtonian fluids (performing the same motion) as particular cases of the results obtained earlier. The impact of the different parameters, individually and in comparison, are represented by graphical demonstrations. Secondly the numerical solutions for velocity and stress are also obtained with the help of Laplace transformation, Gaver Stehfest's algorithm and MATHCAD. Finally a comparison of both methods for the same problem is done and shows the consistency of results.
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)
Generalized reduced fluid model with finite ion-gyroradius effects
Hsu, C.T.; Hazeltine, R.D.; Morrison, P.J.
1985-04-01
Reduced fluid models have become important tools for studying the nonlinear dynamics of plasma in a large aspect-ratio tokamak. A self-consistent nonlinear reduced fluid model, with finite ion-gyroradius effects is presented. The model is distinctive in allowing for arbitrary beta and in satisfying an exact, relatively simple energy conservation law
Symposium on the Foundations of Newtonian Scholarship
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.
Hamiltonian models for the Madelung fluid and generalized Langevin equations
Nonnenmacher, T.F.
1985-01-01
We present a Hamiltonian formulation of some type of an 'electromagnetic' Madelung fluid leading to a fluid mechanics interpretation of the Aharonov-Bohm effect and to a subsidary condition to be required in order to make the correspondence between Schroedinger's quantum mechanics and Madelung's fluid mechanics unique. Then we discuss some problems related with the Brownian oscillator. Our aim is to start out with a Hamiltonian for the composite system with surrounding heat bath) and to finally arrive at a stochastic differential equation with completely determined statistical properties. (orig./HSI)
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.
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.
Lie group analysis of flow and heat transfer of non-Newtonian
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 ...
Was Newtonian cosmology really inconsistent?
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.
Non-Newtonian ink transfer in gravure-offset printing
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.
Exact solution for MHD flow of a generalized Oldroyd-B fluid with modified Darcy's law
Khan, M.; Hayat, T.; Asghar, S.
2005-12-01
This paper deals with an exact solution for the magnetohydrodynamic (MHD) flow of a generalized Oldroyd-B fluid in a circular pipe. For the description of such a fluid, the fractional calculus approach has been used throughout the analysis. Based on modified Darcy's law for generalized Oldroyd-B fluid, the velocity field is calculated analytically. Several known solutions can be recovered as the limiting cases of our solution. (author)
Orbital motions as gradiometers for post-Newtonian tidal effects
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.
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...
Inhomogeneous generalizations of Bianchi type VIh models with perfect fluid
Roy, S. R.; Prasad, A.
1991-07-01
Inhomogeneous universes admitting an Abelian G2 of isometry and filled with perfect fluid have been derived. These contain as special cases exact homogeneous universes of Bianchi type VIh. Many of these universes asymptotically tend to homogeneous Bianchi VIh universes. The models have been discussed for their physical and kinematical behaviors.
Perturbed Newtonian description of the Lemaître model with non-negligible pressure
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.
Perturbed Newtonian description of the Lemaître model with non-negligible pressure
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
Similarity solution of axisymmetric non-Newtonian wall jets with swirl
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
General fluid theories, variational principles and self-organization
Mahajan, S.M.
2002-01-01
This paper reports two distinct but related advances: (1) The development and application of fluid theories that transcend conventional magnetohydrodynamics (MHD), in particular, theories that are valid in the long-mean-free-path limit and in which pressure anisotropy, heat flow, and arbitrarily strong sheared flows are treated consistently. (2) The discovery of new pressure-confining plasma configurations that are self-organized relaxed states. (author)
Generalized added masses computation for fluid structure interaction
Lazzeri, L.; Cecconi, S.; Scala, M.
1983-01-01
The aim of this paper a description of a method to simulate the dynamic effect of a fluid between two structures by means of an added mass and an added stiffness. The method is based on a potential theory which assumes the fluid is inviscid and incompressible (the case of compressibility is discussed); a solution of the corresponding field equation is given as a superposition of elementary conditions (i.e. applicable to elementary boundary conditions). Consequently the pressure and displacements of the fluid on the boundary are given as a function of the series coefficients; the ''work lost'' (i.e. the work done by the pressures on the difference between actual and estimated displacements) is minimized, in this way the expansion coefficients are related to the displacements on the boundaries. Virtual work procedures are then used to compute added masses. The particular case of a free surface (with gravity effects) is discussed, it is shown how the effect can be modelled by means of an added stiffness term. Some examples relative to vibrations in reservoirs are given and discussed. (orig.)
Description of a general method to compute the fluid-structure interaction
Jeanpierre, F.; Gibert, R.J.; Hoffmann, A.; Livolant, M.
1979-01-01
The vibrational characteristics of a structure in air may be considerably modified when the structure is immersed in a dense fluid. Such fluid structure interaction effects are important for the seismic or flow induced vibrational studies of various nuclear equipments, as for example the PWR internals, the fast reactor vessels, heat exchangers and fuel elements. In some simple situations, the fluid effects can be simulate by added masses, but in general, they are much more complicated. A general formulation to calculate precisely the vibrational behaviour of structures containing dense fluids is presented in this paper. That formulation can be easily introduced in finite elements computer codes, the fluid being described by special fluid elements. Its use is in principle limited to the linear range: small movements of structures, small pressure fluctuations. (orig.)
Parametrized post-Newtonian approximation and Rastall's gravitational field equations
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
Deposition Velocities of Newtonian and Non-Newtonian Slurries in Pipelines
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
The WTP pipe plugging issue, as stated by the External Flowsheet Review Team (EFRT) Executive Summary, is as follows: “Piping that transports slurries will plug unless it is properly designed to minimize this risk. This design approach has not been followed consistently, which will lead to frequent shutdowns due to line plugging.” A strategy was employed to perform critical-velocity tests on several physical simulants. Critical velocity is defined as the point where a stationary bed of particles deposits on the bottom of a straight horizontal pipe during slurry transport operations. Results from the critical velocity testing provide an indication of slurry stability as a function of fluid rheological properties and transport conditions. The experimental results are compared to the WTP design guide on slurry transport velocity in an effort to confirm minimum waste velocity and flushing velocity requirements as established by calculations and critical line velocity correlations in the design guide. The major findings of this testing is discussed below. Experimental results indicate that the use of the Oroskar and Turian (1980) correlation in the design guide is conservative—Slurry viscosity has a greater affect on particles with a large surface area to mass ratio. The increased viscous forces on these particles result in a decrease in predicted critical velocities from this traditional industry derived equations that focus on particles large than 100 μm in size. Since the Hanford slurry particles generally have large surface area to mass ratios, the reliance on such equations in the Hall (2006) design guide is conservative. Additionally, the use of the 95% percentile particle size as an input to this equation is conservative. However, test results indicate that the use of an average particle density as an input to the equation is not conservative. Particle density has a large influence on the overall result returned by the correlation. Lastly, the viscosity
Orbital motions as gradiometers for post-Newtonian tidal effects
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.
Generalized fluid impulse functions for oscillating marine structures
Janardhanan, K.; Price, W. G.; Wu, Y.
1992-03-01
A selection of generalized impulse response functions is presented for a variety of rigid and flexible marine structures (i.e. mono-hull, SWATH, floating drydock and twin dock, fixed flexible pile). These functions are determined from calculated and experimental frequency-dependent hydrodynamic data, and the characteristics of these data depend on the type of structure considered. This information is reflected in the shape and duration of the generalized impulse response functions which are pre-requisites for a generalized integro-differential mathematical model describing the dynamic behaviour of the structures to seaway excitation.
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.
M. C. Sagis, Leonard
2001-03-01
In this paper, we develop a theory for the calculation of the surface diffusion coefficient for an arbitrarily curved fluid-fluid interface. The theory is valid for systems in hydrodynamic equilibrium, with zero mass-averaged velocities in the bulk and interfacial regions. We restrict our attention to systems with isotropic bulk phases, and an interfacial region that is isotropic in the plane parallel to the dividing surface. The dividing surface is assumed to be a simple interface, without memory effects or yield stresses. We derive an expression for the surface diffusion coefficient in terms of two parameters of the interfacial region: the coefficient for plane-parallel diffusion D (AB)aa(ξ) , and the driving force d(B)I||(ξ) . This driving force is the parallel component of the driving force for diffusion in the interfacial region. We derive an expression for this driving force using the entropy balance.
Conformal collineations and anisotropic fluids in general relativity
Duggal, K.L.; Sharma, R.
1986-01-01
Recently, Herrera et al. [L. Herrera, J. Jimenez, L. Leal, J. Ponce de Leon, M. Esculpi, and V. Galino, J. Math. Phys. 25, 3274 (1984)] studied the consequences of the existence of a one-parameter group of conformal motions for anisotropic matter. They concluded that for special conformal motions, the stiff equation of state (p = μ) is singled out in a unique way, provided the generating conformal vector field is orthogonal to the four-velocity. In this paper, the same problem is studied by using conformal collineations (which include conformal motions as subgroups). It is shown that, for a special conformal collineation, the stiff equation of state is not singled out. Non-Einstein Ricci-recurrent spaces are considered as physical models for the fluid matter
Spreading dynamics of power-law fluid droplets
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.
Dominique Brun-Battistini
2017-10-01
Full Text Available Richard C. Tolman analyzed the relation between a temperature gradient and a gravitational field in an equilibrium situation. In 2012, Tolman’s law was generalized to a non-equilibrium situation for a simple dilute relativistic fluid. The result in that scenario, obtained by introducing the gravitational force through the molecular acceleration, couples the heat flux with the metric coefficients and the gradients of the state variables. In the present paper it is shown, by explicitly describing the single particle orbits as geodesics in Boltzmann’s equation, that a gravitational field drives a heat flux in this type of system. The calculation is devoted solely to the gravitational field contribution to this heat flux in which a Newtonian limit to the Schwarzschild metric is assumed. The corresponding transport coefficient, which is obtained within a relaxation approximation, corresponds to the dilute fluid in a weak gravitational field. The effect is negligible in the non-relativistic regime, as evidenced by the direct evaluation of the corresponding limit.
Forced fluid dynamics from blackfolds in general supergravity backgrounds
Armas, Jay [Physique Théorique et Mathématique,Université Libre de Bruxelles and International Solvay Institutes,ULB-Campus Plaine CP231, B-1050 Brussels (Belgium); Gath, Jakob [Centre de Physique Théorique, École Polytechnique,CNRS UMR 7644, Université Paris-Saclay,F-91128 Palaiseau (France); Niarchos, Vasilis [Crete Center for Theoretical Physics, Institute of Theoretical and Computational Physics,Crete Center for Quantum Complexity and Nanotechnology,Department of Physics, University of Crete,Heraklion, 71303 (Greece); Obers, Niels A.; Pedersen, Andreas Vigand [The Niels Bohr Institute, Copenhagen University,Blegdamsvej 17, DK-2100 Copenhagen Ø (Denmark)
2016-10-27
We present a general treatment of the leading order dynamics of the collective modes of charged dilatonic p-brane solutions of (super)gravity theories in arbitrary backgrounds. To this end we employ the general strategy of the blackfold approach which is based on a long-wavelength derivative expansion around an exact or approximate solution of the (super)gravity equations of motion. The resulting collective mode equations are formulated as forced hydrodynamic equations on dynamically embedded hypersurfaces. We derive them in full generality (including all possible asymptotic fluxes and dilaton profiles) in a far-zone analysis of the (super)gravity equations and in representative examples in a near-zone analysis. An independent treatment based on the study of external couplings in hydrostatic partition functions is also presented. Special emphasis is given to the forced collective mode equations that arise in type IIA/B and eleven-dimensional supergravities, where besides the standard Lorentz force couplings our analysis reveals additional couplings to the background, including terms that arise from Chern-Simons interactions. We also present a general overview of the blackfold approach and some of the key conceptual issues that arise when applied to arbitrary backgrounds.
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...
Newtonian hydrodynamic equations with relativistic pressure and velocity
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.
Theoretical frameworks for testing relativistic gravity. V - Post-Newtonian limit of Rosen's theory
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.
A Paradox of Newtonian Gravitation and Laplace's Solution
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 ...
Eckhardt, Donald H.; Garrido Pestaña, José Luis
2014-06-01
The nineteenth century's quest for the missing matter (Vulcan) ended with the publication of Einstein's General Theory of Relativity. We contend that the current quest for the missing matter is parallel in its perseverance and in its ultimate futility. After setting the search for dark matter in its historic perspective, we critique extant dark matter models and offer alternative explanations -- derived from a Lorentz-invariant Lagrangian -- that will, at the very least, sow seeds of doubt about the existence of dark matter.
Non-Newtonian Flow-Induced Deformation From Pressurized Cavities in Absorbing Porous Tissues
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.
Dynamics of Newtonian annular jets
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
Post-Newtonian N-body simulations
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.
A general theory of non-equilibrium dynamics of lipid-protein fluid membranes
Lomholt, Michael Andersen; Hansen, Per Lyngs; Miao, L.
2005-01-01
We present a general and systematic theory of non-equilibrium dynamics of multi-component fluid membranes, in general, and membranes containing transmembrane proteins, in particular. Developed based on a minimal number of principles of statistical physics and designed to be a meso...
On exact solutions for some oscillating motions of a generalized Oldroyd-B fluid
Khan, M.; Anjum, Asia; Qi, Haitao; Fetecau, C.
2010-02-01
This paper deals with exact solutions for some oscillating motions of a generalized Oldroyd-B fluid. The fractional calculus approach is used in the constitutive relationship of fluid model. Analytical expressions for the velocity field and the corresponding shear stress for flows due to oscillations of an infinite flat plate as well as those induced by an oscillating pressure gradient are determined using Fourier sine and Laplace transforms. The obtained solutions are presented under integral and series forms in terms of the Mittag-Leffler functions. For α = β = 1, our solutions tend to the similar solutions for ordinary Oldroyd-B fluid. A comparison between generalized and ordinary Oldroyd-B fluids is shown by means of graphical illustrations.
Slip effects on a generalized Burgers’ fluid flow between two side walls with fractional derivative
Shihao Han
2016-01-01
Full Text Available This paper presents a research for the 3D flow of a generalized Burgers’ fluid between two side walls generated by an exponential accelerating plate and a constant pressure gradient, where the no-slip assumption between the exponential accelerating plate and the Burgers’ fluid is no longer valid. The governing equations of the generalized Burgers’ fluid flow are established by using the fractional calculus approach. Exact analytic solutions for the 3D flow are established by employing the Laplace transform and the finite Fourier sine transform. Furthermore, some 3D and 2D figures for the fluid velocity and shear stress are plotted to analyze and discuss the effects of various parameters.
Nonrotating black hole in a post-Newtonian tidal environment
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.
GUP parameter from quantum corrections to the Newtonian potential
Scardigli, Fabio, E-mail: fabio@phys.ntu.edu.tw [Dipartimento di Matematica, Politecnico di Milano, Piazza L. da Vinci 32, 20133 Milano (Italy); Department of Applied Mathematics, University of Waterloo, Ontario N2L 3G1 (Canada); Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan); Lambiase, Gaetano, E-mail: lambiase@sa.infn.it [Dipartimento di Fisica “E.R. Caianiello”, Universita' di Salerno, I-84084 Fisciano (Italy); INFN – Gruppo Collegato di Salerno (Italy); Vagenas, Elias C., E-mail: elias.vagenas@ku.edu.kw [Theoretical Physics Group, Department of Physics, Kuwait University, P.O. Box 5969, Safat 13060 (Kuwait)
2017-04-10
We propose a technique to compute the deformation parameter of the generalized uncertainty principle by using the leading quantum corrections to the Newtonian potential. We just assume General Relativity as theory of Gravitation, and the thermal nature of the GUP corrections to the Hawking spectrum. With these minimal assumptions our calculation gives, to first order, a specific numerical result. The physical meaning of this value is discussed, and compared with the previously obtained bounds on the generalized uncertainty principle deformation parameter.
On exact solutions for oscillatory flows in a generalized Burgers fluid with slip condition
Hayat, Tasawar [Dept. of Mathematics, Quaid-i-Azam Univ., Islamabad (Pakistan); Dept. of Mathematics, Coll. of Sciences, KS Univ., Riyadh (Saudi Arabia); Najam, Saher [Theoretical Plasma Physics Div., PINSTECH, P.O. Nilore, Islamabad (Pakistan); Sajid, Muhammad; Mesloub, Said [Dept. of Mathematics, Coll. of Sciences, KS Univ., Riyadh (Saudi Arabia); Ayub, Muhammad [Dept. of Mathematics, Quaid-i-Azam Univ., Islamabad (Pakistan)
2010-05-15
An analysis is performed for the slip effects on the exact solutions of flows in a generalized Burgers fluid. The flow modelling is based upon the magnetohydrodynamic (MHD) nature of the fluid and modified Darcy law in a porous space. Two illustrative examples of oscillatory flows are considered. The results obtained are compared with several limiting cases. It has been shown here that the derived results hold for all values of frequencies including the resonant frequency. (orig.)
Rate-Dependent Slip of Newtonian Liquid at Smooth Surfaces
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
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
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.
Increasing heat transfer of non-Newtonian nanofluid in rectangular microchannel with triangular ribs
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).
Relativistic gravitation theory for the modified Newtonian dynamics paradigm
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
Generalized Hamiltonians, functional integration and statistics of continuous fluids and plasmas
Tasso, H.
1985-05-01
Generalized Hamiltonian formalism including generalized Poisson brackets and Lie-Poisson brackets is presented in Section II. Gyroviscous magnetohydrodynamics is treated as a relevant example in Euler and Clebsch variables. Section III is devoted to a short review of functional integration containing the definition and a discussion of ambiguities and methods of evaluation. The main part of the contribution is given in Section IV, where some of the content of the previous sections is applied to Gibbs statistics of continuous fluids and plasmas. In particular, exact fluctuation spectra are calculated for relevant equations in fluids and plasmas. (orig.)
Thirukkanesh, S. [Eastern University, Department of Mathematics, Chenkalady (Sri Lanka); Ragel, F.C. [Eastern University, Department of Physics, Chenkalady (Sri Lanka); Sharma, Ranjan; Das, Shyam [P.D. Women' s College, Department of Physics, Jalpaiguri (India)
2018-01-15
We present an algorithm to generalize a plethora of well-known solutions to Einstein field equations describing spherically symmetric relativistic fluid spheres by relaxing the pressure isotropy condition on the system. By suitably fixing the model parameters in our formulation, we generate closed-form solutions which may be treated as an anisotropic generalization of a large class of solutions describing isotropic fluid spheres. From the resultant solutions, a particular solution is taken up to show its physical acceptability. Making use of the current estimate of mass and radius of a known pulsar, the effects of anisotropic stress on the gross physical behaviour of a relativistic compact star is also highlighted. (orig.)
Virial Theorem in Nonlocal Newtonian Gravity
Bahram Mashhoon
2016-05-01
Full Text Available Nonlocal gravity is the recent classical nonlocal generalization of Einstein’s theory of gravitation in which the past history of the gravitational field is taken into account. In this theory, nonlocality appears to simulate dark matter. The virial theorem for the Newtonian regime of nonlocal gravity theory is derived and its consequences for “isolated” astronomical systems in virial equilibrium at the present epoch are investigated. In particular, for a sufficiently isolated nearby galaxy in virial equilibrium, the galaxy’s baryonic diameter D 0 —namely, the diameter of the smallest sphere that completely surrounds the baryonic system at the present time—is predicted to be larger than the effective dark matter fraction f D M times a universal length that is the basic nonlocality length scale λ 0 ≈ 3 ± 2 kpc.
Burkhardt, Z.; Ramachandran, N.; Majumdar, A.
2017-01-01
Fluid Transient analysis is important for the design of spacecraft propulsion system to ensure structural stability of the system in the event of sudden closing or opening of the valve. Generalized Fluid System Simulation Program (GFSSP), a general purpose flow network code developed at NASA/MSFC is capable of simulating pressure surge due to sudden opening or closing of valve when thermodynamic properties of real fluid are available for the entire range of simulation. Specifically GFSSP needs an accurate representation of pressure-density relationship in order to predict pressure surge during a fluid transient. Unfortunately, the available thermodynamic property programs such as REFPROP, GASP or GASPAK does not provide the thermodynamic properties of Monomethylhydrazine (MMH). This paper will illustrate the process used for building a customized table of properties of state variables from available properties and speed of sound that is required by GFSSP for simulation. Good agreement was found between the simulations and measured data. This method can be adopted for modeling flow networks and systems with other fluids whose properties are not known in detail in order to obtain general technical insight. Rigorous code validation of this approach will be done and reported at a future date.
Pore scale simulations for the extension of the Darcy-Forchheimer law to shear thinning fluids
Tosco, Tiziana; Marchisio, Daniele; Lince, Federica; Boccardo, Gianluca; Sethi, Rajandrea
2014-05-01
Flow of non-Newtonian fluids through porous media at high Reynolds numbers is often encountered in chemical, pharmaceutical and food as well as petroleum and groundwater engineering and in many other industrial applications (1 - 2). In particular, the use of shear thinning polymeric solutions has been recently proposed to improve colloidal stability of micro- and nanoscale zerovalent iron particles (MZVI and NZVI) for groundwater remediation. In all abovementioned applications, it is of paramount importance to correctly predict the pressure drop resulting from non-Newtonian fluid flow through the porous medium. For small Reynolds numbers, usually up to 1, typical of laboratory column tests, the extended Darcy law is known to be applicable also to non Newtonian fluids, provided that all non-Newtonian effects are lumped together into a proper viscosity parameter (1,3). For higher Reynolds numbers (eg. close to the injection wells) non linearities between pressure drop and flow rate arise, and the Darcy-Forchheimer law holds for Newtonian fluids, while for non-Newtonian fluids, it has been demonstrated that, at least for simple rheological models (eg. power law fluids) a generalized Forchheimer law can be applied, even if the determination of the flow parameters (permeability K, inertial coefficient β, and equivalent viscosity) is not straightforward. This work (co-funded by European Union project AQUAREHAB FP7 - Grant Agreement Nr. 226565) aims at proposing an extended formulation of the Darcy-Forchheimer law also for shear-thinning fluids, and validating it against results of pore-scale simulations via computational fluid dynamics (4). Flow simulations were performed using Fluent 12.0 on four different 2D porous domains for Newtonian and non-Newtonian fluids (Cross, Ellis and Carreau models). The micro-scale flow simulation results are analyzed in terms of 'macroscale' pressure drop between inlet and outlet of the model domain as a function of flow rate. The
General proof of the entropy principle for self-gravitating fluid in f(R) gravity
Fang, Xiongjun [Department of Physics and Key Laboratory of Low Dimensional Quantum Structures andQuantum Control of Ministry of Education, Hunan Normal University,Changsha, Hunan 410081 (China); Guo, Minyong [Department of Physics, Beijing Normal University,Beijing 100875 (China); Jing, Jiliang [Department of Physics and Key Laboratory of Low Dimensional Quantum Structures andQuantum Control of Ministry of Education, Hunan Normal University,Changsha, Hunan 410081 (China)
2016-08-29
The discussions on the connection between gravity and thermodynamics attract much attention recently. We consider a static self-gravitating perfect fluid system in f(R) gravity, which is an important theory could explain the accelerated expansion of the universe. We first show that the Tolman-Oppenheimer-Volkoff equation of f(R) theories can be obtained by thermodynamical method in spherical symmetric spacetime. Then we prove that the maximum entropy principle is also valid for f(R) gravity in general static spacetimes beyond spherical symmetry. The result shows that if the constraint equation is satisfied and the temperature of fluid obeys Tolmans law, the extrema of total entropy implies other components of gravitational equations. Conversely, if f(R) gravitational equation hold, the total entropy of the fluid should be extremum. Our work suggests a general and solid connection between f(R) gravity and thermodynamics.
Interfacing a General Purpose Fluid Network Flow Program with the SINDA/G Thermal Analysis Program
Schallhorn, Paul; Popok, Daniel
1999-01-01
A general purpose, one dimensional fluid flow code is currently being interfaced with the thermal analysis program Systems Improved Numerical Differencing Analyzer/Gaski (SINDA/G). The flow code, Generalized Fluid System Simulation Program (GFSSP), is capable of analyzing steady state and transient flow in a complex network. The flow code is capable of modeling several physical phenomena including compressibility effects, phase changes, body forces (such as gravity and centrifugal) and mixture thermodynamics for multiple species. The addition of GFSSP to SINDA/G provides a significant improvement in convective heat transfer modeling for SINDA/G. The interface development is conducted in multiple phases. This paper describes the first phase of the interface which allows for steady and quasi-steady (unsteady solid, steady fluid) conjugate heat transfer modeling.
Parameterized post-Newtonian cosmology
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)
Parameterized post-Newtonian cosmology
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).
Inhomogeneous generalizations of Bianchi Type VIh universes with stiff perfect fluid and radiation
Roy, S. R.; Prasad, A.
1995-03-01
Families of inhomogeneous models filled with a stiff perfect fluid and radiation have been derived in which there is no flow of total momentum. The models are generalizations of those of Bianchi Type VIh and are discussed for some particular forms of the arbitrary functions appearing in them.
Generalized Couette flow of a third-grade fluid with slip. The exact solutions
Ellahi, Rahmat [IIUI, Islamabad (Pakistan). Dept. of Mathematics; Hayat, Tasawar [Quaid-i-Azam Univ., Islamabad (Pakistan). Dept. of Mathematics; King Saud Univ., Riyadh (Saudi Arabia). Dept. of Mathematics; Mahomed, Fazal Mahmood [Univ. of the Witwatersrand, Wits (South Africa). Centre for Differential Equations, Continuum, Mechanics and Applications
2010-12-15
The present note investigates the influence of slip on the generalized Couette flows of a third-grade fluid. Two flow problems are considered. The resulting equations and the boundary conditions are nonlinear. Analytical solutions of the governing nonlinear problems are found in closed form. (orig.)
Generation of Oil Droplets in a Non-Newtonian Liquid Using a Microfluidic T-Junction
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.
Cosmology with modified Newtonian dynamics (MOND)
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
Urinary Analysis of Fluid Retention in the General Population: A Cross-Sectional Study.
Robert G Hahn
Full Text Available Renal conservation (retention of fluid might affect the outcome of hospital care and can be indicated by increased urinary concentrations of metabolic waste products. We obtained a reference material for further studies by exploring the prevalence of fluid retention in a healthy population.Spot urine sampling was performed in 300 healthy hospital workers. A previously validated algorithm summarized the urine-specific gravity, osmolality, creatinine, and color to a fluid retention index (FRI, where 4.0 is the cut-off for fluid retention consistent with dehydration. In 50 of the volunteers, we also studied the relationships between FRI, plasma osmolality, and water-retaining hormones.The cut-off for fluid retention (FRI ≥ 4.0 was reached by 38% of the population. No correlation was found between the FRI and the time of the day of urine sample collection, and the FRI was only marginally correlated with the time period spent without fluid intake. Volunteers with fluid retention were younger, generally men, and more often had albuminuria (88% vs. 34%, P < 0.001. Plasma osmolality and plasma sodium were somewhat higher in those with a high FRI (mean 294.8 vs. 293.4 mosmol/kg and 140.3 vs. 139.9 mmol/l. Plasma vasopressin was consistently below the limit of detection, and the plasma cortisol, aldosterone, and renin concentrations were similar in subjects with a high or low FRI. The very highest FRI values (≥ 5.0, N = 61 were always accompanied by albuminuria.Fluid retention consistent with moderate dehydration is common in healthy staff working in a Swedish hospital.
Post-Newtonian approximation of the maximum four-dimensional Yang-Mills gauge theory
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
A General Nonlinear Fluid Model for Reacting Plasma-Neutral Mixtures
Meier, E T; Shumlak, U
2012-04-06
A generalized, computationally tractable fluid model for capturing the effects of neutral particles in plasmas is derived. The model derivation begins with Boltzmann equations for singly charged ions, electrons, and a single neutral species. Electron-impact ionization, radiative recombination, and resonant charge exchange reactions are included. Moments of the reaction collision terms are detailed. Moments of the Boltzmann equations for electron, ion, and neutral species are combined to yield a two-component plasma-neutral fluid model. Separate density, momentum, and energy equations, each including reaction transfer terms, are produced for the plasma and neutral equations. The required closures for the plasma-neutral model are discussed.
Waqar Azeem Khan
Full Text Available The present paper deals with the analysis of melting heat and mass transfer characteristics in the stagnation point flow of an incompressible generalized Burgers fluid over a stretching sheet in the presence of non-linear radiative heat flux. A uniform magnetic field is applied normal to the flow direction. The governing equations in dimensional form are reduced to a system of dimensionless expressions by implementation of suitable similarity transformations. The resulting dimensionless problem governing the generalized Burgers is solved analytically by using the homotopy analysis method (HAM. The effects of different flow parameters like the ratio parameter, magnetic parameter, Prandtl number, melting parameter, radiation parameter, temperature ratio parameter and Schmidt number on the velocity, heat and mass transfer characteristics are computed and presented graphically. Moreover, useful discussions in detail are carried out with the help of plotted graphs and tables. Keywords: Generalized Burgers fluid, Non-linear radiative flow, Magnetic field, Melting heat transfer
RESONANT POST-NEWTONIAN ECCENTRICITY EXCITATION IN HIERARCHICAL THREE-BODY SYSTEMS
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.
The significance of Newtonian cosmology
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.)
Modeling Two-Phase Flow and Vapor Cycles Using the Generalized Fluid System Simulation Program
Smith, Amanda D.; Majumdar, Alok K.
2017-01-01
This work presents three new applications for the general purpose fluid network solver code GFSSP developed at NASA's Marshall Space Flight Center: (1) cooling tower, (2) vapor-compression refrigeration system, and (3) vapor-expansion power generation system. These systems are widely used across engineering disciplines in a variety of energy systems, and these models expand the capabilities and the use of GFSSP to include fluids and features that are not part of its present set of provided examples. GFSSP provides pressure, temperature, and species concentrations at designated locations, or nodes, within a fluid network based on a finite volume formulation of thermodynamics and conservation laws. This paper describes the theoretical basis for the construction of the models, their implementation in the current GFSSP modeling system, and a brief evaluation of the usefulness of the model results, as well as their applicability toward a broader spectrum of analytical problems in both university teaching and engineering research.
Newtonian potential and geodesic completeness in infinite derivative gravity
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.
Parameterised post-Newtonian expansion in screened regions
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.
Theoretical frameworks for testing relativistic gravity. 5: Post-Newtonian limit of Rosen's theory
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.
Equilibrium configurations of fluids and their stability in higher dimensions
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
Actual Romanian research in post-newtonian dynamics
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.
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.
Zhao, Guangpu [School of Mathematical Science, Inner Mongolia University, Hohhot, Inner Mongolia 010021 (China); Jian, Yongjun, E-mail: jianyj@imu.edu.cn [School of Mathematical Science, Inner Mongolia University, Hohhot, Inner Mongolia 010021 (China); Chang, Long [School of Mathematics and Statistics, Inner Mongolia University of Finance and Economics, Hohhot, Inner Mongolia 010051 (China); Buren, Mandula [School of Mathematical Science, Inner Mongolia University, Hohhot, Inner Mongolia 010021 (China)
2015-08-01
By using the method of separation of variables, an analytical solution for the magnetohydrodynamic (MHD) flow of the generalized Maxwell fluids under AC electric field through a two-dimensional rectangular micropump is reduced. By the numerical computation, the variations of velocity profiles with the electrical oscillating Reynolds number Re, the Hartmann number Ha, the dimensionless relaxation time De are studied graphically. Further, the comparison with available experimental data and relevant researches is presented. - Highlights: • MHD flow of the generalized Maxwell fluids under AC electric field is analyzed. • The MHD flow is confined to a two-dimensional rectangular micropump. • Analytical solution is obtained by using the method of separation of variables. • The influences of related parameters on the MHD velocity are discussed.
Zhao, Guangpu; Jian, Yongjun; Chang, Long; Buren, Mandula
2015-01-01
By using the method of separation of variables, an analytical solution for the magnetohydrodynamic (MHD) flow of the generalized Maxwell fluids under AC electric field through a two-dimensional rectangular micropump is reduced. By the numerical computation, the variations of velocity profiles with the electrical oscillating Reynolds number Re, the Hartmann number Ha, the dimensionless relaxation time De are studied graphically. Further, the comparison with available experimental data and relevant researches is presented. - Highlights: • MHD flow of the generalized Maxwell fluids under AC electric field is analyzed. • The MHD flow is confined to a two-dimensional rectangular micropump. • Analytical solution is obtained by using the method of separation of variables. • The influences of related parameters on the MHD velocity are discussed
Conway, Andrew R. A.; Cowan, Nelsin; Bunting, Michael F.; Therriault, David J.; Minkoff, Scott R. B.
2002-01-01
Studied the interrelationships among general fluid intelligence, short-term memory capacity, working memory capacity, and processing speed in 120 young adults and used structural equation modeling to determine the best predictor of general fluid intelligence. Results suggest that working memory capacity, but not short-term memory capacity or…
A Lagrangian finite element method for the simulation of flow of non-newtonian liquids
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...
Break-up of a non-Newtonian jet injected downwards in a ...
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.
Conservation form of the equations of fluid dynamics in general nonsteady coordinates
Zhang, H.; Camarero, R.; Kahawita, R.
1985-11-01
Many of the differential equations arising in fluid dynamics may be stated in conservation-law form. A number of investigations have been conducted with the aim to derive the conservation-law form of the Navier-Stokes equations in general nonsteady coordinate systems. The present note has the objective to illustrate a mathematical methodology with which such forms of the equations may be derived in an easier and more general fashion. For numerical applications, the scalar form of the equations is eventually provided. Attention is given to the conservation form of equations in curvilinear coordinates and numerical considerations.
Conservation form of the equations of fluid dynamics in general nonsteady coordinates
Zhang, H.; Camarero, R.; Kahawita, R.
1985-01-01
Many of the differential equations arising in fluid dynamics may be stated in conservation-law form. A number of investigations have been conducted with the aim to derive the conservation-law form of the Navier-Stokes equations in general nonsteady coordinate systems. The present note has the objective to illustrate a mathematical methodology with which such forms of the equations may be derived in an easier and more general fashion. For numerical applications, the scalar form of the equations is eventually provided. Attention is given to the conservation form of equations in curvilinear coordinates and numerical considerations. 6 references
Determining Rheological Parameters of Generalized Yield-Power-Law Fluid Model
Stryczek Stanislaw
2004-09-01
Full Text Available The principles of determining rheological parameters of drilling muds described by a generalized yield-power-law are presented in the paper. Functions between tangent stresses and shear rate are given. The conditions of laboratory measurements of rheological parameters of generalized yield-power-law fluids are described and necessary mathematical relations for rheological model parameters given. With the block diagrams, the methodics of numerical solution of these relations has been presented. Rheological parameters of an exemplary drilling mud have been calculated with the use of this numerical program.
Parameterized Post-Newtonian Expansion of Scalar-Vector-Tensor Theory of Gravity
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.
A note on the post-Newtonian limit of quasi-local energy expressions
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)
Time in Newtonian physics and special relativity
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
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.
Spiral waves in driven dusty plasma medium: Generalized hydrodynamic fluid description
Kumar, Sandeep; Patel, Bhavesh; Das, Amita
2018-04-01
Spiral waves are observed in many natural phenomena. They have been extensively represented by the mathematical FitzHugh-Nagumo model [Barkley et al., Phys. Rev. A 42, 2489 (1990)] of excitable media. Also, in incompressible fluid simulations, the excitation of thermal spiral waves has been reported by Li et al. [Phys. of Fluids 22, 011701 (2010)]. In the present paper, the spatiotemporal development of spiral waves in the context of weak and strong coupling limits has been shown. While the weakly coupled medium has been represented by a simple fluid description, for strong coupling, a generalized visco-elastic fluid description has been employed. The medium has been driven by an external force in the form of a rotating electric field. It is shown that when the amplitude of force is small, the density perturbations in the medium are also small. In this case, the excitations do not develop as a spiral wave. Only when the amplitude of force is high so as to drive the density perturbations to nonlinear amplitudes does the spiral density wave formation occurs. The role of the forcing frequency and the effect of strong coupling and the sound velocity of medium in the formation and evolution of spiral waves have been investigated in detail.
GUP parameter from quantum corrections to the Newtonian potential
Fabio Scardigli
2017-04-01
Full Text Available We propose a technique to compute the deformation parameter of the generalized uncertainty principle by using the leading quantum corrections to the Newtonian potential. We just assume General Relativity as theory of Gravitation, and the thermal nature of the GUP corrections to the Hawking spectrum. With these minimal assumptions our calculation gives, to first order, a specific numerical result. The physical meaning of this value is discussed, and compared with the previously obtained bounds on the generalized uncertainty principle deformation parameter.
Newtonian versus black-hole scattering
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
Congested Aggregation via Newtonian Interaction
Craig, Katy; Kim, Inwon; Yao, Yao
2018-01-01
We consider a congested aggregation model that describes the evolution of a density through the competing effects of nonlocal Newtonian attraction and a hard height constraint. This provides a counterpoint to existing literature on repulsive-attractive nonlocal interaction models, where the repulsive effects instead arise from an interaction kernel or the addition of diffusion. We formulate our model as the Wasserstein gradient flow of an interaction energy, with a penalization to enforce the constraint on the height of the density. From this perspective, the problem can be seen as a singular limit of the Keller-Segel equation with degenerate diffusion. Two key properties distinguish our problem from previous work on height constrained equations: nonconvexity of the interaction kernel (which places the model outside the scope of classical gradient flow theory) and nonlocal dependence of the velocity field on the density (which causes the problem to lack a comparison principle). To overcome these obstacles, we combine recent results on gradient flows of nonconvex energies with viscosity solution theory. We characterize the dynamics of patch solutions in terms of a Hele-Shaw type free boundary problem and, using this characterization, show that in two dimensions patch solutions converge to a characteristic function of a disk in the long-time limit, with an explicit rate on the decay of the energy. We believe that a key contribution of the present work is our blended approach, combining energy methods with viscosity solution theory.
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
Gravitational radiation from nearly Newtonian systems
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)
Hansen, J S; Daivis, Peter J; Dyre, Jeppe C; Todd, B D; Bruus, Henrik
2013-01-21
The extended Navier-Stokes theory accounts for the coupling between the translational and rotational molecular degrees of freedom. In this paper, we generalize this theory to non-zero frequencies and wavevectors, which enables a new study of spatio-temporal correlation phenomena present in molecular fluids. To discuss these phenomena in detail, molecular dynamics simulations of molecular chlorine are performed for three different state points. In general, the theory captures the behavior for small wavevector and frequencies as expected. For example, in the hydrodynamic regime and for molecular fluids with small moment of inertia like chlorine, the theory predicts that the longitudinal and transverse intrinsic angular velocity correlation functions are almost identical, which is also seen in the molecular dynamics simulations. However, the theory fails at large wavevector and frequencies. To account for the correlations at these scales, we derive a phenomenological expression for the frequency dependent rotational viscosity and wavevector and frequency dependent longitudinal spin viscosity. From this we observe a significant coupling enhancement between the molecular angular velocity and translational velocity for large frequencies in the gas phase; this is not observed for the supercritical fluid and liquid state points.
Farassat, Fereidoun; Myers, Michael K.
2011-01-01
This paper is the first part of a three part tutorial on multidimensional generalized functions (GFs) and their applications in aeroacoustics and fluid mechanics. The subject is highly fascinating and essential in many areas of science and, in particular, wave propagation problems. In this tutorial, we strive to present rigorously and clearly the basic concepts and the tools that are needed to use GFs in applications effectively and with ease. We give many examples to help the readers in understanding the mathematical ideas presented here. The first part of the tutorial is on the basic concepts of GFs. Here we define GFs, their properties and some common operations on them. We define the important concept of generalized differentiation and then give some interesting elementary and advanced examples on Green's functions and wave propagation problems. Here, the analytic power of GFs in applications is demonstrated with ease and elegance. Part 2 of this tutorial is on the diverse applications of generalized derivatives (GDs). Part 3 is on generalized Fourier transformations and some more advanced topics. One goal of writing this tutorial is to convince readers that, because of their powerful operational properties, GFs are absolutely essential and useful in engineering and physics, particularly in aeroacoustics and fluid mechanics.
Relativistic thermodynamics of Fluids. l
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
Conceptual evolution of Newtonian and relativistic mechanics
Ghosh, Amitabha
2018-01-01
This book provides an introduction to Newtonian and relativistic mechanics. Unlike other books on the topic, which generally take a 'top-down' approach, it follows a novel system to show how the concepts of the 'science of motion' evolved through a veritable jungle of intermediate ideas and concepts. Starting with Aristotelian philosophy, the text gradually unravels how the human mind slowly progressed towards the fundamental ideas of inertia physics. The concepts that now appear so obvious to even a high school student took great intellectuals more than a millennium to clarify. The book explores the evolution of these concepts through the history of science. After a comprehensive overview of the discovery of dynamics, it explores fundamental issues of the properties of space and time and their relation with the laws of motion. It also explores the concepts of spatio-temporal locality and fields, and offers a philosophical discussion of relative motion versus absolute motion, as well as the concept of an abso...
Generalized Einstein relation for the mutual diffusion coefficient of a binary fluid mixture.
Felderhof, B U
2017-08-21
The method employed by Einstein to derive his famous relation between the diffusion coefficient and the friction coefficient of a Brownian particle is used to derive a generalized Einstein relation for the mutual diffusion coefficient of a binary fluid mixture. The expression is compared with the one derived by de Groot and Mazur from irreversible thermodynamics and later by Batchelor for a Brownian suspension. A different result was derived by several other workers in irreversible thermodynamics. For a nearly incompressible solution, the generalized Einstein relation agrees with the expression derived by de Groot and Mazur. The two expressions also agree to first order in solute density. For a Brownian suspension, the result derived from the generalized Smoluchowski equation agrees with both expressions.
Effective fluid description of the dark universe
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.
The parameterized post-Newtonian limit of bimetric theories of gravity
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.
On the spherical symmetry of static perfect fluids in general relativity
Beig, R.; Simon, W.
1990-01-01
We present a theorem which establishes uniqueness, in particular spherical symmetry, of a wide class of general relativistic, static perfect-fluid models provided there exists a spherically symmetric model with the same equation of state and surface potential. The method of proof, which is inspired by recent work of Masood-ul-Alam, is illustrated by demonstrating uniqueness of a class of solutions due to Buchdahl which correspond to an extreme case of the inequality on the equation of state required by our theorem. 16 refs. (Authors)
General Approach to Characterize Reservoir Fluids Using a Large PVT Database
Varzandeh, Farhad; Yan, Wei; Stenby, Erling Halfdan
2016-01-01
methods. We proposed a general approach to develop correlations for model parameters and applied it to the characterization for the PC-SAFT EoS. The approach consists in first developing the correlations based on the DIPPR database, and then adjusting the correlations based on a large PVT database......, the approach gives better PVT calculation results for the tested systems. Comparison was also made between PC-SAFT with the proposed characterization method and other EoS models. The proposed approach can be applied to other EoS models for improving their fluid characterization. Besides, the challenges...
Stability analysis on the free surface phenomena of a magnetic fluid for general use
Mizuta, Yo
2011-01-01
This paper presents an analysis for elucidating a variety of physical processes on the interface (free surface) of magnetic fluid. The present analysis is composed of the magnetic and the fluid analysis, both of which have no limitations concerning the interface elevation or its profile. The magnetic analysis provides rigorous interface magnetic field under arbitrary distributions of applied magnetic field. For the fluid analysis, the equation for interface motion includes all nonlinear effects. Physical quantities such as the interface magnetic field or the interface stresses, obtained first as the wavenumber components, facilitate confirming the relations with those by the conventional theoretical analyses. The nonlinear effect is formulated as the nonlinear mode coupling between the interface profile and the applied magnetic field. The stability of the horizontal interface profile is investigated by the dispersion relation, and summarized as the branch line. Furthermore, the balance among the spectral components of the interface stresses are shown, within the sufficient range of the wavenumber space. - Research Highlights: → General, rigorous but compact analysis for free surface phenomena is shown. → Analysis is applied without limitations on the interface elevation or its profile. → Nonlinear effects are formulated as the nonlinear mode coupling. → Bifurcation of stability is summarized as the branch line. → Balance among the interface stresses are shown in the wavenumber space.
Viscous Flow with Large Fluid-Fluid Interface Displacement
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....
Point-of-care Devices: Non-Newtonian Whole Blood Behavior and Capillary Flow on Reagent-coated Walls
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.
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
Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries
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.
Blair, Clancy
2006-04-01
This target article considers the relation of fluid cognitive functioning to general intelligence. A neurobiological model differentiating working memory/executive function cognitive processes of the prefrontal cortex from aspects of psychometrically defined general intelligence is presented. Work examining the rise in mean intelligence-test performance between normative cohorts, the neuropsychology and neuroscience of cognitive function in typically and atypically developing human populations, and stress, brain development, and corticolimbic connectivity in human and nonhuman animal models is reviewed and found to provide evidence of mechanisms through which early experience affects the development of an aspect of cognition closely related to, but distinct from, general intelligence. Particular emphasis is placed on the role of emotion in fluid cognition and on research indicating fluid cognitive deficits associated with early hippocampal pathology and with dysregulation of the hypothalamic-pituitary-adrenal axis stress-response system. Findings are seen to be consistent with the idea of an independent fluid cognitive construct and to assist with the interpretation of findings from the study of early compensatory education for children facing psychosocial adversity and from behavior genetic research on intelligence. It is concluded that ongoing development of neurobiologically grounded measures of fluid cognitive skills appropriate for young children will play a key role in understanding early mental development and the adaptive success to which it is related, particularly for young children facing social and economic disadvantage. Specifically, in the evaluation of the efficacy of compensatory education efforts such as Head Start and the readiness for school of children from diverse backgrounds, it is important to distinguish fluid cognition from psychometrically defined general intelligence.
Imaz Iglesia, I; Gómez López, L I; Fernández Martínez, J A; Mareca Doñate, R; Sangrador Arenas, L A
1996-01-01
To assess the informative usefulness of the Registry, to calculate the incidence rates of accident with biological fluids among health care workers and in the community, to know about the postaccident rate of seroconversion to HIV and to identify risk groups. A descriptive study of the HIV records file of the Registry of Accidental Contacts to Biological Fluids in the Clinic Hospital of Zaragoza was conducted, between January 1987 and September 1993. The registry includes the reports of health care workers and the general population of Health Area III in Aragón (Spain), except for the Calatayud's Hospital. Incidence rates, rate ratios and their 95% confidence intervals were calculated. A total number of 595 accidents were reported, in none of them and HIV infection occurred subsequently. The incidence rate in health care workers was of 1.7 reports per 100 workers per year, while in the community it was of 8.1 per 100,000 people. The housekeeping staff was the group with a higher incidence (rate = 6.7; 95% IC: 3-14.8) and the type of accident more frequently described was needlestick injury. The incidence of reported accidents has increased in the community and in health care workers, which may be due to the increase in the reporting. In health care workers, the incidence in 1993 was within the range reported from other countries. The perception of risk is universal after accidents with unknown biological fluids. The correct disposal of material with biological contamination should be the more important preventive action.
Minimal gravitational coupling in the Newtonian theory and the covariant Schroedinger equation
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
Minimal gravitational coupling in the Newtonian theory and the covariant Schroedinger equation
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)
Appplication of a general fluid mechanics program to NTP system modeling
Lee, S.K.
1993-01-01
An effort is currently underway at NASA and the Department of Energy (DOE) to develop an accurate model for predicting nuclear thermal propulsion (NTP) system performance. The objective of the effort is to develop several levels of computer programs which vary in detail and complexity according to user's needs. The current focus is on the Level 1 steady-state, parametric system model. This system model will combine a general fluid mechanics program, SAFSIM, with the ability to analyze turbines, pumps, nozzles, and reactor physics. SAFSIM (System Analysis Flow SIMulator) is a FORTRAN computer program that simulates integrated performance of systems involving fluid mechanics, heat transfer, and reactor dynamics. SAFSIM has the versatility to allow simulation of almost any system, including a nuclear reactor system. The focus of this paper is the validation of SAFSIM's capabilities as a base computational engine for a nuclear thermal propulsion system model. Validation is being accomplished by modeling of a nuclear engine test using SAFSIM and comparing the results to known experimental data
Generalized extended Navier-Stokes theory: multiscale spin relaxation in molecular fluids.
Hansen, J S
2013-09-01
This paper studies the relaxation of the molecular spin angular velocity in the framework of generalized extended Navier-Stokes theory. Using molecular dynamics simulations, it is shown that for uncharged diatomic molecules the relaxation time decreases with increasing molecular moment of inertia per unit mass. In the regime of large moment of inertia the fast relaxation is wave-vector independent and dominated by the coupling between spin and the fluid streaming velocity, whereas for small inertia the relaxation is slow and spin diffusion plays a significant role. The fast wave-vector-independent relaxation is also observed for highly packed systems. The transverse and longitudinal spin modes have, to a good approximation, identical relaxation, indicating that the longitudinal and transverse spin viscosities have same value. The relaxation is also shown to be isomorphic invariant. Finally, the effect of the coupling in the zero frequency and wave-vector limit is quantified by a characteristic length scale; if the system dimension is comparable to this length the coupling must be included into the fluid dynamical description. It is found that the length scale is independent of moment of inertia but dependent on the state point.
Empirical resistive-force theory for slender biological filaments in shear-thinning fluids
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.
Analytical solutions of couple stress fluid flows with slip boundary conditions
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.
Pulmonary Circulation Transvascular Fluid Fluxes Do Not Change during General Anesthesia in Dogs
Olga Frlic
2018-02-01
Full Text Available General anesthesia (GA can cause abnormal lung fluid redistribution. Pulmonary circulation transvascular fluid fluxes (JVA are attributed to changes in hydrostatic forces and erythrocyte volume (EV regulation. Despite the very low hydraulic conductance of pulmonary microvasculature it is possible that GA may affect hydrostatic forces through changes in pulmonary vascular resistance (PVR, and EV through alteration of erythrocyte transmembrane ion fluxes (ionJVA. Furosemide (Fur was also used because of its potential to affect pulmonary hydrostatic forces and ionJVA. A hypothesis was tested that JVA, with or without furosemide treatment, will not change with time during GA. Twenty dogs that underwent castration/ovariectomy were randomly assigned to Fur (n = 10 (4 mg/kg IV or placebo treated group (Con, n = 10. Baseline arterial (BL and mixed venous blood were sampled during GA just before treatment with Fur or placebo and then at 15, 30 and 45 min post-treatment. Cardiac output (Q and pulmonary artery pressure (PAP were measured. JVA and ionJVA were calculated from changes in plasma protein, hemoglobin, hematocrit, plasma and whole blood ions, and Q. Variables were analyzed using random intercept mixed model (P < 0.05. Data are expressed as means ± SE. Furosemide caused a significant volume depletion as evident from changes in plasma protein and hematocrit (P < 0.001. However; Q, PAP, and JVA were not affected by time or Fur, whereas erythrocyte fluid flux was affected by Fur (P = 0.03. Furosemide also affected erythrocyte transmembrane K+ and Cl−, and transvascular Cl− metabolism (P ≤ 0.05. No other erythrocyte transmembrane or transvascular ion fluxes were affected by time of GA or Fur. Our hypothesis was verified as JVA was not affected by GA or ion metabolism changes due to Fur treatment. Furosemide and 45 min of GA did not cause significant hydrostatic changes based on Q and PAP. Inhibition of Na+/K+/2Cl− cotransport caused by Fur
General exact solution for homogeneous time-dependent self-gravitating perfect fluids
Gaete, P.; Hojman, R.
1988-01-01
A procedure to obtain the general exact solution of Einstein equations for a self-gravitating spherically-symmetric static perfect fluid obeying an arbitrary equation of state, is applied to time-dependent Kantowsky-Sachs line elements (with spherical, planar and hyperbolic symmetry). As in the static case, the solution is generated by an arbitrary function of the independent variable and its first derivative. To illustrate the results, the whole family of (plane-symmetric) solutions with a ''gamma-law'' equation of state is explicity obtained in terms of simple known functions. It is also shown that, while in the static plane-symmtric line elements, every metric is in one to one correspondence with a ''partner-metric'' (both originated from the same generatrix function), in this case every generatrix function univocally determines one metric. (author) [pt
Sieniutycz, S.; Berry, R.S.
1993-01-01
A Lagrangian with dissipative (e.g., Onsager's) potentials is constructed for the field description of irreversible heat-conducting fluids, off local equilibrium. Extremum conditions of action yield Clebsch representations of temperature, chemical potential, velocities, and generalized momenta, including a thermal momentum introduced recently [R. L. Selinger and F. R. S. Whitham, Proc. R. Soc. London, Ser. A 302, 1 (1968); S. Sieniutycz and R. S. Berry, Phys. Rev. A 40, 348 (1989)]. The basic question asked is ''To what extent may irreversibility, represented by a given form of the entropy source, influence the analytical form of the conservation laws for the energy and momentum?'' Noether's energy for a fluid with heat flow is obtained, which leads to a fundamental equation and extended Hamiltonian dynamics obeying the second law of thermodynamics. While in the case of the Onsager potentials this energy coincides numerically with the classical energy E, it contains an extra term (vanishing along the path) still contributing to an irreversible evolution. Components of the energy-momentum tensor preserve all terms regarded standardly as ''irreversible'' (heat, tangential stresses, etc.) generalized to the case when thermodynamics includes the state gradients and the so-called thermal phase, which we introduce here. This variable, the Lagrange multiplier of the entropy generation balance, is crucial for consistent treatment of irreversible processes via an action formalism. We conclude with the hypothesis that embedding the first and second laws in the context of the extremal behavior of action under irreversible conditions may imply accretion of an additional term to the classical energy
Leading quantum correction to the Newtonian potential
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
Newtonian gravity and the Bargmann algebra
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
Dynamics of polymeric liquids. Vol. 1, 2nd Ed.: Fluid mechanics
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
Pressure drop coefficient of laminar Newtonian flow in axisymmetric diffusers
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
Pressure drop coefficient of laminar Newtonian flow in axisymmetric diffusers
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.
Reviving the shear-free perfect fluid conjecture in general relativity
Sikhonde, Muzikayise E.; Dunsby, Peter K. S.
2017-12-01
Employing a Mathematica symbolic computer algebra package called xTensor, we present (1+3) -covariant special case proofs of the shear-free perfect fluid conjecture in general relativity. We first present the case where the pressure is constant, and where the acceleration is parallel to the vorticity vector. These cases were first presented in their covariant form by Senovilla et al. We then provide a covariant proof for the case where the acceleration and vorticity vectors are orthogonal, which leads to the existence of a Killing vector along the vorticity. This Killing vector satisfies the new constraint equations resulting from the vanishing of the shear. Furthermore, it is shown that in order for the conjecture to be true, this Killing vector must have a vanishing spatially projected directional covariant derivative along the velocity vector field. This in turn implies the existence of another basic vector field along the direction of the vorticity for the conjecture to hold. Finally, we show that in general, there exists a basic vector field parallel to the acceleration for which the conjecture is true.
Extended ΛCDM: generalized non-minimal coupling for dark matter fluids
Bettoni, Dario; Liberati, Stefano; Sindoni, Lorenzo
2011-01-01
In this paper we discuss a class of models that address the issue of explaining the gravitational dynamics at the galactic scale starting from a geometric point of view. Instead of claiming the existence of some hidden coupling between dark matter and baryons, or abandoning the existence of dark matter itself, we consider the possibility that dark matter and gravity have some non trivial interaction able to modify the dynamics at astrophysical scales. This interaction is implemented assuming that dark matter gets non-minimally coupled with gravity at suitably small scales and late times. After showing the predictions of the model in the Newtonian limit we also discuss the possible origin of it non-minimal coupling. This investigation seems to suggest that phenomenological mechanisms envisaged for the dark matter dynamics, such as the Bose-Einstein condensation of dark matter halos, could be connected to this class of models
A Novel Approach for Modeling Chemical Reaction in Generalized Fluid System Simulation Program
Sozen, Mehmet; Majumdar, Alok
2002-01-01
The Generalized Fluid System Simulation Program (GFSSP) is a computer code developed at NASA Marshall Space Flight Center for analyzing steady state and transient flow rates, pressures, temperatures, and concentrations in a complex flow network. The code, which performs system level simulation, can handle compressible and incompressible flows as well as phase change and mixture thermodynamics. Thermodynamic and thermophysical property programs, GASP, WASP and GASPAK provide the necessary data for fluids such as helium, methane, neon, nitrogen, carbon monoxide, oxygen, argon, carbon dioxide, fluorine, hydrogen, water, a hydrogen, isobutane, butane, deuterium, ethane, ethylene, hydrogen sulfide, krypton, propane, xenon, several refrigerants, nitrogen trifluoride and ammonia. The program which was developed out of need for an easy to use system level simulation tool for complex flow networks, has been used for the following purposes to name a few: Space Shuttle Main Engine (SSME) High Pressure Oxidizer Turbopump Secondary Flow Circuits, Axial Thrust Balance of the Fastrac Engine Turbopump, Pressurized Propellant Feed System for the Propulsion Test Article at Stennis Space Center, X-34 Main Propulsion System, X-33 Reaction Control System and Thermal Protection System, and International Space Station Environmental Control and Life Support System design. There has been an increasing demand for implementing a combustion simulation capability into GFSSP in order to increase its system level simulation capability of a liquid rocket propulsion system starting from the propellant tanks up to the thruster nozzle for spacecraft as well as launch vehicles. The present work was undertaken for addressing this need. The chemical equilibrium equations derived from the second law of thermodynamics and the energy conservation equation derived from the first law of thermodynamics are solved simultaneously by a Newton-Raphson method. The numerical scheme was implemented as a User
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)
Change in the flow curves of non-Newtonian oils due to a magnetic field
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
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
Simulating non-Newtonian flows with the moving particle semi-implicit method with an SPH kernel
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)
A DNS Investigation of Non-Newtonian Turbulent Open Channel Flow
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.
Slip-flow and heat transfer of a non-newtonian nanofluid in a microtube.
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.
Controllability of Non-Newtonian Fluids Under Homogeneous Flows
Wilson, Lynda M
2007-01-01
.... The constitutive models are as follows: the Phan-Thien-Tanner model; the Johnson-Segalman model; and the Doi model. The effect of extensional flow on these models and the effect of shear flow on the Doi model have not been explored previous to this work...
Vivian, Jacopo; Manente, Giovanni; Lazzaretto, Andrea
2015-01-01
Highlights: • General guidelines are proposed to select ORC working fluid and cycle layout. • Distance between critical and heat source temperature for optimal fluid selection. • Separate contributions of cycle efficiency and heat recovery factor. - Abstract: The selection of the most suitable working fluid and cycle configuration for a given heat source is a fundamental step in the search for the optimum design of Organic Rankine Cycles. In this phase cycle efficiency and heat source recovery factor lead to opposite design choices in the achievement of maximum system efficiency and, in turn, maximum power output. In this work, both separate and combined effects of these two performance factors are considered to supply a thorough understanding of the compromise resulting in maximum performance. This goal is pursued by carrying out design optimizations of four different ORC configurations operating with twenty-seven working fluids and recovering heat from sensible heat sources in the temperature range 120–180 °C. Optimum working fluids and thermodynamic parameters are those which simultaneously allow high cycle efficiency and high heat recovery from the heat source to be obtained. General guidelines are suggested to reach this target for any system configuration. The distance between fluid critical temperature and inlet temperature of the heat source is found to play a key role in predicting the optimum performance of all system configurations regardless of the inlet temperature of the heat source
Majumdar, A. K.
2011-01-01
The Generalized Fluid System Simulation Program (GFSSP) is a finite-volume based general-purpose computer program for analyzing steady state and time-dependent flow rates, pressures, temperatures, and concentrations in a complex flow network. The program is capable of modeling real fluids with phase changes, compressibility, mixture thermodynamics, conjugate heat transfer between solid and fluid, fluid transients, pumps, compressors and external body forces such as gravity and centrifugal. The thermofluid system to be analyzed is discretized into nodes, branches, and conductors. The scalar properties such as pressure, temperature, and concentrations are calculated at nodes. Mass flow rates and heat transfer rates are computed in branches and conductors. The graphical user interface allows users to build their models using the point, drag and click method; the users can also run their models and post-process the results in the same environment. The integrated fluid library supplies thermodynamic and thermo-physical properties of 36 fluids and 21 different resistance/source options are provided for modeling momentum sources or sinks in the branches. This Technical Memorandum illustrates the application and verification of the code through 12 demonstrated example problems. This supplement gives the input and output data files for the examples.
Newtonian and non-newtonian limits of gravitational fields
Koppel', A.A.
1975-01-01
The nonrelativistic limit of the exact stationary axially-symmetric vacuum solution to Einstein equations, which is called the unified (generalized) Kerr-NUT solution, is investigated. Potentials for nonrelativistic gravitational fields, corresponding to this solution, have been calculated. The character of the c→infinity limit (c is the velocity of light) has been shown to depend on the structure of parameters of the Kerr-NUT solution. An example is given that shows the possibility of the existence of a nonrelativistic limit having an absolutely new, non-Newton (vortex) character. From the mathematically proved possibility of the existence of nonrelativistic vortex fields there follow also some implications of a more fundamental character. The Newton limit is commonly supposed to be the only nonrelativistic limit in the Einstein theory. Now there arises a dilemma: either gravitational fields having a non-Newton limit exist in nature and thus the Newton theory does not embrace all gravitational phenomena of nonrelativistic character or in the Newton solutions to the nonrelativistic gravitational equations a certain element of the Einstein theory is revealed that is alien to the true nonrelativistic theory of gravitation. In the former case, one cannot exclude the possibility that owing to a comprehensive analysis of properties, possible sources, etc. the vortex soltions to Einstein equations may prove important in cosmological and astrophysical applications of the general relativity theory. In the latter case, a detailed analysis of the non-Newton-limit solutions will at least enable one to gain a deeper insight into the structure of Einstein equations and their solutions
Newtonian and non-newtonian limits of gravitational fields
Koppel, A A [Tartuskij Gosudarstvennyj Univ., (USSR)
1975-09-01
The nonrelativistic limit of the exact stationary axially-symmetric vacuum solution to Einstein equations, which is called the unified (generalized) Kerr-NUT solution, is investigated. Potentials for nonrelativistic gravitational fields, corresponding to this solution, have been calculated. The character of the c..-->..infinity limit (c is the velocity of light) has been shown to depend on the structure of parameters of the Kerr-NUT solution. An example is given that shows the possibility of the existence of a nonrelativistic limit having an absolutely new, non-Newton (vortex) character. From the mathematically proved possibility of the existence of nonrelativistic vortex fields there follow also some implications of a more fundamental character. The Newton limit is commonly supposed to be the only nonrelativistic limit in the Einstein theory. Now there arises a dilemma: either gravitational fields having a non-Newton limit exist in nature and thus the Newton theory does not embrace all gravitational phenomena of nonrelativistic character or in the Newton solutions to the nonrelativistic gravitational equations a certain element of the Einstein theory is revealed that is alien to the true nonrelativistic theory of gravitation. In the former case, one cannot exclude the possibility that owing to a comprehensive analysis of properties, possible sources, etc. the vortex soltions to Einstein equations may prove important in cosmological and astrophysical applications of the general relativity theory. In the latter case, a detailed analysis of the non-Newton-limit solutions will at least enable one to gain a deeper insight into the structure of Einstein equations and their solutions.
Non-newtonian deformation of co-based metallic glass at low stresses
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)
Application of volume of fluid method for simulation of a droplet impacting a fiber
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.
An analysis of the Rayleigh–Stokes problem for a generalized second-grade fluid
Bazhlekova, Emilia
2014-11-26
© 2014, The Author(s). We study the Rayleigh–Stokes problem for a generalized second-grade fluid which involves a Riemann–Liouville fractional derivative in time, and present an analysis of the problem in the continuous, space semidiscrete and fully discrete formulations. We establish the Sobolev regularity of the homogeneous problem for both smooth and nonsmooth initial data v, including v∈^{L2}(Ω). A space semidiscrete Galerkin scheme using continuous piecewise linear finite elements is developed, and optimal with respect to initial data regularity error estimates for the finite element approximations are derived. Further, two fully discrete schemes based on the backward Euler method and second-order backward difference method and the related convolution quadrature are developed, and optimal error estimates are derived for the fully discrete approximations for both smooth and nonsmooth initial data. Numerical results for one- and two-dimensional examples with smooth and nonsmooth initial data are presented to illustrate the efficiency of the method, and to verify the convergence theory.
An analysis of the Rayleigh–Stokes problem for a generalized second-grade fluid
Bazhlekova, Emilia; Jin, Bangti; Lazarov, Raytcho; Zhou, Zhi
2014-01-01
© 2014, The Author(s). We study the Rayleigh–Stokes problem for a generalized second-grade fluid which involves a Riemann–Liouville fractional derivative in time, and present an analysis of the problem in the continuous, space semidiscrete and fully discrete formulations. We establish the Sobolev regularity of the homogeneous problem for both smooth and nonsmooth initial data v, including v∈^{L2}(Ω). A space semidiscrete Galerkin scheme using continuous piecewise linear finite elements is developed, and optimal with respect to initial data regularity error estimates for the finite element approximations are derived. Further, two fully discrete schemes based on the backward Euler method and second-order backward difference method and the related convolution quadrature are developed, and optimal error estimates are derived for the fully discrete approximations for both smooth and nonsmooth initial data. Numerical results for one- and two-dimensional examples with smooth and nonsmooth initial data are presented to illustrate the efficiency of the method, and to verify the convergence theory.
Bavio, José; Marrón, Beatriz
2014-01-01
Quality of service (QoS) for internet traffic management requires good traffic models and good estimation of sharing network resource. A link of a network processes all traffic and it is designed with certain capacity C and buffer size B. A Generalized Markov Fluid model (GMFM), introduced by Marrón (2011), is assumed for the sources because describes in a versatile way the traffic, allows estimation based on traffic traces, and also consistent effective bandwidth estimation can be done. QoS, interpreted as buffer overflow probability, can be estimated for GMFM through the effective bandwidth estimation and solving the optimization problem presented in Courcoubetis (2002), the so call inf-sup formulas. In this work we implement a code to solve the inf-sup problem and other optimization related with it, that allow us to do traffic engineering in links of data networks to calculate both, minimum capacity required when QoS and buffer size are given or minimum buffer size required when QoS and capacity are given
Probabilistic approach to diffusion in shear flows of generalized viscoelastic second-grade fluids
Wafo Soh, C
2010-01-01
We study diffusion in point-source-driven shear flows of generalized second-grade fluids. We start by obtaining exact solutions of shear flows triggered by point sources under various boundary conditions. For unrestricted flows, we demonstrate that the velocity distribution is the probability density function of a coupled or uncoupled continuous-time random walk. In the first instance, the motion is described by a compound Poisson process with an explicit probability density function corresponding to the velocity distribution. The average waiting time in this situation is finite and is identified with the structural relaxation time. In the second case, we obtain an explicit formula for the probability density function in terms of special functions. In both cases, the probability density functions of the associated stochastic processes are leptokurtic at all finite times with variances linear in time. By using the method of images, we infer velocity fields for restricted flows from those of unrestricted flows. Equipped with some exact expressions of the velocity field, we analyze advection–diffusion via the Feynman–Kac formula, which lends itself naturally to Monte Carlo simulation
Jakubov, T.S.; Mainwaring, D.E.
2006-01-01
In the present work a generalized Kelvin equation for a fluid confined in thick-walled cylindrical capillary is developed. This has been accomplished by including the potential energy function for interaction between a solid wall of a capillary and a confined fluid into the Kelvin equation. Using the Lennard-Jones 12-6 potential, an explicit form of the potential energy functions as expressed by hypergeometrical functions have been derived-firstly, for the interaction between a solid wall and a test atom placed at an arbitrary point in a long open-end capillary, and thereafter for the body-body interaction between the solid wall and a confined Lennard-Jones fluid. Further, this generalized Kelvin equation has been applied to detailed description hysteresis phenomena in such capillaries. All numerical calculations have been carried out for the model argon-graphite system at 90 K
Transient flows of a Burgers' fluid
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)
Fractional magnetohydrodynamics Oldroyd-B fluid over an oscillating plate
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.
Batey, Mark; Chamorro-Premuzic, Tomas; Furnham, Adrian
2009-01-01
Two studies examined the relationships between measures of intelligence, personality and divergent thinking (DT) in student samples. Study one investigated the incremental validity of measures of IQ and fluid intelligence with the Big Five Personality Inventory with regards to DT. Significant relationships of DT to fluid intelligence, Extraversion…
Smoothed particle hydrodynamics model for phase separating fluid mixtures. I. General equations
Thieulot, C; Janssen, LPBM; Espanol, P
We present a thermodynamically consistent discrete fluid particle model for the simulation of a recently proposed set of hydrodynamic equations for a phase separating van der Waals fluid mixture [P. Espanol and C.A.P. Thieulot, J. Chem. Phys. 118, 9109 (2003)]. The discrete model is formulated by
A Wall Boundary Condition for the Simulation of a Turbulent Non-Newtonian Domestic Slurry in Pipes
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
Fasano, Andrea; Rasmussen, Henrik K.
2017-01-01
A third order accurate, in time and space, finite element scheme for the numerical simulation of three- dimensional time-dependent flow of the molecular stress function type of fluids in a generalized formu- lation is presented. The scheme is an extension of the K-BKZ Lagrangian finite element me...
Post-Newtonian conservation laws in rigid quasilocal frames
McGrath, Paul L; Chanona, Melanie; Epp, Richard J; Mann, Robert B; Koop, Michael J
2014-01-01
In recent work we constructed completely general conservation laws for energy (McGrath et al 2012 Class. Quantum Grav. 29 215012) and linear and angular momentum (Epp et al 2013 Class. Quantum Grav. 30 195019) of extended systems in general relativity based on the notion of a rigid quasilocal frame (RQF). We argued at a fundamental level that these RQF conservation laws are superior to conservation laws based on the local stress–energy–momentum tensor of matter because (1) they do not rely on spacetime symmetries and (2) they properly account for both matter and gravitational effects. Moreover, they provide simple, exact, operational expressions for fluxes of gravitational energy and linear and angular momentum. In this paper we derive the form of these laws in a general first post-Newtonian (1PN) approximation, and then apply these approximate laws to the problem of gravitational tidal interactions. We obtain formulas for tidal heating and tidal torque that agree with the literature, but without resorting to the use of pseudotensors. We describe the physical mechanism of these tidal interactions not in the traditional terms of a Newtonian gravitational force, but in terms of a much simpler and universal mechanism that is an exact, quasilocal manifestation of the equivalence principle in general relativity. As concrete examples, we look at the tidal heating of Jupiter’s moon Io and angular momentum transfer in the Earth–Moon system that causes a gradual spin-down of the Earth and recession of the Moon. In both examples we find agreement with observation. (paper)
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.
A two-phase theory for non-Newtonian suspensions
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.
Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries
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.
Shin, Hyun Kyung; Choi, Bongsik; Talkner, Peter; Lee, Eok Kyun
2014-12-01
Based on the generalized Langevin equation for the momentum of a Brownian particle a generalized asymptotic Einstein relation is derived. It agrees with the well-known Einstein relation in the case of normal diffusion but continues to hold for sub- and super-diffusive spreading of the Brownian particle's mean square displacement. The generalized asymptotic Einstein relation is used to analyze data obtained from molecular dynamics simulations of a two-dimensional soft disk fluid. We mainly concentrated on medium densities for which we found super-diffusive behavior of a tagged fluid particle. At higher densities a range of normal diffusion can be identified. The motion presumably changes to sub-diffusion for even higher densities.
Spray Formation of Herschel-Bulkley Fluids using Impinging Jets
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.
Majumdar, A. K.; Hedayat, A.
2015-01-01
This paper describes the experience of the authors in using the Generalized Fluid System Simulation Program (GFSSP) in teaching Design of Thermal Systems class at University of Alabama in Huntsville. GFSSP is a finite volume based thermo-fluid system network analysis code, developed at NASA/Marshall Space Flight Center, and is extensively used in NASA, Department of Defense, and aerospace industries for propulsion system design, analysis, and performance evaluation. The educational version of GFSSP is freely available to all US higher education institutions. The main purpose of the paper is to illustrate the utilization of this user-friendly code for the thermal systems design and fluid engineering courses and to encourage the instructors to utilize the code for the class assignments as well as senior design projects.
Pawaskar, Sainath Shrikant; Fisher, John; Jin, Zhongmin
2010-03-01
Contact detection in cartilage contact mechanics is an important feature of any analytical or computational modeling investigation when the biphasic nature of cartilage and the corresponding tribology are taken into account. The fluid flow boundary conditions will change based on whether the surface is in contact or not, which will affect the interstitial fluid pressurization. This in turn will increase or decrease the load sustained by the fluid phase, with a direct effect on friction, wear, and lubrication. In laboratory experiments or clinical hemiarthroplasty, when a rigid indenter or metallic prosthesis is used to apply load to the cartilage, there will not be any fluid flow normal to the surface in the contact region due to the impermeable nature of the indenter/prosthesis. In the natural joint, on the other hand, where two cartilage surfaces interact, flow will depend on the pressure difference across the interface. Furthermore, in both these cases, the fluid would flow freely in non-contacting regions. However, it should be pointed out that the contact area is generally unknown in advance in both cases and can only be determined as part of the solution. In the present finite element study, a general and robust algorithm was proposed to decide nodes in contact on the cartilage surface and, accordingly, impose the fluid flow boundary conditions. The algorithm was first tested for a rigid indenter against cartilage model. The algorithm worked well for two-dimensional four-noded and eight-noded axisymmetric element models as well as three-dimensional models. It was then extended to include two cartilages in contact. The results were in excellent agreement with the previous studies reported in the literature.
Modified Newtonian dynamics and the Coma cluster
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
Swimming efficiency in a shear-thinning fluid
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.
MAGIA - using atom interferometry to determine the Newtonian gravitational constant
Stuhler, J; Fattori, M; Petelski, T; Tino, G M
2003-01-01
We describe our experiment MAGIA (misura accurata di G mediante interferometria atomica), in which we will use atom interferometry to perform a high precision measurement of the Newtonian gravitational constant G. Free-falling laser-cooled atoms in a vertical atomic fountain will be accelerated due to the gravitational potential of nearby source masses (SMs). Detecting this acceleration with techniques of Raman atom interferometry will enable us to assign a value to G. To suppress systematic effects we will implement a double-differential measurement. This includes launching two atom clouds in a gradiometer configuration and moving the SMs to different vertical positions. We briefly summarize the general idea of the MAGIA experiment and put it in the context of other high precision G-measurements. We present the current status of the experiment and report on analyses of the expected measurement accuracy
Variational description of multifluid hydrodynamics: Uncharged fluids
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.
Reduced viscosity interpreted for fluid/gas mixtures
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.
A review on rising bubble dynamics in viscosity-stratified fluids
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.
Fluid spheres and R- and T-regions in general relativity
McVittie, G C; Wiltshire, R J [Kent Univ., Canterbury (UK)
1975-10-01
R- and T-regions of spacetime are first defined in a particular coordinate system and then with the aid of the Schwarzschild vacuum solution are shown to represent the outside and inside of a black hole respectively. A certain class of interior solutions, relating to a perfect fluid, are also considered and it is found that these R- and T-solutions have distinct physical properties. The R-solutions are static, spherically symmetric, permanent, and have a classical analogue, while the corresponding T-solutions, which are wholly time dependent, are cylindrical, temporary, and do not have a classical analogue. It is shown that these T-solutions cannot be generated from their R-region counterparts. Particular T-solutions are also presented in which the corresponding fluid occupies the whole of a T-region. The fluid would under certain circumstances be black body radiation while for other cases the internal pressure is always greater than the density.
Majumdar, A. K.; Hedayat, A.
2015-01-01
This paper describes the experience of the authors in using the Generalized Fluid System Simulation Program (GFSSP) in teaching Design of Thermal Systems class at University of Alabama in Huntsville. GFSSP is a finite volume based thermo-fluid system network analysis code, developed at NASA/Marshall Space Flight Center, and is extensively used in NASA, Department of Defense, and aerospace industries for propulsion system design, analysis, and performance evaluation. The educational version of GFSSP is freely available to all US higher education institutions. The main purpose of the paper is to illustrate the utilization of this user-friendly code for the thermal systems design and fluid engineering courses and to encourage the instructors to utilize the code for the class assignments as well as senior design projects. The need for a generalized computer program for thermofluid analysis in a flow network has been felt for a long time in aerospace industries. Designers of thermofluid systems often need to know pressures, temperatures, flow rates, concentrations, and heat transfer rates at different parts of a flow circuit for steady state or transient conditions. Such applications occur in propulsion systems for tank pressurization, internal flow analysis of rocket engine turbopumps, chilldown of cryogenic tanks and transfer lines, and many other applications of gas-liquid systems involving fluid transients and conjugate heat and mass transfer. Computer resource requirements to perform time-dependent, three-dimensional Navier-Stokes computational fluid dynamic (CFD) analysis of such systems are prohibitive and therefore are not practical. Available commercial codes are generally suitable for steady state, single-phase incompressible flow. Because of the proprietary nature of such codes, it is not possible to extend their capability to satisfy the above-mentioned needs. Therefore, the Generalized Fluid System Simulation Program (GFSSP1) has been developed at NASA
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)
Comparing scalar-tensor gravity and f(R)-gravity in the Newtonian limit
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.
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.
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.
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.)
Newtonian Version of the Variable Mass Theory of Gravity
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
O'Keeffe, C J; Ren, Ruichao; Orkoulas, G
2007-11-21
Spatial updating grand canonical Monte Carlo algorithms are generalizations of random and sequential updating algorithms for lattice systems to continuum fluid models. The elementary steps, insertions or removals, are constructed by generating points in space either at random (random updating) or in a prescribed order (sequential updating). These algorithms have previously been developed only for systems of impenetrable spheres for which no particle overlap occurs. In this work, spatial updating grand canonical algorithms are generalized to continuous, soft-core potentials to account for overlapping configurations. Results on two- and three-dimensional Lennard-Jones fluids indicate that spatial updating grand canonical algorithms, both random and sequential, converge faster than standard grand canonical algorithms. Spatial algorithms based on sequential updating not only exhibit the fastest convergence but also are ideal for parallel implementation due to the absence of strict detailed balance and the nature of the updating that minimizes interprocessor communication. Parallel simulation results for three-dimensional Lennard-Jones fluids show a substantial reduction of simulation time for systems of moderate and large size. The efficiency improvement by parallel processing through domain decomposition is always in addition to the efficiency improvement by sequential updating.
Shear-induced structural transitions in Newtonian non-Newtonian two-phase flow
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 %.
Non-Gaussian initial conditions in ΛCDM: Newtonian, relativistic, and primordial contributions
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
Morparia, Kavita G; Reddy, Srijaya K; Olivieri, Laura J; Spaeder, Michael C; Schuette, Jennifer J
2018-04-01
The determination of fluid responsiveness in the critically ill child is of vital importance, more so as fluid overload becomes increasingly associated with worse outcomes. Dynamic markers of volume responsiveness have shown some promise in the pediatric population, but more research is needed before they can be adopted for widespread use. Our aim was to investigate effectiveness of respiratory variation in peak aortic velocity and pulse pressure variation to predict fluid responsiveness, and determine their optimal cutoff values. We performed a prospective, observational study at a single tertiary care pediatric center. Twenty-one children with normal cardiorespiratory status undergoing general anesthesia for neurosurgery were enrolled. Respiratory variation in peak aortic velocity (ΔVpeak ao) was measured both before and after volume expansion using a bedside ultrasound device. Pulse pressure variation (PPV) value was obtained from the bedside monitor. All patients received a 10 ml/kg fluid bolus as volume expansion, and were qualified as responders if stroke volume increased >15% as a result. Utility of ΔVpeak ao and PPV and to predict responsiveness to volume expansion was investigated. A baseline ΔVpeak ao value of greater than or equal to 12.3% best predicted a positive response to volume expansion, with a sensitivity of 77%, specificity of 89% and area under receiver operating characteristic curve of 0.90. PPV failed to demonstrate utility in this patient population. Respiratory variation in peak aortic velocity is a promising marker for optimization of perioperative fluid therapy in the pediatric population and can be accurately measured using bedside ultrasonography. More research is needed to evaluate the lack of effectiveness of pulse pressure variation for this purpose.
Coupled Effects of non-Newtonian Rheology and Aperture Variability on Flow in a Single Fracture
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.
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.
Failure and nonfailure of fluid filaments in extension
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...
A general coarse and fine mesh solution scheme for fluid flow modeling in VHTRS
Clifford, I; Ivanov, K; Avramova, M.
2011-01-01
Coarse mesh Computational Fluid Dynamics (CFD) methods offer several advantages over traditional coarse mesh methods for the safety analysis of helium-cooled graphite-moderated Very High Temperature Reactors (VHTRs). This relatively new approach opens up the possibility for system-wide calculations to be carried out using a consistent set of field equations throughout the calculation, and subsequently the possibility for hybrid coarse/fine mesh or hierarchical multi scale CFD simulations. To date, a consistent methodology for hierarchical multi-scale CFD has not been developed. This paper describes work carried out in the initial development of a multi scale CFD solver intended to be used for the safety analysis of VHTRs. The VHTR is considered on any scale to consist of a homogenized two-phase mixture of fluid and stationary solid material of varying void fraction. A consistent set of conservation equations was selected such that they reduce to the single-phase conservation equations for the case where void fraction is unity. The discretization of the conservation equations uses a new pressure interpolation scheme capable of capturing the discontinuity in pressure across relatively large changes in void fraction. Based on this, a test solver was developed which supports fully unstructured meshes for three-dimensional time-dependent compressible flow problems, including buoyancy effects. For typical VHTR flow phenomena the new solver shows promise as an effective candidate for predicting the flow behavior on multiple scales, as it is capable of modeling both fine mesh single phase flows as well as coarse mesh flows in homogenized regions containing both fluid and solid materials. (author)
Stability of orbits around a spinning body in a pseudo-Newtonian Hill problem
Steklain, A.F.; Letelier, P.S.
2009-01-01
A pseudo-Newtonian Hill problem based on a potential proposed by Artemova et al. [I.A. Artemova, G. Bjoernsson, I.D. Novikov, Astrophys. J. 461 (1996) 565] is presented. This potential reproduces some of the general relativistic effects due to the spin angular momentum of the bodies, like the dragging of inertial frames. Poincare maps, Lyapunov exponents and fractal escape techniques are employed to study the stability of bounded and unbounded orbits for different spins of the central body
Spinorial relativistic rotator: the transformation from quasi-Newtonian to Minkowski coordinates
Biedenharn, L.C.; Bohm, A.; Tarlini, M.; van Dam, H.; Mukunda, N.
1983-12-01
There exists a remarkably close relationship between the operator algebra of the Dirac equation and the corresponding operators of the spinorial relativistic rotator (an indecomposable object lying on a mass-spin Regge trajectory). The analog of the Foldy-Wouthuysen transformation (more generally, the transformation between quasi-Newtonian and Minkowski coordinates) is constructed and explicit results are discussed for the spin and position operators. Zitterbewegung is shown to exist for a system having only positive energies. 31 references
On the uniqueness of static perfect-fluid solutions in general relativity
Beig, R.; Simon, W.
1990-01-01
Following earlier work of Masood-ul-Alam, we consider a uniqueness problem for nonrotating stellar models. Given a static, asymptotically flat perfect-fluid spacetime with barotropic equation of state ρ(p), and given another such spacetime which is spherically symmetric and has the same ρ(p) and the same surface potential: we prove that both are identical provided ρ(p) satisfies a certain differential inequality. This inequality is more natural and less restrictive that the conditions required by Masood-ul-Alam. 30 refs. (Authors)
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.
Numerical investigation of non-Newtonian nanofluid flow in a converging microchannel
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.
Non-Newtonian behavior and molecular structure of Cooee bitumen under shear flow
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...
Handbook of mathematical analysis in mechanics of viscous fluids
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.
Tilted Bianchi type I dust fluid cosmological model in general relativity
Home; Journals; Pramana – Journal of Physics; Volume 58; Issue 3. Tilted Bianchi type I dust ﬂuid cosmological model in general ... In this paper, we have investigated a tilted Bianchi type I cosmological model ﬁlled with dust of perfect ﬂuid in general relativity. To get a determinate solution, we have assumed a condition ...
Tilted Bianchi type I dust fluid cosmological model in general relativity
Tilted Bianchi type I dust ﬂuid cosmological model in general relativity ... In this paper, we have investigated a tilted Bianchi type I cosmological model ﬁlled with dust of perfect ﬂuid in general relativity. ... Pramana – Journal of Physics | News ...
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.
Miranda, Jose; Brandao, Rodolfo
2017-11-01
We study a family of generalized elastica-like equilibrium shapes that arise at the interface separating two fluids in a curved rotating Hele-Shaw cell. This family of stationary interface solutions consists of shapes that balance the competing capillary and centrifugal forces in such a curved flow environment. We investigate how the emerging interfacial patterns are impacted by changes in the geometric properties of the curved Hele-Shaw cell. A vortex-sheet formalism is used to calculate the two-fluid interface curvature, and a gallery of possible shapes is provided to highlight a number of peculiar morphological features. A linear perturbation theory is employed to show that the most prominent aspects of these complex stationary patterns can be fairly well reproduced by the interplay of just two interfacial modes. The connection of these dominant modes to the geometry of the curved cell, as well as to the fluid dynamic properties of the flow, is discussed. We thank CNPq (Brazilian Research Council) for financial support under Grant No. 304821/2015-2.
Generalized fluid equations for parallel transport in collisional to weakly collisional plasmas
Zawaideh, E.; Najmabadi, F.; Conn, R.W.
1986-01-01
A new set of two-fluid equations that are valid from collisional to weakly collisional limits is derived. Starting from gyrokinetic equations in flux coordinates with no zero-order drifts, a set of moment equations describing plasma transport along the field lines of a space- and time-dependent magnetic field is derived. No restriction on the anisotropy of the ion distribution function is imposed. In the highly collisional limit, these equations reduce to those of Braginskii, while in the weakly collisional limit they are similar to the double adiabatic or Chew, Goldberger, and Low (CGL) equations [Proc. R. Soc. London, Ser. A 236, 112 (1956)]. The new set of equations also exhibits a physical singularity at the sound speed. This singularity is used to derive and compute the sound speed. Numerical examples comparing these equations with conventional transport equations show that in the limit where the ratio of the mean free path lambda to the scale length of the magnetic field gradient L/sub B/ approaches zero, there is no significant difference between the solution of the new and conventional transport equations. However, conventional fluid equations, ordinarily expected to be correct to the order (lambda/L/sub B/) 2 , are found to have errors of order (lambda/L/sub u/) 2 = (lambda/L/sub B/) 2 /(1-M 2 ) 2 , where L/sub u/ is the scale length of the flow velocity gradient and M is the Mach number. As such, the conventional equations may contain large errors near the sound speed (Mroughly-equal1)
Jankiewicz, Cz; Sikora, D [Wyzsza Szkola Pedagogiczna, Rzeszow (Poland)
1980-01-01
It is shwon that in the post-Newtonian approximation the gravitational momentum of a system of point particles is equal to the sum of field momentum and inertial momentum only in two classes of coordinate systems. This equality may be treated as a natural condition on a coordinate system in which the generally covariant Einstein equations are to be solved.
Pacôme Delva
2017-03-01
Full Text Available An extensive review of past work on relativistic gravimetry, gradiometry and chronometric geodesy is given. Then, general theoretical tools are presented and applied for the case of a stationary parameterized post-Newtonian metric. The special case of a stationary clock on the surface of the Earth is studied.
Constraint on the post-Newtonian parameter γ on galactic size scales
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
Newtonian semiclassical gravity in the Ghirardi–Rimini–Weber theory with matter density ontology
Derakhshani, Maaneli
2014-01-01
We propose a Newtonian semiclassical gravity theory based on the GRW collapse theory with matter density ontology (GRWm), which we term GRWmN. The theory is proposed because, as we show from previous arguments in the literature, the standard Newtonian semiclassical gravity theory based on the Schroedinger–Newton equations does not have a consistent Born rule probability interpretation for gravitationally self-interacting particles and implies gravitational cat states for macroscopic mass superpositions. By contrast, we show that GRWmN has a consistent statistical description of gravitationally self-interacting particles and adequately suppresses the cat states for macroscopic superpositions. Two possible routes to experimentally testing GRWmN are also considered. We conclude with a discussion of possible variants of GRWmN, what a general relativistic extension would involve, and various objections that might be raised against semiclassical gravity theories like GRWmN.
Newtonian semiclassical gravity in the Ghirardi–Rimini–Weber theory with matter density ontology
Derakhshani, Maaneli, E-mail: maanelid@yahoo.com
2014-03-01
We propose a Newtonian semiclassical gravity theory based on the GRW collapse theory with matter density ontology (GRWm), which we term GRWmN. The theory is proposed because, as we show from previous arguments in the literature, the standard Newtonian semiclassical gravity theory based on the Schroedinger–Newton equations does not have a consistent Born rule probability interpretation for gravitationally self-interacting particles and implies gravitational cat states for macroscopic mass superpositions. By contrast, we show that GRWmN has a consistent statistical description of gravitationally self-interacting particles and adequately suppresses the cat states for macroscopic superpositions. Two possible routes to experimentally testing GRWmN are also considered. We conclude with a discussion of possible variants of GRWmN, what a general relativistic extension would involve, and various objections that might be raised against semiclassical gravity theories like GRWmN.
Five decades of tackling models for stiff fluid dynamics problems a scientific autobiography
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...
Parametrized tests of post-Newtonian theory using Advanced LIGO and Einstein Telescope
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.
Numerical Modeling of Fluid-Structure Interaction with Rheologically Complex Fluids
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...
Generalized fluid equations for parallel transport in collisional to weakly collisional plasmas
Zawaideh, E.S.
1985-01-01
A new set of two-fluid equations which are valid from collisional to weakly collisional limits are derived. Starting from gyrokinetic equations in flux coordinates with no zeroth order drifts, a set of moment equations describing plasma transport along the field lines of a space and time dependent magnetic field are derived. No restriction on the anisotropy of the ion distribution function is imposed. In the highly collisional limit, these equations reduce to those of Braginskii while in the weakly collisional limit, they are similar to the double adiabatic or Chew, Goldberger, and Low (CGL) equations. The new transport equations are used to study the effects of collisionality, magnetic field structure, and plasma anisotropy on plasma parallel transport. Numerical examples comparing these equations with conventional transport equations show that the conventional equations may contain large errors near the sound speed (M approx. = 1). It is also found that plasma anisotropy, which is not included in the conventional equations, is a critical parameter in determining plasma transport in varying magnetic field. The new transport equations are also used to study axial confinement in multiple mirror devices from the strongly to weakly collisional regime. A new ion conduction model was worked out to extend the regime of validity of the transport equations to the low density multiple mirror regime
Generalized extended Navier-Stokes theory: Multiscale spin relaxation in molecular fluids
Hansen, Jesper Schmidt
2013-01-01
This paper studies the relaxation of the molecular spin angular velocity in the framework of generalized extended Navier-Stokes theory. Using molecular dynamics simulations, it is shown that for uncharged diatomic molecules the relaxation time decreases with increasing molecular moment of inertia...
Multiple scales and singular limits for compressible rotating fluids with general initial data
Feireisl, Eduard; Novotný, A.
2014-01-01
Roč. 39, č. 6 (2014), s. 1104-1127 ISSN 0360-5302 Keywords : compressible Navier-Stokes equations * multiple scales * oscillatory integrals Subject RIV: BA - General Mathematics Impact factor: 1.013, year: 2014 http://www.tandfonline.com/doi/full/10.1080/03605302.2013.856917
Microgravity Fluids for Biology, Workshop
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.
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.
Comparing Post-Newtonian and Numerical-Relativity Precession Dynamics
Kidder, Lawrence; Ossokine, Sergei; Boyle, Michael; Pfeiffer, Harald; Scheel, Mark; Szilagyi, Bela
2015-04-01
Binary black-hole systems are expected to be important sources of gravitational waves for upcoming gravitational-wave detectors. If the spins are not colinear with each other or with the orbital angular momentum, these systems exhibit complicated precession dynamics that are imprinted on the gravitational waveform. We develop a new procedure to match the precession dynamics computed by post-Newtonian (PN) theory to those of numerical binary black-hole simulations in full general relativity. For numerical relativity (NR) simulations lasting approximately two precession cycles, we find that the PN and NR predictions for the directions of the orbital angular momentum and the spins agree to better than ~1° with NR during the inspiral, increasing to 5° near merger. Nutation of the orbital plane on the orbital time-scale agrees well between NR and PN, whereas nutation of the spin direction shows qualitatively different behavior in PN and NR. We also examine how the PN equations for precession and orbital-phase evolution converge with PN order, and we quantify the impact of various choices for handling partially known PN terms.
Test of post-newtonian conservation laws in the binary system PSR 1913+16
Will, C.M.
1976-01-01
Observations that set upper limits on secular changes in the pulsar period and orbital period in the binary system PSR 1913+16 may provide a test of post-Newtonian conservation laws. According to some metric theories of gravitation, the center of mass of a binary system may be accelerated in the direction of the periastron of the orbit because of a violation of post-Newtonian momentum conservation. In the binary system PSR 1913+16, this effect could produce secular changes in both pulsar and orbital periods (changing overall Doppler shift) as large as two parts in 10 6 per year. The size of the effect is proportional to the sine of the angle of periastron, to the difference in the masses of the components of the binary system, and to the combination of parametrized post-Newtonian parameters α 3 +zeta 2 -zeta/subw/. This combination is zero in any theory that predicts conserved total momentum for isolated systems (including general relativity and Brans-Dicke theory). Although solar-system experiments constrain α 3 and zeta/subw/ to be small, no decent direct limit has been placed on zeta 2 . Other possible sources of secular period changes in PSR 1913+16 are discussed and compared with this effect. It is also shown that a breakdown in the equality of active and passive gravitational masses (violation of ''Newton's third law'') leads only to periodic, unobservable orbital effects in a system like PSR 1913+16
Non-Newtonian plastic flow of a Ni-Si-B metallic glass at low stresses
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
Interplay between inertial and non-Newtonian effects on the flow in weakly modulated channel
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)
The Boundary Layer Flows of a Rivlin-Ericksen Fluid
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.
Numerical study of shear thickening fluid with discrete particles embedded in a base fluid
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.
Non-Newtonian Aspects of Artificial Intelligence
Zak, Michail
2016-05-01
The challenge of this work is to connect physics with the concept of intelligence. By intelligence we understand a capability to move from disorder to order without external resources, i.e., in violation of the second law of thermodynamics. The objective is to find such a mathematical object described by ODE that possesses such a capability. The proposed approach is based upon modification of the Madelung version of the Schrodinger equation by replacing the force following from quantum potential with non-conservative forces that link to the concept of information. A mathematical formalism suggests that a hypothetical intelligent particle, besides the capability to move against the second law of thermodynamics, acquires such properties like self-image, self-awareness, self-supervision, etc. that are typical for Livings. However since this particle being a quantum-classical hybrid acquires non-Newtonian and non-quantum properties, it does not belong to the physics matter as we know it: the modern physics should be complemented with the concept of the information force that represents a bridge to intelligent particle. As a follow-up of the proposed concept, the following question is addressed: can artificial intelligence (AI) system composed only of physical components compete with a human? The answer is proven to be negative if the AI system is based only on simulations, and positive if digital devices are included. It has been demonstrated that there exists such a quantum neural net that performs simulations combined with digital punctuations. The universality of this quantum-classical hybrid is in capability to violate the second law of thermodynamics by moving from disorder to order without external resources. This advanced capability is illustrated by examples. In conclusion, a mathematical machinery of the perception that is the fundamental part of a cognition process as well as intelligence is introduced and discussed.
Yoon, Young Dae
2017-10-01
A generalized, intuitive two-fluid picture of 2D non-driven collisionless magnetic reconnection is described using results from a full-3D numerical simulation. The relevant two-fluid equations simplify to the condition that the flux associated with canonical circulation Q =me ∇ ×ue +qe B is perfectly frozen into the electron fluid. Q is the curl of P =meue +qe A , which is the electron canonical momenrum. Since ∇ . Q = 0 , the Q flux tubes are incompressible and so have a fixed volume. Because they are perfectly frozen into the electron fluid, the Q flux tubes cannot reconnect. Following the behavior of these Q flux tubes provides an intuitive insight into 2D collisionless reconnection of B . In the reconnection geometry, a small perturbation to the central electron current sheet effectively brings a localized segment of a Q flux tube towards the X-point. This flux tube segment is convected downwards with the central electron current, effectively stretching the flux tube, decreasing its cross-section to maintain a fixed volume and so increasing the magnitude of Q . Also, because Q is the sum of the electron vorticity and the magnetic field, the two terms may change in such a way that one term becomes smaller while the other becomes larger while preserving constant Q flux. This allows magnetic reconnection, which is a conversion of magnetic field into particle velocity, to occur without any dissipation mechanism. The entire process has positive feedback with no restoring mechanism and therefore is an instability. The Q motion provides an interpretation for other phenomena as well, such as spiked central electron current filaments. The simulated reconnection rate was found to agree with a previous analytical calculation having the same geometry. Energy analysis shows that the magnetic energy is converted and propagated mainly in the form of the Poynting flux, while helicity analysis shows that the canonical helicity ∫ P . QdV as a whole must be considered when
Bandyopadhyay, Alak; Majumdar, Alok
2007-01-01
The present paper describes the verification and validation of a quasi one-dimensional pressure based finite volume algorithm, implemented in Generalized Fluid System Simulation Program (GFSSP), for predicting compressible flow with friction, heat transfer and area change. The numerical predictions were compared with two classical solutions of compressible flow, i.e. Fanno and Rayleigh flow. Fanno flow provides an analytical solution of compressible flow in a long slender pipe where incoming subsonic flow can be choked due to friction. On the other hand, Raleigh flow provides analytical solution of frictionless compressible flow with heat transfer where incoming subsonic flow can be choked at the outlet boundary with heat addition to the control volume. Nonuniform grid distribution improves the accuracy of numerical prediction. A benchmark numerical solution of compressible flow in a converging-diverging nozzle with friction and heat transfer has been developed to verify GFSSP's numerical predictions. The numerical predictions compare favorably in all cases.
Contracting bubbles in Hele-Shaw cells with a power-law fluid
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
Flapping motion and force generation in a viscoelastic fluid
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.
Broniarz-Press, L; Sosnowski, T R; Matuszak, M; Ochowiak, M; Jabłczyńska, K
2015-05-15
The paper contains results of the experimental study on atomization process of aqueous solutions of glycerol and aqueous solutions of glycerol-polyacrylamide (Rokrysol WF1) in an ultrasonic inhaler. In experiments the different concentration aqueous solutions of glycerol and glycerol-polyacrylamide have been tested. The results have been obtained by the use of laser diffraction technique. The differences between characteristics of ultrasonic atomization for test liquids have been observed. The analysis of drop size histograms shows that the different sizes of drops have been formed during atomization process. The present study confirmed the previous reports which suggested that the drops size changes with the increase in viscosity of solution changes in spray characteristics were also observed. It has been shown that the shear and extensional viscosities affect the process of atomization. Copyright © 2015 Elsevier B.V. All rights reserved.
Steady laminar flow of fractal fluids
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.
Second post-Newtonian Lagrangian dynamics of spinning compact binaries
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.)
Thermal convection of viscoelastic shear-thinning fluids
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)
Comparative study of Newtonian physiological blood flow through normal and stenosed carotid artery
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.
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.
Nonlinear convective flow of Powell-Erying magneto nanofluid with Newtonian heating
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
The fluid dynamics of the chocolate fountain
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)
The fluid dynamics of the chocolate fountain
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.
Nonlinear shear wave in a non Newtonian visco-elastic medium
Banerjee, D.; Janaki, M. S.; Chakrabarti, N. [Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Calcutta 700 064 (India); Chaudhuri, M. [Max-Planck-Institut fuer extraterrestrische Physik, 85741 Garching (Germany)
2012-06-15
An analysis of nonlinear transverse shear wave has been carried out on non-Newtonian viscoelastic liquid using generalized hydrodynamic model. The nonlinear viscoelastic behavior is introduced through velocity shear dependence of viscosity coefficient by well known Carreau-Bird model. The dynamical feature of this shear wave leads to the celebrated Fermi-Pasta-Ulam problem. Numerical solution has been obtained which shows that initial periodic solutions reoccur after passing through several patterns of periodic waves. A possible explanation for this periodic solution is given by constructing modified Korteweg de Vries equation. This model has application from laboratory to astrophysical plasmas as well as in biological systems.
Numerical analysis of capillary compensated micropolar fluid lubricated hole-entry journal bearings
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.
Tupper, B.O.J.
1983-01-01
The work of a previous article is extended to show that space-times which are the exact solutions of the field equations for a perfect fluid also may be exact solutions of the field equations for a viscous magnetohydrodynamic fluid. Conditions are found for this equivalence to exist and viscous magnetohydrodynamic solutions are found for a number of known perfect fluid space-times. (author)
Xin Zhang
2014-01-01
Full Text Available Vitamin D-binding protein (DBP is the main transport protein of vitamin D and plays an important role in the immune system and host defenses. The purpose of this study was to measure DBP levels in plasma and gingival crevicular fluid (GCF of patients with generalized aggressive periodontitis (GAgP, in comparison to healthy controls, with the goal of elucidating the relationship between DBP and GAgP. Fifty-nine GAgP patients and 58 healthy controls were recruited for the study; clinical parameters of probing depths (PD, bleeding index, and attachment loss (AL were recorded. DBP levels were measured by enzyme-linked immunosorbent assay. From the results, GAgP patients had higher plasma DBP concentrations (P<0.001 but lower GCF DBP concentrations (P<0.001 than healthy controls. In GAgP group, after controlling the potential confounders of age, gender, smoking status, and BMI index, GCF DBP concentrations correlated negatively with PD (P<0.001 and AL (P=0.009. Within the limits of the study, we concluded that decreased GCF DBP level and increased plasma DBP level are associated with periodontitis.
Mitri, Farid G
2012-08-01
This work presents the general theory of resonance scattering (GTRS) by an elastic spherical shell immersed in a nonviscous fluid and placed arbitrarily in an acoustic beam. The GTRS formulation is valid for a spherical shell of any size and material regardless of its location relative to the incident beam. It is shown here that the scattering coefficients derived for a spherical shell immersed in water and placed in an arbitrary beam equal those obtained for plane wave incidence. Numerical examples for an elastic shell placed in the field of acoustical Bessel beams of different types, namely, a zero-order Bessel beam and first-order Bessel vortex and trigonometric (nonvortex) beams are provided. The scattered pressure is expressed using a generalized partial-wave series expansion involving the beam-shape coefficients (BSCs), the scattering coefficients of the spherical shell, and the half-cone angle of the beam. The BSCs are evaluated using the numerical discrete spherical harmonics transform (DSHT). The far-field acoustic resonance scattering directivity diagrams are calculated for an albuminoidal shell immersed in water and filled with perfluoropropane gas, by subtracting an appropriate background from the total far-field form function. The properties related to the arbitrary scattering are analyzed and discussed. The results are of particular importance in acoustical scattering applications involving imaging and beam-forming for transducer design. Moreover, the GTRS method can be applied to investigate the scattering of any beam of arbitrary shape that satisfies the source-free Helmholtz equation, and the method can be readily adapted to viscoelastic spherical shells or spheres.
Transport Coefficients of Fluids
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.
The LS-STAG immersed boundary/cut-cell method for non-Newtonian flows in 3D extruded geometries
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).
On preconditioning incompressible non-Newtonian flow problems
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
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...
Ni, W.-T.
1972-01-01
Metric theories of gravity are compiled and classified according to the types of gravitational fields they contain, and the modes of interaction among those fields. The gravitation theories considered are classified as (1) general relativity, (2) scalar-tensor theories, (3) conformally flat theories, and (4) stratified theories with conformally flat space slices. The post-Newtonian limit of each theory is constructed and its Parametrized Post-Newtonian (PPN) values are obtained by comparing it with Will's version of the formalism. Results obtained here, when combined with experimental data and with recent work by Nordtvedt and Will and by Ni, show that, of all theories thus far examined by our group, the only currently viable ones are general relativity, the Bergmann-Wagoner scalar-tensor theory and its special cases (Nordtvedt; Brans-Dicke-Jordan), and a recent, new vector-tensor theory by Nordtvedt, Hellings, and Will.
Radiative flow of Carreau liquid in presence of Newtonian heating and chemical reaction
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.
Experimental investigation of non-Newtonian/Newtonian liquid-liquid flow in microchannel
Roumpea, Eynagelia-Panagiota; Weheliye, Weheliye; Chinaud, Maxime; Angeli, Panagiota; Lyes Kahouadji Collaboration; Omar. K. Matar Collaboration
2015-11-01
Plug flow of an organic phase and an aqueous non-Newtonian solution was investigated experimentally in a quartz microchannel with I.D. 200 μm. The aqueous phase was a glycerol solution where 1000 and 2000 ppm of xanthan gum was added while the organic phase was silicon oil with 155 and 5 cSt viscosity. The two phases were brought together in a T-junction and their flowrates varied from 0.3 to 6 ml/hr. High speed imaging was used to study the characteristics of the plugs and the effect of the liquid properties on the flow patterns while a two-colour micro-PIV technique was used to investigate velocity profiles and circulation patterns within the plugs. The experimental results revealed that plug length was affected by both flowrate and viscosity. In all cases investigated, a film of the continuous phase always surrounded the plugs and its thickness was compared with existing literature models. Circulation patterns inside plugs were obtained by subtracting the plug velocity and found to be depended on the plug length and the amount of xanthan gum in the aqueous phase. Finally, the dimensionless circulation time was calculated and plotted as a function of the plug length. Department of Chemical Engineering South Kensington Campus Imperial College London SW7 2AZ.
Anon.
1991-01-01
Fluids engineering has played an important role in many applications, from ancient flood control to the design of high-speed compact turbomachinery. New applications of fluids engineering, such as in high-technology materials processing, biotechnology, and advanced combustion systems, have kept up unwaining interest in the subject. More accurate and sophisticated computational and measurement techniques are also constantly being developed and refined. On a more fundamental level, nonlinear dynamics and chaotic behavior of fluid flow are no longer an intellectual curiosity and fluid engineers are increasingly interested in finding practical applications for these emerging sciences. Applications of fluid technology to new areas, as well as the need to improve the design and to enhance the flexibility and reliability of flow-related machines and devices will continue to spur interest in fluids engineering. The objectives of the present seminar were: to exchange current information on arts, science, and technology of fluids engineering; to promote scientific cooperation between the fluids engineering communities of both nations, and to provide an opportunity for the participants and their colleagues to explore possible joint research programs in topics of high priority and mutual interest to both countries. The Seminar provided an excellent forum for reviewing the current state and future needs of fluids engineering for the two nations. With the Seminar ear-marking the first formal scientific exchange between Korea and the United States in the area of fluids engineering, the scope was deliberately left broad and general
XXII Fluid Mechanics Conference (KKMP2016)
2016-01-01
to aerodynamics, atmospheric science, bio-fluids, combustion and reacting flows, computational fluid dynamics, experimental fluid mechanics, flow machinery, general fluid dynamics, hydromechanics, heat and fluid flow, measurement techniques, micro- and nano-flow, multi-phase flow, non-Newtonian fluids, rotating and stratified flows and turbulence. Within the general subjects of this conference, the Professor Janusz W. Eisner's Competition for the best fluid mechanics paper presented during the Conference is organized. Authors holding a M.Sc. or a Ph.D. degree and who are not older than 35 may enter the Competition. Authors with a Ph.D. degree must present individual papers; authors with a M.Sc. degree may present papers with their supervisors as coauthors, including original results of experimental, numerical or analytic research. Six state-of-the-art keynote papers will be delivered by world leading experts. All contributed papers were peer reviewed. Recommendations were received from the Scientific Committee of the Conference; reviewers were from all Polish scientific-academic centres that are involved in fluid mechanics. Accordingly, of the 67 eligible extended abstracts submitted, after a review process by the Scientific Committee, all papers were selected for presentation at XXII Fluid Mechanics Conference. We hope that this publication will be used not only as a guide through the conference's programme but also help in the future to access people and topics in fluid mechanics research. (paper)
The Newtonian form of wave mechanics
Kapuscik, E.
1984-01-01
Following the general principles of both Newton's mechanics and quantum mechanics a new formulation of wave mechanics is proposed. The new basic equations do not contain physical parameters and admit a different interpretation of the Planck constant. (author)
Mathematical modeling for laminar flow of power law fluid in porous media
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)
Modelling non-dust fluids in cosmology
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
Numerical methods for multi-scale modeling of non-Newtonian flows
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
Effect on Non-Newtonian Rheology on Mixing in Taylor-Couette Flow
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.
Physics of Life: A Model for Non-Newtonian Properties of Living Systems
Zak, Michail
2010-01-01
the expected scenario is different from the originally planned one. This approach postulates that even a primitive living species possesses additional, non-Newtonian properties that are not included in the laws of Newtonian or statistical mechanics. These properties follow from a privileged ability of living systems to possess a self-image (a concept introduced in psychology) and to interact with it. The proposed mathematical system is based on the coupling of the classical dynamical system representing the motor dynamics with the corresponding Liouville equation describing the evolution of initial uncertainties in terms of the probability density and representing the mental dynamics. The coupling is implemented by the information-based supervising forces that can be associated with self-awareness. These forces fundamentally change the pattern of the probability evolution, and therefore, lead to a major departure of the behavior of living systems from the patterns of both Newtonian and statistical mechanics. This innovation is meant to capture the signature of life based only on observable behavior, not on any biochemistry. This will not prevent the use of this model for developing artificial living systems, as well as for studying some general properties of behavior of natural, living systems.
Zafar, A. A.; Riaz, M. B.; Shah, N. A.; Imran, M. A.
2018-03-01
The objective of this article is to study some unsteady Couette flows of an Oldroyd-B fluid with non-integer derivatives. The fluid fills an annular region of two infinite co-axial circular cylinders. Flows are due to the motion of the outer cylinder, that rotates about its axis with an arbitrary time-dependent velocity while the inner cylinder is held fixed. Closed form solutions of dimensionless velocity field and tangential tension are obtained by means of the finite Hankel transform and the theory of Laplace transform for fractional calculus. Several results in the literature including the rotational flows through an infinite cylinder can be obtained as limiting cases of our general solutions. Finally, the control of the fractional framework on the dynamics of fluid is analyzed by numerical simulations and graphical illustrations.
Heat Transfer in Complex Fluids
Mehrdad Massoudi
2012-01-01
Amongst the most important constitutive relations in Mechanics, when characterizing the behavior of complex materials, one can identify the stress tensor T, the heat flux vector q (related to heat conduction) and the radiant heating (related to the radiation term in the energy equation). Of course, the expression 'complex materials' is not new. In fact, at least since the publication of the paper by Rivlin & Ericksen (1955), who discussed fluids of complexity (Truesdell & Noll, 1992), to the recently published books (Deshpande et al., 2010), the term complex fluids refers in general to fluid-like materials whose response, namely the stress tensor, is 'non-linear' in some fashion. This non-linearity can manifest itself in variety of forms such as memory effects, yield stress, creep or relaxation, normal-stress differences, etc. The emphasis in this chapter, while focusing on the constitutive modeling of complex fluids, is on granular materials (such as coal) and non-linear fluids (such as coal-slurries). One of the main areas of interest in energy related processes, such as power plants, atomization, alternative fuels, etc., is the use of slurries, specifically coal-water or coal-oil slurries, as the primary fuel. Some studies indicate that the viscosity of coal-water mixtures depends not only on the volume fraction of solids, and the mean size and the size distribution of the coal, but also on the shear rate, since the slurry behaves as shear-rate dependent fluid. There are also studies which indicate that preheating the fuel results in better performance, and as a result of such heating, the viscosity changes. Constitutive modeling of these non-linear fluids, commonly referred to as non-Newtonian fluids, has received much attention. Most of the naturally occurring and synthetic fluids are non-linear fluids, for example, polymer melts, suspensions, blood, coal-water slurries, drilling fluids, mud, etc. It should be noted that sometimes these
Peron, Roberto; Lucchesi, David
The pericenter shift of a binary system represents a suitable observable to be used to test for possible deviations from the Newtonian gravitational inverse—square—law in favor of pos-sible new weak interactions between macroscopic objects. These very weak and long-range interactions are usually described by means of a Yukawa—like potential with strength α and range λ. Moreover, these supplementary interactions may be either consistent with Einstein Equivalence Principle or not. In this work, we analyzed 11 years of LAGEOS II normal points using the GEODYN II code with suitable models for both gravitational and non—gravitational perturbations. However, we do not included in the models the general relativity corrections to Newtonian gravity, such as the ones due to the Earth's gravitoelectric and gravitomagnetic fields. From the fit of the satellite pericenter residuals we have been able to obtain a 99% agreement with the predictions of Einstein theory of gravitation. Therefore, the present mea-surement of the LAGEOS II pericenter shift represents a 1% measurement in the field of the Earth of the combination of the Parametrized Post—Newtonian parameters g and b of general relativity. This result may be also used to put limits on the strength α of a possible Yukawa— like interaction with a characteristic range of about 1 Earth radii. We obtained |α| ≈ 4 · 10-11 , that represents a significant improvement with respect to the previous constraints based on Earth—LAGEOS or Lunar—LAGEOS data.
Test of modified Newtonian dynamics with recent Boomerang data
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
Against Laplacian Reduction of Newtonian Mass to Spatiotemporal Quantities
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.
A Lagrangian PFEM approach for non-Newtonian viscoplastic materials
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...
Tidal interaction of black holes and Newtonian viscous bodies
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.
Gas holdup in a reciprocating plate bioreactor: Non-Newtonian - liquid phase
Naseva Olivera S.
2002-01-01
Full Text Available The gas holdup was studied in non-newtonian liquids in a gas-liquid and gas-liquid-solid reciprocating plate bioreactor. Aqueous solutions of carboxy methyl cellulose (CMC; Lucel, Lučane, Yugoslavia of different degrees of polymerization (PP 200 and PP 1000 and concentration (0,5 and 1%, polypropylene spheres (diameter 8.3 mm; fraction of spheres: 3.8 and 6.6% by volume and air were used as the liquid, solid and gas phase. The gas holdup was found to be dependent on the vibration rate, the superficial gas velocity, volume fraction of solid particles and Theological properties of the liquid ohase. Both in the gas-liquid and gas-liquid-solid systems studied, the gas holdup increased with increasing vibration rate and gas flow rate. The gas holdup was higher in three-phase systems than in two-phase ones under otter operating conditions being the same. Generally the gas holdup increased with increasing the volume fraction of solid particles, due to the dispersion action of the solid particles, and decreased with increasing non-Newtonian behaviour (decreasing flow index i.e. with increasing degree of polymerization and solution concentration of CMC applied, as a result of gas bubble coalescence.
Hardin, G. R.; Sani, R. L.; Henry, D.; Roux, B.
1990-01-01
The buoyancy-driven instability of a monocomponent or binary fluid completely contained in a vertical circular cylinder is investigated, including the influence of the Soret effect for the binary mixture. The Boussinesq approximation is used, and the resulting linear stability problem is solved using a Galerkin technique. The analysis considers fluid mixtures ranging from gases to liquid metals. The flow structure is found to depend strongly on both the cylinder aspect ratio and the magnitude of the Soret effect. The predicted stability limits are shown to agree closely with experimental observations.
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.
Influence of fluid structure upon the shape of RTD curve at a sugar crystallizer
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)
Study of blood flow in several benchmark micro-channels using a two-fluid approach.
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.
Introduction of small velocity and pressure variation into a stationary compressible fluid
Trancong, Ton [Defence Science and Technology Organisation Australia, Fishermens Bend (Australia). Aeronautical Research Lab.
1992-06-01
This work formulates the aerodynamic time-dependent Coulomb and Biot-Savart laws with inherent transmission retardation. It generalizes the theory by Baskin et al. (for only the isentropic propagation of small vortex disturbances) to deal with the propagation of small disturbances caused by a distributed system of both vortices and variation in specific entropy of a thermodynamically simple compressible fluid. The proof here uses an alternative, more appealing derivation with the help of a novel wave-cone transformation (which changes Kirchhoff's retarded potentials into Newtonian potentials). The results suggest the possibility of using a focused laser spot to simulate the effect of a source in a compressible fluid; the source may even move at a supersonic speed to create a shock wave. They also suggest a time-dependent, three-dimensional formula for lifts caused by small disturbances that is in agreement with Blasius' formula for two-dimensional, time-independent, inviscid flows. (orig.).
Engineering Fracking Fluids with Computer Simulation
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.
Lue Xing; Zhu Hongwu; Yao Zhenzhi; Meng Xianghua; Zhang Cheng; Zhang Chunyi; Tian Bo
2008-01-01
In this paper, the multisoliton solutions in terms of double Wronskian determinant are presented for a generalized variable-coefficient nonlinear Schroedinger equation, which appears in space and laboratory plasmas, arterial mechanics, fluid dynamics, optical communications and so on. By means of the particularly nice properties of Wronskian determinant, the solutions are testified through direct substitution into the bilinear equations. Furthermore, it can be proved that the bilinear Baecklund transformation transforms between (N - 1)- and N-soliton solutions
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...
Computational simulation of a non-newtonian model of the blood separation process.
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.
Zhang, Lucy T; Yang, Jubiao
2016-12-01
In this work we explore the aerodynamics flow characteristics of a coupled fluid-structure interaction system using a generalized Bernoulli equation derived directly from the Cauchy momentum equations. Unlike the conventional Bernoulli equation where incompressible, inviscid, and steady flow conditions are assumed, this generalized Bernoulli equation includes the contributions from compressibility, viscous, and unsteadiness, which could be essential in defining aerodynamic characteristics. The application of the derived Bernoulli's principle is on a fully-coupled fluid-structure interaction simulation of the vocal folds vibration. The coupled system is simulated using the immersed finite element method where compressible Navier-Stokes equations are used to describe the air and an elastic pliable structure to describe the vocal fold. The vibration of the vocal fold works to open and close the glottal flow. The aerodynamics flow characteristics are evaluated using the derived Bernoulli's principles for a vibration cycle in a carefully partitioned control volume based on the moving structure. The results agree very well to experimental observations, which validate the strategy and its use in other types of flow characteristics that involve coupled fluid-structure interactions.
Zhang, Lucy T.; Yang, Jubiao
2017-01-01
In this work we explore the aerodynamics flow characteristics of a coupled fluid-structure interaction system using a generalized Bernoulli equation derived directly from the Cauchy momentum equations. Unlike the conventional Bernoulli equation where incompressible, inviscid, and steady flow conditions are assumed, this generalized Bernoulli equation includes the contributions from compressibility, viscous, and unsteadiness, which could be essential in defining aerodynamic characteristics. The application of the derived Bernoulli’s principle is on a fully-coupled fluid-structure interaction simulation of the vocal folds vibration. The coupled system is simulated using the immersed finite element method where compressible Navier-Stokes equations are used to describe the air and an elastic pliable structure to describe the vocal fold. The vibration of the vocal fold works to open and close the glottal flow. The aerodynamics flow characteristics are evaluated using the derived Bernoulli’s principles for a vibration cycle in a carefully partitioned control volume based on the moving structure. The results agree very well to experimental observations, which validate the strategy and its use in other types of flow characteristics that involve coupled fluid-structure interactions. PMID:29527541
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
Two-Fluid Mathematical Models for Blood Flow in Stenosed Arteries: A Comparative Study
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.
McConaghy, C. F. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Gascoyne, P. R. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2017-09-28
The purpose ofthis project was to develop a general-purpose analysis system based on a programmable fluid processor (PFP). The PFP is an array of electrodes surrounded by fluid reservoirs and injectors. Injected droplets of various reagents are manjpulated and combined on the array by Dielectrophoretic (DEP) forces. The goal was to create a small handheld device that could accomplish the tasks currently undertaken by much larger, time consuming, manual manipulation in the lab. The entire effo1t was funded by DARPA under the Bio-Flips program. MD Anderson Cancer Center was the PI for the DARPA effort. The Bio-Flips program was a 3- year program that ran from September 2000 to September 2003. The CRADA was somewhat behind the Bi-Flips program running from June 2001 to June 2004 with a no cost extension to September 2004.
Heijden, Harm van der; Mullen, Joost van der
2002-01-01
A general ray-trace method for calculating the effects of radiative transfer in a control volume (CV) fluid code is presented. The method makes use of the structured CV grid of the fluid code, and is suited for geometries with a point or axis of symmetry. In particular, the specific equations for spherical and cylindrical (without z dependence) configurations are developed. The application of this method to local thermal equilibrium (LTE) and non-LTE plasma models is discussed. Various opportunities for sacrificing precision for calculation speed are pointed out. As a case study, the effects of radiative transfer in a sulphur lamp are calculated. Since an LTE description of the molecular radiation yields a computed spectrum that differs significantly from a measured one, the possibility of a non-LTE vibrational distribution of the radiating S 2 -B state is investigated. The results indicate that the vibrational populations may be inversed. (author)
Viscosity of Heterogeneous Silicate Melts: A Non-Newtonian Model
Liu, Zhuangzhuang; Blanpain, Bart; Guo, Muxing
2017-12-01
The recently published viscosity data of heterogeneous silicate melts with well-documented structure and experimental conditions are critically re-analyzed and tabulated. By using these data, a non-Newtonian viscosity model incorporating solid fraction, solid shape, and shear rate is proposed on the basis of the power-law equation. This model allows calculating the viscosity of the heterogeneous silicate melts with solid fraction up to 34 vol pct. The error between the calculated and measured data is evaluated to be 32 pct, which is acceptable considering the large error in viscosity measurement of the completely liquid silicate melt.
The intergalactic Newtonian gravitational field and the shell theorem
Zaninetti L.
2012-01-01
Full Text Available The release of the 2MASS Redshift Survey (2MRS with its 44599 galaxies allows the deduction of their masses in nearly complete sample. A cubic box with side of 37 Mpc containing 2429 galaxies is extracted and the Newtonian gravitational field is evaluated both at the center of the box as well as in 101 x 101 x 101 grid points of the box. The obtained results are then discussed in the light of the shell theorem which states that inside of a sphere the gravitational field is zero.
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.
Inertia effects in the laminar radial flow of a power law fluid with an electromagnetic field
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.)
Selected topics of fluid mechanics
Kindsvater, Carl E.
1958-01-01
The fundamental equations of fluid mechanics are specific expressions of the principles of motion which are ascribed to Isaac Newton. Thus, the equations which form the framework of applied fluid mechanics or hydraulics are, in addition to the equation of continuity, the Newtonian equations of energy and momentum. These basic relationships are also the foundations of river hydraulics. The fundamental equations are developed in this report with sufficient rigor to support critical examinations of their applicability to most problems met by hydraulic engineers of the Water Resources Division of the United States Geological Survey. Physical concepts are emphasized, and mathematical procedures are the simplest consistent with the specific requirements of the derivations. In lieu of numerical examples, analogies, and alternative procedures, this treatment stresses a brief methodical exposition of the essential principles. An important objective of this report is to prepare the user to read the literature of the science. Thus, it begins With a basic vocabulary of technical symbols, terms, and concepts. Throughout, emphasis is placed on the language of modern fluid mechanics as it pertains to hydraulic engineering. The basic differential and integral equations of simple fluid motion are derived, and these equations are, in turn, used to describe the essential characteristics of hydrostatics and piezometry. The one-dimensional equations of continuity and motion are defined and are used to derive the general discharge equation. The flow net is described as a means of demonstrating significant characteristics of two-dimensional irrotational flow patterns. A typical flow net is examined in detail. The influence of fluid viscosity is described as an obstacle to the derivation of general, integral equations of motion. It is observed that the part played by viscosity is one which is usually dependent on experimental evaluation. It follows that the dimensionless ratios known as
Fluid Structure Interaction Techniques For Extrusion And Mixing Processes
Valette, Rudy; Vergnes, Bruno; Coupez, Thierry
2007-05-01
This work focuses on the development of numerical techniques devoted to the simulation of mixing processes of complex fluids such as twin-screw extrusion or batch mixing. In mixing process simulation, the absence of symmetry of the moving boundaries (the screws or the rotors) implies that their rigid body motion has to be taken into account by using a special treatment We therefore use a mesh immersion technique (MIT), which consists in using a P1+/P1-based (MINI-element) mixed finite element method for solving the velocity-pressure problem and then solving the problem in the whole barrel cavity by imposing a rigid motion (rotation) to nodes found located inside the so called immersed domain, each sub-domain (screw, rotor) being represented by a surface CAD mesh (or its mathematical equation in simple cases). The independent meshes are immersed into a unique background computational mesh by computing the distance function to their boundaries. Intersections of meshes are accounted for, allowing to compute a fill factor usable as for the VOF methodology. This technique, combined with the use of parallel computing, allows to compute the time-dependent flow of generalized Newtonian fluids including yield stress fluids in a complex system such as a twin screw extruder, including moving free surfaces, which are treated by a "level set" and Hamilton-Jacobi method.