Convection and reaction in a diffusive boundary layer in a porous medium: nonlinear dynamics.
Andres, Jeanne Therese H; Cardoso, Silvana S S
2012-09-01
We study numerically the nonlinear interactions between chemical reaction and convective fingering in a diffusive boundary layer in a porous medium. The reaction enhances stability by consuming a solute that is unstably distributed in a gravitational field. We show that chemical reaction profoundly changes the dynamics of the system, by introducing a steady state, shortening the evolution time, and altering the spatial patterns of velocity and concentration of solute. In the presence of weak reaction, finger growth and merger occur effectively, driving strong convective currents in a thick layer of solute. However, as the reaction becomes stronger, finger growth is inhibited, tip-splitting is enhanced and the layer of solute becomes much thinner. Convection enhances the mass flux of solute consumed by reaction in the boundary layer but has a diminishing effect as reaction strength increases. This nonlinear behavior has striking differences to the density fingering of traveling reaction fronts, for which stronger chemical kinetics result in more effective finger merger owing to an increase in the speed of the front. In a boundary layer, a strong stabilizing effect of reaction can maintain a long-term state of convection in isolated fingers of wavelength comparable to that at onset of instability.
Tredenick, Eloise C; Farrell, Troy W; Forster, W Alison; Psaltis, Steven T P
2017-01-01
The agricultural industry requires improved efficacy of sprays being applied to crops and weeds in order to reduce their environmental impact and deliver improved financial returns. Enhanced foliar uptake is one means of improving efficacy. The plant leaf cuticle is known to be the main barrier to diffusion of agrochemicals within the leaf. The usefulness of a mathematical model to simulate uptake of agrochemicals in plant cuticles has been noted previously in the literature, as the results of each uptake experiment are specific to each formulation of active ingredient, plant species and environmental conditions. In this work we develop a mathematical model and numerical simulation for the uptake of hydrophilic ionic agrochemicals through aqueous pores in plant cuticles. We propose a novel, nonlinear, porous diffusion model for ionic agrochemicals in isolated cuticles, which extends simple diffusion through the incorporation of parameters capable of simulating: plant species variations, evaporation of surface droplet solutions, ion binding effects on the cuticle surface and swelling of the aqueous pores with water. We validate our theoretical results against appropriate experimental data, discuss the key sensitivities in the model and relate theoretical predictions to appropriate physical mechanisms. Major influencing factors have been found to be cuticle structure, including tortuosity and density of the aqueous pores, and to a lesser extent humidity and cuticle surface ion binding effects.
Directory of Open Access Journals (Sweden)
Eloise C. Tredenick
2017-05-01
Full Text Available The agricultural industry requires improved efficacy of sprays being applied to crops and weeds in order to reduce their environmental impact and deliver improved financial returns. Enhanced foliar uptake is one means of improving efficacy. The plant leaf cuticle is known to be the main barrier to diffusion of agrochemicals within the leaf. The usefulness of a mathematical model to simulate uptake of agrochemicals in plant cuticles has been noted previously in the literature, as the results of each uptake experiment are specific to each formulation of active ingredient, plant species and environmental conditions. In this work we develop a mathematical model and numerical simulation for the uptake of hydrophilic ionic agrochemicals through aqueous pores in plant cuticles. We propose a novel, nonlinear, porous diffusion model for ionic agrochemicals in isolated cuticles, which extends simple diffusion through the incorporation of parameters capable of simulating: plant species variations, evaporation of surface droplet solutions, ion binding effects on the cuticle surface and swelling of the aqueous pores with water. We validate our theoretical results against appropriate experimental data, discuss the key sensitivities in the model and relate theoretical predictions to appropriate physical mechanisms. Major influencing factors have been found to be cuticle structure, including tortuosity and density of the aqueous pores, and to a lesser extent humidity and cuticle surface ion binding effects.
Nonlinear Diffusion and Transient Osmosis
International Nuclear Information System (INIS)
Igarashi, Akira; Rondoni, Lamberto; Botrugno, Antonio; Pizzi, Marco
2011-01-01
We investigate both analytically and numerically the concentration dynamics of a solution in two containers connected by a narrow and short channel, in which diffusion obeys a porous medium equation. We also consider the variation of the pressure in the containers due to the flow of matter in the channel. In particular, we identify a phenomenon, which depends on the transport of matter across nano-porous membranes, which we call ''transient osmosis . We find that nonlinear diffusion of the porous medium equation type allows numerous different osmotic-like phenomena, which are not present in the case of ordinary Fickian diffusion. Experimental results suggest one possible candidate for transiently osmotic processes. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
Degenerate nonlinear diffusion equations
Favini, Angelo
2012-01-01
The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asympt...
Wu Zhuo Qun; Li Hui Lai; Zhao Jun Ning
2001-01-01
Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which
Nonlinear degenerate cross-diffusion systems with nonlocal interaction
Di Francesco, M.; Esposito, A.; Fagioli, S.
2017-01-01
We investigate a class of systems of partial differential equations with nonlinear cross-diffusion and nonlocal interactions, which are of interest in several contexts in social sciences, finance, biology, and real world applications. Assuming a uniform "coerciveness" assumption on the diffusion part, which allows to consider a large class of systems with degenerate cross-diffusion (i.e. of porous medium type) and relaxes sets of assumptions previously considered in the literature, we prove g...
Nonlinear dynamics of capacitive charging and desalination by porous electrodes
Biesheuvel, P. M.; Bazant, M. Z.
2010-03-01
The rapid and efficient exchange of ions between porous electrodes and aqueous solutions is important in many applications, such as electrical energy storage by supercapacitors, water desalination and purification by capacitive deionization, and capacitive extraction of renewable energy from a salinity difference. Here, we present a unified mean-field theory for capacitive charging and desalination by ideally polarizable porous electrodes (without Faradaic reactions or specific adsorption of ions) valid in the limit of thin double layers (compared to typical pore dimensions). We illustrate the theory for the case of a dilute, symmetric, binary electrolyte using the Gouy-Chapman-Stern (GCS) model of the double layer, for which simple formulae are available for salt adsorption and capacitive charging of the diffuse part of the double layer. We solve the full GCS mean-field theory numerically for realistic parameters in capacitive deionization, and we derive reduced models for two limiting regimes with different time scales: (i) in the “supercapacitor regime” of small voltages and/or early times, the porous electrode acts like a transmission line, governed by a linear diffusion equation for the electrostatic potential, scaled to the RC time of a single pore, and (ii) in the “desalination regime” of large voltages and long times, the porous electrode slowly absorbs counterions, governed by coupled, nonlinear diffusion equations for the pore-averaged potential and salt concentration.
Review of enhanced vapor diffusion in porous media
International Nuclear Information System (INIS)
Webb, S.W.; Ho, C.K.
1998-01-01
Vapor diffusion in porous media in the presence of its own liquid has often been treated similar to gas diffusion. The gas diffusion rate in porous media is much lower than in free space due to the presence of the porous medium and any liquid present. However, enhanced vapor diffusion has also been postulated such that the diffusion rate may approach free-space values. Existing data and models for enhanced vapor diffusion, including those in TOUGH2, are reviewed in this paper
Intermittent Motion, Nonlinear Diffusion Equation and Tsallis Formalism
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Ervin K. Lenzi
2017-01-01
Full Text Available We investigate an intermittent process obtained from the combination of a nonlinear diffusion equation and pauses. We consider the porous media equation with reaction terms related to the rate of switching the particles from the diffusive mode to the resting mode or switching them from the resting to the movement. The results show that in the asymptotic limit of small and long times, the spreading of the system is essentially governed by the diffusive term. The behavior exhibited for intermediate times depends on the rates present in the reaction terms. In this scenario, we show that, in the asymptotic limits, the distributions for this process are given by in terms of power laws which may be related to the q-exponential present in the Tsallis statistics. Furthermore, we also analyze a situation characterized by different diffusive regimes, which emerges when the diffusive term is a mixing of linear and nonlinear terms.
Nonlinear Cross-Diffusion with Size Exclusion
Burger, Martin; Di Francesco, Marco; Pietschmann, Jan-Frederik; Schlake, Bä rbel
2010-01-01
The aim of this paper is to investigate the mathematical properties of a continuum model for diffusion of multiple species incorporating size exclusion effects. The system for two species leads to nonlinear cross-diffusion terms with double
Diffusion of oriented particles in porous media
Energy Technology Data Exchange (ETDEWEB)
Haber, René [Institut für Physik, Technische Universität Chemnitz, D-09107 Chemnitz (Germany); Centre for Nonlinear Studies, Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn (Estonia); Prehl, Janett [Institut für Physik, Technische Universität Chemnitz, D-09107 Chemnitz (Germany); Herrmann, Heiko [Centre for Nonlinear Studies, Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn (Estonia); Hoffmann, Karl Heinz, E-mail: hoffmann@physik.tu-chemnitz.de [Institut für Physik, Technische Universität Chemnitz, D-09107 Chemnitz (Germany)
2013-11-29
Diffusion of particles in porous media often shows subdiffusive behavior. Here, we analyze the dynamics of particles exhibiting an orientation. The features we focus on are geometrical restrictions and the dynamical consequences of the interactions between the local surrounding structure and the particle orientation. This interaction can lead to particles getting temporarily stuck in parts of the structure. Modeling this interaction by a particular random walk dynamics on fractal structures we find that the random walk dimension is not affected while the diffusion constant shows a variety of interesting and surprising features.
Diffusion of oriented particles in porous media
International Nuclear Information System (INIS)
Haber, René; Prehl, Janett; Herrmann, Heiko; Hoffmann, Karl Heinz
2013-01-01
Diffusion of particles in porous media often shows subdiffusive behavior. Here, we analyze the dynamics of particles exhibiting an orientation. The features we focus on are geometrical restrictions and the dynamical consequences of the interactions between the local surrounding structure and the particle orientation. This interaction can lead to particles getting temporarily stuck in parts of the structure. Modeling this interaction by a particular random walk dynamics on fractal structures we find that the random walk dimension is not affected while the diffusion constant shows a variety of interesting and surprising features.
Diffusion Driven Combustion Waves in Porous Media
Aldushin, A. P.; Matkowsky, B. J.
2000-01-01
Filtration of gas containing oxidizer, to the reaction zone in a porous medium, due, e.g., to a buoyancy force or to an external pressure gradient, leads to the propagation of Filtration combustion (FC) waves. The exothermic reaction occurs between the fuel component of the solid matrix and the oxidizer. In this paper, we analyze the ability of a reaction wave to propagate in a porous medium without the aid of filtration. We find that one possible mechanism of propagation is that the wave is driven by diffusion of oxidizer from the environment. The solution of the combustion problem describing diffusion driven waves is similar to the solution of the Stefan problem describing the propagation of phase transition waves, in that the temperature on the interface between the burned and unburned regions is constant, the combustion wave is described by a similarity solution which is a function of the similarity variable x/square root of(t) and the wave velocity decays as 1/square root of(t). The difference between the two problems is that in the combustion problem the temperature is not prescribed, but rather, is determined as part of the solution. We will show that the length of samples in which such self-sustained combustion waves can occur, must exceed a critical value which strongly depends on the combustion temperature T(sub b). Smaller values of T(sub b) require longer sample lengths for diffusion driven combustion waves to exist. Because of their relatively small velocity, diffusion driven waves are considered to be relevant for the case of low heat losses, which occur for large diameter samples or in microgravity conditions, Another possible mechanism of porous medium combustion describes waves which propagate by consuming the oxidizer initially stored in the pores of the sample. This occurs for abnormally high pressure and gas density. In this case, uniformly propagating planar waves, which are kinetically controlled, can propagate, Diffusion of oxidizer decreases
Random-walk diffusion and drying of porous materials
Mehrafarin, M.; Faghihi, M.
2001-12-01
Based on random-walk diffusion, a microscopic model for drying is proposed to explain the characteristic features of the drying-rate curve of porous materials. The constant drying-rate period is considered as a normal diffusion process. The transition to the falling-rate regime is attributed to the fractal nature of porous materials which results in crossover to anomalous diffusion.
Evaluation of diffusion parameters of radon in porous material by flow-through diffusion experiment
International Nuclear Information System (INIS)
Chunnan Hsu; Shihchin Tsai; Shihming Liang
1994-01-01
The effectiveness of a material in reducing the fluence rate of Rn from soil was assessed in this study by using a flow-through diffusion experiment to evaluate the diffusion parameters -apparent diffusion coefficient and capacity factor - of radon (Rn) in a porous material. An improved method based on the nonlinear least-squares and Marquardt's method (NLSM method) was proposed to provide more reliable analyses of experimental data than the graphical method. The NLSM method was confirmed by the experimental results to be capable of estimating the diffusion parameters, even if the process was transient. This method was also demonstrated to correlate sufficiently with the results by the conventional method while the process had already reached steady-state. Natural mordenite was employed in this study as a testing material because it has more effective sorption for noble gas than any other earthen material. (author)
Turing instability in reaction-diffusion systems with nonlinear diffusion
Energy Technology Data Exchange (ETDEWEB)
Zemskov, E. P., E-mail: zemskov@ccas.ru [Russian Academy of Sciences, Dorodnicyn Computing Center (Russian Federation)
2013-10-15
The Turing instability is studied in two-component reaction-diffusion systems with nonlinear diffusion terms, and the regions in parametric space where Turing patterns can form are determined. The boundaries between super- and subcritical bifurcations are found. Calculations are performed for one-dimensional brusselator and oregonator models.
Analysis of fractional non-linear diffusion behaviors based on Adomian polynomials
Directory of Open Access Journals (Sweden)
Wu Guo-Cheng
2017-01-01
Full Text Available A time-fractional non-linear diffusion equation of two orders is considered to investigate strong non-linearity through porous media. An equivalent integral equation is established and Adomian polynomials are adopted to linearize non-linear terms. With the Taylor expansion of fractional order, recurrence formulae are proposed and novel numerical solutions are obtained to depict the diffusion behaviors more accurately. The result shows that the method is suitable for numerical simulation of the fractional diffusion equations of multi-orders.
Nonlinear diffusion problem arising in plasma physics
International Nuclear Information System (INIS)
Berryman, J.G.; Holland, C.J.
1978-01-01
In earlier studies of plasma diffusion with Okuda-Dawson scaling (D approx. n/sup -1/2/), perturbation theory indicated that arbitrary initial data should evolve rapidly toward the separation solution of the relevant nonlinear diffusion equation. Now a Lyapunov functional has been found which is strictly decreasing in time and bounded below. The rigorous proof that arbitrary initial data evolve toeard the separable solution is summarized. Rigorous bounds on the decay time are also presented
A mixed finite element method for nonlinear diffusion equations
Burger, Martin; Carrillo, José
2010-01-01
We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model. © American Institute of Mathematical Sciences.
Nonlinear Cross-Diffusion with Size Exclusion
Burger, Martin
2010-01-01
The aim of this paper is to investigate the mathematical properties of a continuum model for diffusion of multiple species incorporating size exclusion effects. The system for two species leads to nonlinear cross-diffusion terms with double degeneracy, which creates significant novel challenges in the analysis of the system. We prove global existence of weak solutions and well-posedness of strong solutions close to equilibrium. We further study some asymptotics of the model, and in particular we characterize the large-time behavior of solutions. 2010 © Society for Industrial and Applied Mathematics.
Nonlinear radiative peristaltic flow of hydromagnetic fluid through porous medium
Directory of Open Access Journals (Sweden)
Q. Hussain
2018-06-01
Full Text Available The radiative heat and mass transfer in wall induced flow of hydromagnetic fluid through porous medium in an asymmetric channel is analyzed. The fluid viscosity is considered temperature dependent. In the theory of peristalsis, the radiation effects are either ignored or taken as linear approximation of radiative heat flux. Such approximation is only possible when there is sufficiently small temperature differences in the flow field; however, nonlinear radiation effects are valid for large temperature differences as well (the new feature added in the present study. Mathematical modeling of the problems include the complicated system of highly nonlinear differential equations. Semi-analytical solutions are established in the wave reference frame. Results are displayed graphically and discussed in detail for the variation of various physical parameters with the special attention to viscosity, radiation, and temperature ratio parameters. Keywords: Nonlinear thermal radiation, Variable viscosity, Porous medium, Soret and Dufour effects, Peristalsis
Brem, Gerrit; Brouwers, J.J.H.
1990-01-01
Analytical description are presented for non-linear heterogeneous conversion of a porous solid particle reacting with a surrounding gas. Account has been taken of a reaction rate of general order with respect to gas concentration, intrinsic reaction surface area and pore diffusion, which change with
Polycrystalline Silicon Gettered by Porous Silicon and Heavy Phosphorous Diffusion
Institute of Scientific and Technical Information of China (English)
LIU Zuming(刘祖明); Souleymane K Traore; ZHANG Zhongwen(张忠文); LUO Yi(罗毅)
2004-01-01
The biggest barrier for photovoltaic (PV) utilization is its high cost, so the key for scale PV utilization is to further decrease the cost of solar cells. One way to improve the efficiency, and therefore lower the cost, is to increase the minority carrier lifetime by controlling the material defects. The main defects in grain boundaries of polycrystalline silicon gettered by porous silicon and heavy phosphorous diffusion have been studied. The porous silicon was formed on the two surfaces of wafers by chemical etching. Phosphorous was then diffused into the wafers at high temperature (900℃). After the porous silicon and diffusion layers were removed, the minority carrier lifetime was measured by photo-conductor decay. The results show that the lifetime's minority carriers are increased greatly after such treatment.
Nonlinear diffuse scattering of the random-phased wave
International Nuclear Information System (INIS)
Kato, Yoshiaki; Arinaga, Shinji; Mima, Kunioki.
1983-01-01
First experimental observation of the nonlinear diffuse scattering is reported. This new effect was observed in the propagation of the random-phased wave through a nonlinear dielectric medium. This effect is ascribed to the diffusion of the wavevector of the electro-magnetic wave to the lateral direction due to the randomly distributed nonlinear increase in the refractive index. (author)
Nonlinear analysis of a reaction-diffusion system: Amplitude equations
Energy Technology Data Exchange (ETDEWEB)
Zemskov, E. P., E-mail: zemskov@ccas.ru [Russian Academy of Sciences, Dorodnicyn Computing Center (Russian Federation)
2012-10-15
A reaction-diffusion system with a nonlinear diffusion term is considered. Based on nonlinear analysis, the amplitude equations are obtained in the cases of the Hopf and Turing instabilities in the system. Turing pattern-forming regions in the parameter space are determined for supercritical and subcritical instabilities in a two-component reaction-diffusion system.
Diffusion with condensation and evaporation in porous media
International Nuclear Information System (INIS)
Gu, L.; Plumb, O.A.; Ho, C.K.; Webb, S.W.
1998-03-01
Vapor phase transport in porous media is important in a number of environmental and industrial processes: soil moisture transport, vapor phase transport in the vadose zone, transport in the vicinity of buried nuclear waste, and industrial processes such as drying. The diffusion of water vapor in a packed bed containing residual liquid is examined experimentally. The objective is to quantify the effect of enhanced vapor diffusion resulting from evaporation/condensation in porous media subjected to a temperature gradient. Isothermal diffusion experiments in free-space were conducted to qualify the experimental apparatus and techniques. For these experiments measured diffusion coefficients are within 3.6% of those reported in the literature for the temperature range from 25 C to 40 C. Isothermal experiments in packed beds of glass beads were used to determine the tortuosity coefficient resulting in τ = 0.78 ± 0.028, which is also consistent with previously reported results. Nonisothermal experiments in packed beds in which condensation occurs were conducted to examine enhanced vapor diffusion. The interpretation of the results for these experiments is complicated by a gradual, but continuous, build-up of condensate in the packed beds during the course of the experiment. Results indicate diffusion coefficients which increase as a function of saturation resulting in enhancement of the vapor-phase transport by a factor of approximately four compared to a dry porous medium
International Nuclear Information System (INIS)
Liu, Yanfeng; Zhou, Xiaojun; Wang, Dengjia; Song, Cong; Liu, Jiaping
2015-01-01
Highlights: • Fractal theory is introduced into the prediction of VOC diffusion coefficient. • MSFC model of the diffusion coefficient is developed for porous building materials. • The MSFC model contains detailed pore structure parameters. • The accuracy of the MSFC model is verified by independent experiments. - Abstract: Most building materials are porous media, and the internal diffusion coefficients of such materials have an important influences on the emission characteristics of volatile organic compounds (VOCs). The pore structure of porous building materials has a significant impact on the diffusion coefficient. However, the complex structural characteristics bring great difficulties to the model development. The existing prediction models of the diffusion coefficient are flawed and need to be improved. Using scanning electron microscope (SEM) observations and mercury intrusion porosimetry (MIP) tests of typical porous building materials, this study developed a new diffusivity model: the multistage series-connection fractal capillary-bundle (MSFC) model. The model considers the variable-diameter capillaries formed by macropores connected in series as the main mass transfer paths, and the diameter distribution of the capillary bundles obeys a fractal power law in the cross section. In addition, the tortuosity of the macrocapillary segments with different diameters is obtained by the fractal theory. Mesopores serve as the connections between the macrocapillary segments rather than as the main mass transfer paths. The theoretical results obtained using the MSFC model yielded a highly accurate prediction of the diffusion coefficients and were in a good agreement with the VOC concentration measurements in the environmental test chamber.
Nonlinear radiative peristaltic flow of hydromagnetic fluid through porous medium
Hussain, Q.; Latif, T.; Alvi, N.; Asghar, S.
2018-06-01
The radiative heat and mass transfer in wall induced flow of hydromagnetic fluid through porous medium in an asymmetric channel is analyzed. The fluid viscosity is considered temperature dependent. In the theory of peristalsis, the radiation effects are either ignored or taken as linear approximation of radiative heat flux. Such approximation is only possible when there is sufficiently small temperature differences in the flow field; however, nonlinear radiation effects are valid for large temperature differences as well (the new feature added in the present study). Mathematical modeling of the problems include the complicated system of highly nonlinear differential equations. Semi-analytical solutions are established in the wave reference frame. Results are displayed graphically and discussed in detail for the variation of various physical parameters with the special attention to viscosity, radiation, and temperature ratio parameters.
Exact analytical solutions for nonlinear reaction-diffusion equations
International Nuclear Information System (INIS)
Liu Chunping
2003-01-01
By using a direct method via the computer algebraic system of Mathematica, some exact analytical solutions to a class of nonlinear reaction-diffusion equations are presented in closed form. Subsequently, the hyperbolic function solutions and the triangular function solutions of the coupled nonlinear reaction-diffusion equations are obtained in a unified way
Diffusion in porous structures containing three fluid phases
International Nuclear Information System (INIS)
Galani, A.N.; Kainourgiakis, M.E.; Stubos, A.K.; Kikkinides, E.S.
2005-01-01
In the present study, the tracer diffusion in porous media filled by three fluid phases (a non-wetting, an intermediate wetting and a wetting phase) is investigated. The disordered porous structure of porous systems like random sphere packing and the North Sea chalk, is represented by three-dimensional binary images. The random sphere pack is generated by a standard ballistic deposition procedure, while the chalk matrix by a stochastic reconstruction technique. Physically sound spatial distributions of the three phases filling the pore space are determined by the use of a simulated annealing algorithm, where those phases are initially randomly distributed in the pore space and trial-and-error swaps are performed in order to attain the global minimum of the total interfacial energy. The acceptance rule for a trial move during the annealing is modified properly improving the efficiency of the technique. The diffusivities of the resulting domains are computed by a random walk method. A parametric study with respect to the pore volume fraction occupied by each fluid phase and the ratio of the diffusivities in the fluid phases is performed. (authors)
A family of analytical solutions of a nonlinear diffusion-convection equation
Hayek, Mohamed
2018-01-01
Despite its popularity in many engineering fields, the nonlinear diffusion-convection equation has no general analytical solutions. This work presents a family of closed-form analytical traveling wave solutions for the nonlinear diffusion-convection equation with power law nonlinearities. This kind of equations typically appears in nonlinear problems of flow and transport in porous media. The solutions that are addressed are simple and fully analytical. Three classes of analytical solutions are presented depending on the type of the nonlinear diffusion coefficient (increasing, decreasing or constant). It has shown that the structure of the traveling wave solution is strongly related to the diffusion term. The main advantage of the proposed solutions is that they are presented in a unified form contrary to existing solutions in the literature where the derivation of each solution depends on the specific values of the diffusion and convection parameters. The proposed closed-form solutions are simple to use, do not require any numerical implementation, and may be implemented in a simple spreadsheet. The analytical expressions are also useful to mathematically analyze the structure and properties of the solutions.
Nonlinear interaction and wave breaking with a submerged porous structure
Hsieh, Chih-Min; Sau, Amalendu; Hwang, Robert R.; Yang, W. C.
2016-12-01
Numerical simulations are performed to investigate interactive velocity, streamline, turbulent kinetic energy, and vorticity perturbations in the near-field of a submerged offshore porous triangular structure, as Stokes waves of different heights pass through. The wave-structure interaction and free-surface breaking for the investigated flow situations are established based on solutions of 2D Reynolds Averaged Navier-Stokes equations in a Cartesian grid in combination with K-ɛ turbulent closure and the volume of fluid methodology. The accuracy and stability of the adopted model are ascertained by extensive comparisons of computed data with the existing experimental and theoretical findings and through efficient predictions of the internal physical kinetics. Simulations unfold "clockwise" and "anticlockwise" rotation of fluid below the trough and the crest of the viscous waves, and the penetrated wave energy creates systematic flow perturbation in the porous body. The interfacial growths of the turbulent kinetic energy and the vorticity appear phenomenal, around the apex of the immersed structure, and enhanced significantly following wave breaking. Different values of porosity parameter and two non-porous cases have been examined in combination with varied incident wave height to reveal/analyze the nonlinear flow behavior in regard to local spectral amplification and phase-plane signatures. The evolution of leading harmonics of the undulating free-surface and the vertical velocity exhibits dominating roles of the first and the second modes in inducing the nonlinearity in the post-breaking near-field that penetrates well below the surface layer. The study further suggests the existence of a critical porosity that can substantially enhance the wave-shoaling and interface breaking.
Process for producing a porous diffusion membrane
International Nuclear Information System (INIS)
Kabayama, Shisho; Ikeda, Hirosaka.
1969-01-01
A diffusion membrane having a sandwich construction, the pore diameter of which is 1,000A or less, is provided for the separation and enrichment of, for example, U-235F from U-238F. Flexibility, corrosion resistance and separation efficiency of the barrier are improved by a process which comprises the steps of filling powders of metallic or inorganic materials into a mesh or grid-like support, superimposing onto the filled support a fluorine resin sheet consisting of a fluorine resin and a liquid foaming agent so that the outermost layers are the fluorine resin sheets, adhering them by applying a pressure of 30 to 30,000kg/cm 2 , and removing the foaming agent. Particle size of the powders may be 0.3 microns or less, but preferably 0.1 microns or less. Gold, silver, copper, platinum, nickel, monel metal, stainless steel, alumina and the like can be used with or without fluorine treatment. The powders are filled in the support by slip casting, rolling or electrophoresis. In one example, 100 parts by weight of polytetrafluoroethylene mixed with 50 parts of perfluoroalkane were compressed in a metallic die under a pressure of 25kg/cm 3 and were rolled to a thickness of 0.05m. A 250 mesh nickel wire filled with alumina particles having a diameter of 0.05 microns were compressed under 10 tons/cm 2 . The above sheets were laminated onto the nickel support on opposite surfaces, and thereafter pressed under a pressure of 100kg/cm 2 . The perfluoroalkane was removed. Argon isotope permeability of the product was 1.60 x 10 -5 mol/cm 2 .min.cmHg. The separation efficiency was 78%. (Iwakiri, K.)
Transient diffusion from a waste solid into fractured porous rock
International Nuclear Information System (INIS)
Ahn, J.; Chambre, P.L.; Pigford, T.H.
1988-01-01
Previous analytical studies of the advective transport of dissolved contaminants through fractured rock have emphasized the effect of molecular diffusion in the rock matrix in affecting the space-time-dependent concentration of the contaminant as it moves along the fracture. Matrix diffusion only in the direction normal to the fracture surface was assumed. Contaminant sources were constant-concentration surfaces of width equal to the fracture aperture and of finite or infinite extent in the transverse direction. Such studies illustrate the far-field transport features of fractured media. To predict the time-dependent mass transfer from a long waste cylinder surrounded by porous rock and intersected by a fracture, the present study includes diffusion from the waste surface directly into porous rock, as well as the more realistic geometry. Here the authors present numerical results from Chambre's analytical solution for the time-dependent mass transfer from the cylinder for the low-flow conditions wherein near-field mass transfer is expected to be controlled by molecular diffusion
Suitability of various materials for porous filters in diffusion experiments
Energy Technology Data Exchange (ETDEWEB)
Aldaba, David; Vidal, Miquel; Rigol, Anna [Univ. de Barcelona (Spain). Dept. de Quimica Analitica; Glaus, Martin; Van Loon, Luc [Paul Scherrer Institut, Villigen PSI (Switzerland). Lab. for Waste Management; Leupin, Olivier [Nagra, Wettingen (Switzerland)
2014-10-01
The suitability of different porous materials (stainless steel, VYCOR {sup registered} glass, Al{sub 2}O{sub 3} and PEEK) for use as confining filters in diffusion experiments was evaluated by measuring the effective diffusion coefficients (D{sub e}) of neutral (HTO) and ionic solutes (Na{sup +}, Cs{sup +}, Sr{sup 2+}, Cl{sup -}, SeO{sub 4}{sup 2-}) in the materials in through-diffusion experiments. For stainless steel filters, the D{sub e} values of the target solutes correlated satisfactorily with their bulk diffusion coefficient in water (D{sub w}); thus, the diffusion process in the stainless steel filters was primarily controlled by the diffusivity of the solvated ions. For the remaining materials, the D{sub e} and D{sub w} values were also correlated for the target solutes, and the geometric factors were in the sequence: VYCOR {sup registered} glass < Al{sub 2}O{sub 3} < PEEK. Stainless steel and VYCOR {sup registered} glass were the most appropriate materials because of their high D{sub e} values, but a specific interaction of caesium with VYCOR {sup registered} glass was hypothesised because the D{sub e} values obtained for this solute were slightly higher than expected.
Dynamics of Nano-Chain Diffusing in Porous Media
International Nuclear Information System (INIS)
Chen Jiang-Xing; Zheng Qiang; Huang Chun-Yun; Xu Jiang-Rong; Ying He-Ping
2015-01-01
A coarse-grained model is proposed to study the dynamics of a nano-chain diffusing in porous media. The simulation utilizes a hybrid method which combines stochastic rotation dynamics with molecular dynamics. Solvent molecules are explicitly taken into account to represent the hydrodynamic interactions and random fluctuations. The conformation, relaxation, and diffusion properties of a polymer chain are investigated by changing the density degree of the obstacle matrix. It is found that the average size of the chain is a nonmonotonic function of the obstacle volume fraction ϕ. A dense environment may contribute to extending a linear chain, which can be characterized by larger exponents in the corresponding power law. The relaxation behavior of a stretched chain to a steady state shows dramatic crossover from exponent to power-law relaxation when the values of φ are increased. The dependence of the diffusion coefficient on the chain size is also studied. Various kinds of scaling properties are presented and discussed. The results can give additional insight into the density effect of porous media on polymer structure and dynamics. (paper)
Liu, Yanfeng; Zhou, Xiaojun; Wang, Dengjia; Song, Cong; Liu, Jiaping
2015-12-15
Most building materials are porous media, and the internal diffusion coefficients of such materials have an important influences on the emission characteristics of volatile organic compounds (VOCs). The pore structure of porous building materials has a significant impact on the diffusion coefficient. However, the complex structural characteristics bring great difficulties to the model development. The existing prediction models of the diffusion coefficient are flawed and need to be improved. Using scanning electron microscope (SEM) observations and mercury intrusion porosimetry (MIP) tests of typical porous building materials, this study developed a new diffusivity model: the multistage series-connection fractal capillary-bundle (MSFC) model. The model considers the variable-diameter capillaries formed by macropores connected in series as the main mass transfer paths, and the diameter distribution of the capillary bundles obeys a fractal power law in the cross section. In addition, the tortuosity of the macrocapillary segments with different diameters is obtained by the fractal theory. Mesopores serve as the connections between the macrocapillary segments rather than as the main mass transfer paths. The theoretical results obtained using the MSFC model yielded a highly accurate prediction of the diffusion coefficients and were in a good agreement with the VOC concentration measurements in the environmental test chamber. Copyright © 2015 Elsevier B.V. All rights reserved.
Chaotic dynamics of large-scale double-diffusive convection in a porous medium
Kondo, Shutaro; Gotoda, Hiroshi; Miyano, Takaya; Tokuda, Isao T.
2018-02-01
We have studied chaotic dynamics of large-scale double-diffusive convection of a viscoelastic fluid in a porous medium from the viewpoint of dynamical systems theory. A fifth-order nonlinear dynamical system modeling the double-diffusive convection is theoretically obtained by incorporating the Darcy-Brinkman equation into transport equations through a physical dimensionless parameter representing porosity. We clearly show that the chaotic convective motion becomes much more complicated with increasing porosity. The degree of dynamic instability during chaotic convective motion is quantified by two important measures: the network entropy of the degree distribution in the horizontal visibility graph and the Kaplan-Yorke dimension in terms of Lyapunov exponents. We also present an interesting on-off intermittent phenomenon in the probability distribution of time intervals exhibiting nearly complete synchronization.
Differential constraints and exact solutions of nonlinear diffusion equations
International Nuclear Information System (INIS)
Kaptsov, Oleg V; Verevkin, Igor V
2003-01-01
The differential constraints are applied to obtain explicit solutions of nonlinear diffusion equations. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the determining equations used in the search for classical Lie symmetries
CROSS DIFFUSION AND NONLINEAR DIFFUSION PREVENTING BLOW UP IN THE KELLER–SEGEL MODEL
CARRILLO, JOSÉ ANTONIO; HITTMEIR, SABINE; JÜ NGEL, ANSGAR
2012-01-01
A parabolic-parabolic (Patlak-)Keller-Segel model in up to three space dimensions with nonlinear cell diffusion and an additional nonlinear cross-diffusion term is analyzed. The main feature of this model is that there exists a new entropy
Brem, Gerrit; Brouwers, J.J.H.
1990-01-01
In Part I, analytical solutions were given for the non-linear isothermal heterogeneous conversion of a porous solid particle. Account was taken of a reaction rate of general order with respect to the gas reactant, intrinsic reaction surface area and effective pore diffusion, which change with solid
Brem, G.; Brouwers, J.J.H.
1990-01-01
In Part I, analytical solutions were given for the non-linear isothermal heterogeneous conversion of a porous solid particle. Account was taken of a reaction rate of general order with respect to the gas reactant, intrinsic reaction surface area and effective pore diffusion, which change with solid
Directory of Open Access Journals (Sweden)
S. Srinivas
2016-01-01
Full Text Available The present work investigates the effects of thermal-diffusion and diffusion-thermo on MHD flow of viscous fluid between expanding or contracting rotating porous disks with viscous dissipation. The partial differential equations governing the flow problem under consideration have been transformed by a similarity transformation into a system of coupled nonlinear ordinary differential equations. An analytical approach, namely the homotopy analysis method is employed in order to obtain the solutions of the ordinary differential equations. The effects of various emerging parameters on flow variables have been discussed numerically and explained graphically. Comparison of the HAM solutions with the numerical solutions is performed.
Thermal convection and nonlinear effects of a superfluid 3He-4He mixture in a porous medium
International Nuclear Information System (INIS)
Chien, L.C.L.
1986-01-01
The convective instability of one-component classical fluids in a porous medium confined between two unbounded slabs was studied. This system behaves like a high Prandtl number bulk fluid. It has boundary conditions similar to the stress-free boundary conditions of bulk one-component classical fluids. Both the amplitude expansion method and the Galerkin method were used to investigate the nonlinear steady convection. Two dimensional rolls are the only stable motion at the onset of convection. Beyond threshold, the steady convection rolls become unstable to formation of cross-roll and zigzag instabilities. Applying the phase-dynamics approach for the zigzag instability, the author obtained the diffusion coefficient D, which can signal the onset of instability. Also investigated was the convective instability of superfluid 3 He- 4 He mixtures in porous media. Assuming no interaction between the average superflow and the porous medium and treating the normal flow in the equation of motion like a classical fluid in a porous medium, it was found that the superfluid mixtures in a porous medium. To investigate the effects of a lateral boundary, the convective instability of classical one-component fluids in porous media inside a box was studied. The zigzag instability does not exist because of the boundary conditions at the side of the box
Diffusion of organic pollutants within a biofilm in porous media
Fan, Chihhao; Kao, Chen-Fei; Liu, You-Hsi
2017-04-01
The occurrence of aquatic pollution is an inevitable environmental impact resulting from human civilization and societal advancement. Either from the natural or anthropogenic sources, the aqueous contaminants enter the natural environment and aggravate its quality. To assure the aquatic environment quality, the attached-growth biological degradation is often applied to removing organic contaminants by introducing contaminated water into a porous media which is covered by microorganism. Additionally, many natural aquatic systems also form such similar mechanism to increase their self-purification capability. To better understand this transport phenomenon and degradation mechanism in the biofilm for future application, the mathematic characterization of organic contaminant diffusion within the biofilm requires further exploration. The present study aimed to formulate a mathematic representation to quantify the diffusion of the organic contaminant in the biofilm. The BOD was selected as the target contaminant. A series of experiments were conducted to quantify the BOD diffusion in the biofilm under the conditions of influent BOD variation from 50 to 300 mg/L, COD:N:P ratios of 100:5:1 and 100:15:3, with or without auxiliary aeration. For diffusion coefficient calculation, the boundary condition of zero diffusion at the interface between microbial phase and contact media was assumed. With the principle of conservation of mass, the removed contaminants equal those that diffuse into the biofilm, and eq 1 results, and the diffusion coefficient (i.e., eq 2) can be solved through calculus with equations from table of integral. ∂2Sf- Df ∂z2 = Rf (1) --(QSin--QSout)2Y--- Df = 2μmaxxf(Sb + Ks ln-Ks-) Sb+Ks (2) Using the obtained experimental data, the diffusion coefficient was calculated to be 2.02*10-6 m2/d with influent COD of 50 mg/L at COD:N:P ratio of 100:5:1 with aeration, and this coefficient increased to 6.02*10-6 m2/d as the influent concentration increased to
Nonlinear throughflow and internal heating effects on vibrating porous medium
Directory of Open Access Journals (Sweden)
Palle Kiran
2016-06-01
Full Text Available The effect of vertical throughflow and internal heating effects on fluid saturated porous medium under gravity modulation is investigated. The amplitude of modulation is considered to be very small and the disturbances are expanded in terms of power series of amplitude of convection. A weakly nonlinear stability analysis is proposed to study stationary convection. The Nusselt number is obtained numerically to present the results of heat transfer while using Ginzburg–Landau equation. The vertical throughflow has dual effect either to destabilize or to stabilize the system for downward or upward directions. The effect of internal heat source (Ri>0 enhances or sink (Ri<0 diminishes heat transfer in the system. The amplitude and frequency of modulation have the effects of increasing or diminishing heat transport. For linear model Venezian approach suggested that throughflow and internal heating have both destabilizing and stabilizing effects for suitable ranges of Ω. Further, the study establishes that heat transport can be controlled effectively by a mechanism that is external to the system throughflow and gravity modulation.
Nonlinear Dynamics of a Diffusing Interface
Duval, Walter M. B.
2001-01-01
Excitation of two miscible-viscous liquids inside a bounded enclosure in a microgravity environment has shown the evolution of quasi-stationary waves of various modes for a range of parameters. We examine computationally the nonlinear dynamics of the system as the interface breakup and bifurcates to resonance structures typified by the Rayleigh-Taylor instability mechanism. Results show that when the mean steady field is much smaller than the amplitude of the sinusoidal excitation, the system behaves linearly, and growth of quasi-stationary waves occurs through the Kelvin-Helmholtz instability mechanism. However, as the amplitude of excitation increases, nonlinearity occurs through subharmonic bifurcation prior to broadband chaos.
Solution of linear and nonlinear matrix systems. Application to a nonlinear diffusion equation
International Nuclear Information System (INIS)
Bonnet, M.; Meurant, G.
1978-01-01
Different methods of solution of linear and nonlinear algebraic systems are applied to the nonlinear system obtained by discretizing a nonlinear diffusion equation. For linear systems, methods in general use of alternating directions type or Gauss Seidel's methods are compared to more recent ones of the type of generalized conjugate gradient; the superiority of the latter is shown by numerical examples. For nonlinear systems, a method on nonlinear conjugate gradient is studied as also Newton's method and some of its variants. It should be noted, however that Newton's method is found to be more efficient when coupled with a good method for solution of the linear system. To conclude, such methods are used to solve a nonlinear diffusion problem and the numerical results obtained are to be compared [fr
Solution of linear and nonlinear matrix systems. Application to a nonlinear diffusion equation
International Nuclear Information System (INIS)
Bonnet, M.; Meurant, G.
1978-01-01
The object of this study is to compare different methods of solving linear and nonlinear algebraic systems and to apply them to the nonlinear system obtained by discretizing a nonlinear diffusion equation. For linear systems the conventional methods of alternating direction type or Gauss Seidel's methods are compared to more recent ones of the type of generalized conjugate gradient; the superiority of the latter is shown by numerical examples. For nonlinear systems, a method of nonlinear conjugate gradient is studied together with Newton's method and some of its variants. It should be noted, however, that Newton's method is found to be more efficient when coupled with a good method for solving the linear system. As a conclusion, these methods are used to solve a nonlinear diffusion problem and the numerical results obtained are compared [fr
Intraparticle diffusion of rare earths in porous ion exchanger rounding by EDTA solution
International Nuclear Information System (INIS)
Ling Daren; Xie Weije
1991-01-01
The self-diffusion of rate earth (RE) isotopes in porous cation exchangers with various radii or different pore structures rounding by EDTA solution was studied. The intraparticle effective diffusivity De was calculated by Boyd's method and Kataoka's bi-disperse pore model, and through further calculation the solid phase diffusivity Dg and macropore diffusivity Dp were also obtained. (author)
Double-diffusive convection in a Darcy porous medium saturated with a couple-stress fluid
International Nuclear Information System (INIS)
Malashetty, M S; Kollur, Premila; Pal, Dulal
2010-01-01
The onset of double-diffusive convection in a couple-stress fluid-saturated horizontal porous layer is studied using linear and weak nonlinear stability analyses. The modified Darcy equation that includes the time derivative term and the inertia term is used to model the momentum equation. The expressions for stationary, oscillatory and finite-amplitude Rayleigh number are obtained as a function of the governing parameters. The effect of couple-stress parameter, solute Rayleigh number, Vadasz number and diffusivity ratio on stationary, oscillatory and finite-amplitude convection is shown graphically. It is found that the couple-stress parameter and the solute Rayleigh number have a stabilizing effect on stationary, oscillatory and finite-amplitude convection. The diffusivity ratio has a destabilizing effect in the case of stationary and finite-amplitude modes, with a dual effect in the case of oscillatory convection. The Vadasz number advances the onset of oscillatory convection. The heat and mass transfer decreases with an increase in the values of couple-stress parameter and diffusivity ratio, while both increase with an increase in the value of the solute Rayleigh number.
Nonlinear hydromagnetic Rayleigh-Taylor instability for strong viscous fluids in porous media
El-Dib, Y O
2003-01-01
In the present work a weakly nonlinear stability for magnetic fluid is discussed. The research of an interface between two strong viscous homogeneous incompressible fluids through porous medium is investigated theoretically and graphically. The effect of the vertical magnetic field has been demonstrated in this study. The linear form of equation of motion is solved in the light of the nonlinear boundary conditions. The boundary value problem leads to construct nonlinear characteristic equation having complex coefficients in elevation function. The nonlinearity is kept to third-order expansion. The nonlinear characteristic equation leads to derive the well-known nonlinear Schroedinger equation. This equation having complex coefficients of the disturbance amplitude varies in both space and time. Stability criteria have been performed for nonlinear Chanderasekhar dispersion relation including the porous effects. Stability conditions are discussed through the assumption of equal kinematic viscosity. The calculati...
Pattern formation due to non-linear vortex diffusion
Wijngaarden, Rinke J.; Surdeanu, R.; Huijbregtse, J. M.; Rector, J. H.; Dam, B.; Einfeld, J.; Wördenweber, R.; Griessen, R.
Penetration of magnetic flux in YBa 2Cu 3O 7 superconducting thin films in an external magnetic field is visualized using a magneto-optic technique. A variety of flux patterns due to non-linear vortex diffusion is observed: (1) Roughening of the flux front with scaling exponents identical to those observed in burning paper including two distinct regimes where respectively spatial disorder and temporal disorder dominate. In the latter regime Kardar-Parisi-Zhang behavior is found. (2) Fractal penetration of flux with Hausdorff dimension depending on the critical current anisotropy. (3) Penetration as ‘flux-rivers’. (4) The occurrence of commensurate and incommensurate channels in films with anti-dots as predicted in numerical simulations by Reichhardt, Olson and Nori. It is shown that most of the observed behavior is related to the non-linear diffusion of vortices by comparison with simulations of the non-linear diffusion equation appropriate for vortices.
Evans functions and bifurcations of nonlinear waves of some nonlinear reaction diffusion equations
Zhang, Linghai
2017-10-01
The main purposes of this paper are to accomplish the existence, stability, instability and bifurcation of the nonlinear waves of the nonlinear system of reaction diffusion equations ut =uxx + α [ βH (u - θ) - u ] - w, wt = ε (u - γw) and to establish the existence, stability, instability and bifurcation of the nonlinear waves of the nonlinear scalar reaction diffusion equation ut =uxx + α [ βH (u - θ) - u ], under different conditions on the model constants. To establish the bifurcation for the system, we will study the existence and instability of a standing pulse solution if 0 1; the existence and instability of two standing wave fronts if 2 (1 + αγ) θ = αβγ and 0 traveling wave front as well as the existence and instability of a standing pulse solution if 0 traveling wave front as well as the existence and instability of an upside down standing pulse solution if 0 traveling wave back of the nonlinear scalar reaction diffusion equation ut =uxx + α [ βH (u - θ) - u ] -w0, where w0 = α (β - 2 θ) > 0 is a positive constant, if 0 motivation to study the existence, stability, instability and bifurcations of the nonlinear waves is to study the existence and stability/instability of infinitely many fast/slow multiple traveling pulse solutions of the nonlinear system of reaction diffusion equations. The existence and stability of infinitely many fast multiple traveling pulse solutions are of great interests in mathematical neuroscience.
Diffusion and reaction within porous packing media: a phenomenological model.
Jones, W L; Dockery, J D; Vogel, C R; Sturman, P J
1993-04-25
A phenomenological model has been developed to describe biomass distribution and substrate depletion in porous diatomaceous earth (DE) pellets colonized by Pseudomonas aeruginosa. The essential features of the model are diffusion, attachment and detachment to/from pore walls of the biomass, diffusion of substrate within the pellet, and external mass transfer of both substrate and biomass in the bulk fluid of a packed bed containing the pellets. A bench-scale reactor filled with DE pellets was inoculated with P. aeruginosa and operated in plug flow without recycle using a feed containing glucose as the limiting nutrient. Steady-state effluent glucose concentrations were measured at various residence times, and biomass distribution within the pellet was measured at the lowest residence time. In the model, microorganism/substrate kinetics and mass transfer characteristics were predicted from the literature. Only the attachment and detachment parameters were treated as unknowns, and were determined by fitting biomass distribution data within the pellets to the mathematical model. The rate-limiting step in substrate conversion was determined to be internal mass transfer resistance; external mass transfer resistance and microbial kinetic limitations were found to be nearly negligible. Only the outer 5% of the pellets contributed to substrate conversion.
Coupled diffusion systems with localized nonlinear reactions
DEFF Research Database (Denmark)
Pedersen, M.; Lin, Zhigui
2001-01-01
This paper deals with the blowup rate and profile near the blowup time for the system of diffusion equations uit - Î´ui = ui+1Pi(x0, t), (i = 1,...,k, uk+1 := uu) in Î© Ã— (0, T) with boundary conditions ui = 0 on âˆ‚Î© Ã— [0, T). We show that the solution has a global blowup. The exact rate...
Exact solutions of some coupled nonlinear diffusion-reaction ...
Indian Academy of Sciences (India)
certain coupled diffusion-reaction (D-R) equations of very general nature. In recent years, various direct methods have been proposed to find the exact solu- tions not only of nonlinear partial differential equations but also of their coupled versions. These methods include unified ansatz approach [3], extended hyperbolic func ...
Exact solutions of certain nonlinear chemotaxis diffusion reaction ...
Indian Academy of Sciences (India)
constructed coupled differential equations. The results obtained ... Nonlinear diffusion reaction equation; chemotaxis; auxiliary equation method; solitary wave solutions. ..... fact limits the scope of applications of the derived results. ... Research Fellowship and AP acknowledges DU and DST for PURSE grant for financial.
Nonlinear dynamics of capacitive charging and desalination by porous electrodes
Biesheuvel, P.M.; Bazant, M.Z.
2010-01-01
The rapid and efficient exchange of ions between porous electrodes and aqueous solutions is important in many applications, such as electrical energy storage by supercapacitors, water desalination and purification by capacitive deionization, and capacitive extraction of renewable energy from a
CROSS DIFFUSION AND NONLINEAR DIFFUSION PREVENTING BLOW UP IN THE KELLER–SEGEL MODEL
CARRILLO, JOSÉ ANTONIO
2012-12-01
A parabolic-parabolic (Patlak-)Keller-Segel model in up to three space dimensions with nonlinear cell diffusion and an additional nonlinear cross-diffusion term is analyzed. The main feature of this model is that there exists a new entropy functional, yielding gradient estimates for the cell density and chemical concentration. For arbitrarily small cross-diffusion coefficients and for suitable exponents of the nonlinear diffusion terms, the global-in-time existence of weak solutions is proved, thus preventing finite-time blow up of the cell density. The global existence result also holds for linear and fast diffusion of the cell density in a certain parameter range in three dimensions. Furthermore, we show L∞ bounds for the solutions to the parabolic-elliptic system. Sufficient conditions leading to the asymptotic stability of the constant steady state are given for a particular choice of the nonlinear diffusion exponents. Numerical experiments in two and three space dimensions illustrate the theoretical results. © 2012 World Scientific Publishing Company.
FITTING OF THE DATA FOR DIFFUSION COEFFICIENTS IN UNSATURATED POROUS MEDIA
Energy Technology Data Exchange (ETDEWEB)
B. Bullard
1999-05-01
The purpose of this calculation is to evaluate diffusion coefficients in unsaturated porous media for use in the TSPA-VA analyses. Using experimental data, regression techniques were used to curve fit the diffusion coefficient in unsaturated porous media as a function of volumetric water content. This calculation substantiates the model fit used in Total System Performance Assessment-1995 An Evaluation of the Potential Yucca Mountain Repository (TSPA-1995), Section 6.5.4.
FITTING OF THE DATA FOR DIFFUSION COEFFICIENTS IN UNSATURATED POROUS MEDIA
International Nuclear Information System (INIS)
B. Bullard
1999-01-01
The purpose of this calculation is to evaluate diffusion coefficients in unsaturated porous media for use in the TSPA-VA analyses. Using experimental data, regression techniques were used to curve fit the diffusion coefficient in unsaturated porous media as a function of volumetric water content. This calculation substantiates the model fit used in Total System Performance Assessment-1995 An Evaluation of the Potential Yucca Mountain Repository (TSPA-1995), Section 6.5.4
Effective diffusion coefficients of /sup 3/H/sub 2/O in several porous materials
Energy Technology Data Exchange (ETDEWEB)
Terashima, Y [Kyoto Univ. (Japan). Faculty of Engineering; Kumaki, T
1976-12-01
Diffusion coefficients of radionuclides in some porous structural materials and porous components of earth stratum are important as the basis for the safety evaluation of the storage and disposal of radioactive wastes. In our previous works, the method of analysis and experiment using a permeative type diffusion cell for measurement of effective diffusion coefficient was established, and experimental results were reported. In this paper, effective diffusion coefficients of /sup 3/H/sub 2/O in mortar, concrete, brick, clay layer, and sand layer were measured, and characteristics of these pore structure were discussed on the basis of tourtusity factor.
Effective diffusion coefficients of 3H2O in several porous materials
International Nuclear Information System (INIS)
Terashima, Yutaka; Kumaki, Toru.
1976-01-01
Diffusion coefficients of radionuclides in some porous structural materials and porous components of earth stratum are important as the basis for the safety evaluation of the storage and disposal of radioactive wastes. In our previous works, the method of analysis and experiment using a permeative type diffusion cell for measurement of effective diffusion coefficient was established, and experimental results were reported. In this paper, effective diffusion coefficients of 3 H 2 O in mortar, concrete, brick, clay layer, and sand layer were measured, and characteristics of these pore structure were discussed on the basis of tourtusity factor. (auth.)
Nonlinear simulation of electromagnetic current diffusive interchange mode turbulence
International Nuclear Information System (INIS)
Yagi, M.; Itoh, S.I.; Fukuyama, A.
1998-01-01
The anomalous transport in toroidal plasmas has been investigated extensively. It is pointed out that the nonlinear instability is important in driving the microturbulence[1], i.e., the self-sustained plasma turbulence. This concept is explained as follows; when the electron motion along the magnetic field line is resisted by the background turbulence, it gives rise to the effective resistivity and enhances the level of the turbulence. The nonlinear simulation of the electrostatic current diffusive interchange mode (CDIM) in the two dimensional sheared slab geometry has been performed as an example. The occurrence of the nonlinear instability and the self-sustainment of the plasma turbulence were confirmed by this simulation[2]. On the other hand, the electromagnetic turbulence is sustained in the high pressure limit. The possibility of the self-organization with more variety has been pointed out[3]. It is important to study the electromagnetic turbulence based on the nonlinear simulation. In this paper, the model equation for the electrostatic CDIM turbulence[2] is extended for both electrostatic and electromagnetic turbulence. (1) Not only E x B convective nonlinearity but also the electromagnetic nonlinearity which is related to the parallel flow are incorporated into the model equation. (2) The electron and ion pressure evolution equations are solved separately, making it possible to distinguish the electron and ion thermal diffusivities. The two dimensional nonlinear simulation of the electromagnetic CDIM is performed based on the extended fluid model. This paper is organized as follows. The model equation is explained in section II. The result of simulation is shown in section III. The conclusion and discussion are given in section IV. (author)
Some notes on experiments measuring diffusion of sorbed nuclides through porous media
International Nuclear Information System (INIS)
Lever, D.A.
1986-11-01
Various experimental techniques for measuring the important parameters governing diffusion of sorbed nuclides through water-saturated porous media are described, and the particular parameters obtained from each technique are discussed. Recent experiments in which diffusive transport takes place more rapidly than expected are reviewed. The author recommends that through-transport diffusion experiments are the most satisfactory method of determining whether this arises from surface diffusion of sorbed nuclides. (author)
Anomalous Transport of Cosmic Rays in a Nonlinear Diffusion Model
Energy Technology Data Exchange (ETDEWEB)
Litvinenko, Yuri E. [Department of Mathematics, University of Waikato, P. B. 3105, Hamilton 3240 (New Zealand); Fichtner, Horst; Walter, Dominik [Institut für Theoretische Physik IV, Ruhr-Universität Bochum, Universitätsstrasse 150, D-44780 Bochum (Germany)
2017-05-20
We investigate analytically and numerically the transport of cosmic rays following their escape from a shock or another localized acceleration site. Observed cosmic-ray distributions in the vicinity of heliospheric and astrophysical shocks imply that anomalous, superdiffusive transport plays a role in the evolution of the energetic particles. Several authors have quantitatively described the anomalous diffusion scalings, implied by the data, by solutions of a formal transport equation with fractional derivatives. Yet the physical basis of the fractional diffusion model remains uncertain. We explore an alternative model of the cosmic-ray transport: a nonlinear diffusion equation that follows from a self-consistent treatment of the resonantly interacting cosmic-ray particles and their self-generated turbulence. The nonlinear model naturally leads to superdiffusive scalings. In the presence of convection, the model yields a power-law dependence of the particle density on the distance upstream of the shock. Although the results do not refute the use of a fractional advection–diffusion equation, they indicate a viable alternative to explain the anomalous diffusion scalings of cosmic-ray particles.
Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations
International Nuclear Information System (INIS)
Indekeu, Joseph O; Smets, Ruben
2017-01-01
Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically. (paper)
Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations
Indekeu, Joseph O.; Smets, Ruben
2017-08-01
Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically.
Murthy, P.V.S.N.
2011-12-26
Thermo-diffusion effect on free convection heat and mass transfer from a vertical surface embedded in a liquid saturated thermally stratified non - Darcy porous medium has been analyzed using a local non-similar procedure. The wall temperature and concentration are constant and the medium is linearly stratified in the vertical direction with respect to the thermal conditions. The fluid flow, temperature and concentration fields are affected by the complex interactions among the diffusion ratio Le, buoyancy ratio N, thermo-diffusion parameter Sr and stratification parameter ?. Non-linear interactions of all these parameters on the convective transport has been analyzed and variation of heat and mass transfer coefficients with thermo-diffusion parameter in the thermally stratified non-Darcy porous media is presented through computer generated plots.
Murthy, P.V.S.N.; El-Amin, Mohamed
2011-01-01
Thermo-diffusion effect on free convection heat and mass transfer from a vertical surface embedded in a liquid saturated thermally stratified non - Darcy porous medium has been analyzed using a local non-similar procedure. The wall temperature and concentration are constant and the medium is linearly stratified in the vertical direction with respect to the thermal conditions. The fluid flow, temperature and concentration fields are affected by the complex interactions among the diffusion ratio Le, buoyancy ratio N, thermo-diffusion parameter Sr and stratification parameter ?. Non-linear interactions of all these parameters on the convective transport has been analyzed and variation of heat and mass transfer coefficients with thermo-diffusion parameter in the thermally stratified non-Darcy porous media is presented through computer generated plots.
Diffuse charge and Faradaic reactions in porous electrodes
Biesheuvel, P.M.; Yu, F.; Bazant, M.Z.
2011-01-01
Porous electrodes instead of flat electrodes are widely used in electrochemical systems to boost storage capacities for ions and electrons, to improve the transport of mass and charge, and to enhance reaction rates. Existing porous electrode theories make a number of simplifying assumptions: (i) The
New variable separation approach: application to nonlinear diffusion equations
International Nuclear Information System (INIS)
Zhang Shunli; Lou, S Y; Qu Changzheng
2003-01-01
The concept of the derivative-dependent functional separable solution (DDFSS), as a generalization to the functional separable solution, is proposed. As an application, it is used to discuss the generalized nonlinear diffusion equations based on the generalized conditional symmetry approach. As a consequence, a complete list of canonical forms for such equations which admit the DDFSS is obtained and some exact solutions to the resulting equations are described
Nonlocal Symmetries to Systems of Nonlinear Diffusion Equations
International Nuclear Information System (INIS)
Qu Changzheng; Kang Jing
2008-01-01
In this paper, we study potential symmetries to certain systems of nonlinear diffusion equations. Those systems have physical applications in soil science, mathematical biology, and invariant curve flows in R 3 . Lie point symmetries of the potential system, which cannot be projected to vector fields of the given dependent and independent variables, yield potential symmetries. The class of the system that admits potential symmetries is expanded.
Super Nonlinear Electrodeposition-Diffusion-Controlled Thin-Film Selector.
Ji, Xinglong; Song, Li; He, Wei; Huang, Kejie; Yan, Zhiyuan; Zhong, Shuai; Zhang, Yishu; Zhao, Rong
2018-03-28
Selector elements with high nonlinearity are an indispensable part in constructing high density, large-scale, 3D stackable emerging nonvolatile memory and neuromorphic network. Although significant efforts have been devoted to developing novel thin-film selectors, it remains a great challenge in achieving good switching performance in the selectors to satisfy the stringent electrical criteria of diverse memory elements. In this work, we utilized high-defect-density chalcogenide glass (Ge 2 Sb 2 Te 5 ) in conjunction with high mobility Ag element (Ag-GST) to achieve a super nonlinear selective switching. A novel electrodeposition-diffusion dynamic selector based on Ag-GST exhibits superior selecting performance including excellent nonlinearity (<5 mV/dev), ultra-low leakage (<10 fA), and bidirectional operation. With the solid microstructure evidence and dynamic analyses, we attributed the selective switching to the competition between the electrodeposition and diffusion of Ag atoms in the glassy GST matrix under electric field. A switching model is proposed, and the in-depth understanding of the selective switching mechanism offers an insight of switching dynamics for the electrodeposition-diffusion-controlled thin-film selector. This work opens a new direction of selector designs by combining high mobility elements and high-defect-density chalcogenide glasses, which can be extended to other materials with similar properties.
Multi-diffusive nonlinear Fokker–Planck equation
International Nuclear Information System (INIS)
Ribeiro, Mauricio S; Casas, Gabriela A; Nobre, Fernando D
2017-01-01
Nonlinear Fokker–Planck equations, characterized by more than one diffusion term, have appeared recently in literature. Here, it is shown that these equations may be derived either from approximations in a master equation, or from a Langevin-type approach. An H-theorem is proven, relating these Fokker–Planck equations to an entropy composed by a sum of contributions, each of them associated with a given diffusion term. Moreover, the stationary state of the Fokker–Planck equation is shown to coincide with the equilibrium state, obtained by extremization of the entropy, in the sense that both procedures yield precisely the same equation. Due to the nonlinear character of this equation, the equilibrium probability may be obtained, in most cases, only by means of numerical approaches. Some examples are worked out, where the equilibrium probability distribution is computed for nonlinear Fokker–Planck equations presenting two diffusion terms, corresponding to an entropy characterized by a sum of two contributions. It is shown that the resulting equilibrium distribution, in general, presents a form that differs from a sum of the equilibrium distributions that maximizes each entropic contribution separately, although in some cases one may construct such a linear combination as a good approximation for the equilibrium distribution. (paper)
Nonlinear theory of diffusive acceleration of particles by shock waves
Energy Technology Data Exchange (ETDEWEB)
Malkov, M.A. [University of California at San Diego, La Jolla, CA (United States)]. E-mail: mmalkov@ucsd.edu; Drury, L. O' C. [Dublin Institute for Advanced Studies, 5 Merrion Square, Dublin 2 (Ireland)
2001-04-01
Among the various acceleration mechanisms which have been suggested as responsible for the nonthermal particle spectra and associated radiation observed in many astrophysical and space physics environments, diffusive shock acceleration appears to be the most successful. We review the current theoretical understanding of this process, from the basic ideas of how a shock energizes a few reactionless particles to the advanced nonlinear approaches treating the shock and accelerated particles as a symbiotic self-organizing system. By means of direct solution of the nonlinear problem we set the limit to the test-particle approximation and demonstrate the fundamental role of nonlinearity in shocks of astrophysical size and lifetime. We study the bifurcation of this system, proceeding from the hydrodynamic to kinetic description under a realistic condition of Bohm diffusivity. We emphasize the importance of collective plasma phenomena for the global flow structure and acceleration efficiency by considering the injection process, an initial stage of acceleration and, the related aspects of the physics of collisionless shocks. We calculate the injection rate for different shock parameters and different species. This, together with differential acceleration resulting from nonlinear large-scale modification, determines the chemical composition of accelerated particles. The review concentrates on theoretical and analytical aspects but our strategic goal is to link the fundamental theoretical ideas with the rapidly growing wealth of observational data. (author)
Belyaev, V. P.; Mishchenko, S. V.; Belyaev, P. S.
2018-01-01
Ensuring non-destructive testing of products in industry is an urgent task. Most of the modern methods for determining the diffusion coefficient in porous materials have been developed for bodies of a given configuration and size. This leads to the need for finished products destruction to make experimental samples from them. The purpose of this study is the development of a dynamic method that allows operatively determine the diffusion coefficient in finished products from porous materials without destroying them. The method is designed to investigate the solvents diffusion coefficient in building constructions from materials having a porous structure: brick, concrete and aerated concrete, gypsum, cement, gypsum or silicate solutions, gas silicate blocks, heat insulators, etc. A mathematical model of the method is constructed. The influence of the design and measuring device operating parameters on the method accuracy is studied. The application results of the developed method for structural porous products are presented.
Analysis of boundary layer flow over a porous nonlinearly stretching sheet with partial slip at
Directory of Open Access Journals (Sweden)
Swati Mukhopadhyay
2013-12-01
Full Text Available The boundary layer flow of a viscous incompressible fluid toward a porous nonlinearly stretching sheet is considered in this analysis. Velocity slip is considered instead of no-slip condition at the boundary. Similarity transformations are used to convert the partial differential equation corresponding to the momentum equation into nonlinear ordinary differential equation. Numerical solution of this equation is obtained by shooting method. It is found that the horizontal velocity decreases with increasing slip parameter.
Thermal diffusion in nanostructured porous InP
International Nuclear Information System (INIS)
Srinivasan, R.; Ramachandran, K.
2008-01-01
Nanostructured porous InP samples were prepared by electrochemical anodic dissolution of InP for various current densities and etching periods. The samples were characterized by SEM and photoluminescence (PL) where a blue shift was observed in PL. Thermal properties studies by photoacoustic (PA) spectroscopy revealed one order decrease in thermal conductivity of porous InP compared to the bulk. Further it is shown that the thermal conductivity of porous InP decreases with decrease in size of the particles. (author)
Large time behaviour of oscillatory nonlinear solute transport in porous media
Duijn, van C.J.; Zee, van der S.E.A.T.M.
2018-01-01
Oscillations in flow occur under many different situations in natural porous media, due to tidal, daily or seasonal patterns. In this paper, we investigate how such oscillations in flow affect the transport of an initially sharp solute front, if the solute undergoes nonlinear sorption and,
The effect of Coriolis force on nonlinear convection in a porous medium
Directory of Open Access Journals (Sweden)
D. H. Riahi
1994-01-01
Full Text Available Nonlinear convection in a porous medium and rotating about vertical axis is studied in this paper. An upper bound to the heat flux is calculated by the method initiated first by Howard [6] for the case of infinite Prandtl number.
Numerical analyses on the effect of capillary condensation on gas diffusivities in porous media
Yoshimoto, Yuta; Hori, Takuma; Kinefuchi, Ikuya; Takagi, Shu
2017-11-01
We investigate the effect of capillary condensation on gas diffusivities in porous media composed of randomly packed spheres with moderate wettability. Lattice density functional theory simulations successfully reproduce realistic adsorption/desorption isotherms and provide fluid density distributions inside the porous media. We find that capillary condensations lead to the occlusion of narrow pores because they preferentially occur at confined spaces surrounded by the solid walls. Consequently, the characteristic lengths of the partially wet structures are larger than those of the corresponding dry structures with the same porosities. Subsequent gas diffusion simulations exploiting the mean-square displacement method indicate that while effective diffusion coefficients significantly decrease in the presence of partially condensed liquids, they are larger than those in the dry structures with the same porosities. Most importantly, we find that the porosity-to-tortuosity ratio, which is a crucial parameter that determines the effective diffusion coefficient, can be reasonably related to the porosity even for the partially wet porous media.
DEFF Research Database (Denmark)
Johannesson, Björn
2009-01-01
Results from a systematic continuum mixture theory will be used to establish the governing equations for ionic diffusion and chemical reactions in the pore solution of a porous material subjected to moisture transport. The theory in use is the hybrid mixture theory (HMT), which in its general form......’s law of diffusion and the generalized Darcy’s law will be used together with derived constitutive equations for chemical reactions within phases. The mass balance equations for the constituents and the phases together with the constitutive equations gives the coupled set of non-linear differential...... general description of chemical reactions among constituents is described. The Petrov – Galerkin approach are used in favour of the standard Galerkin weighting in order to improve the solution when the convective part of the problem is dominant. A modified type of Newton – Raphson scheme is derived...
Fast and Accurate Poisson Denoising With Trainable Nonlinear Diffusion.
Feng, Wensen; Qiao, Peng; Chen, Yunjin; Wensen Feng; Peng Qiao; Yunjin Chen; Feng, Wensen; Chen, Yunjin; Qiao, Peng
2018-06-01
The degradation of the acquired signal by Poisson noise is a common problem for various imaging applications, such as medical imaging, night vision, and microscopy. Up to now, many state-of-the-art Poisson denoising techniques mainly concentrate on achieving utmost performance, with little consideration for the computation efficiency. Therefore, in this paper we aim to propose an efficient Poisson denoising model with both high computational efficiency and recovery quality. To this end, we exploit the newly developed trainable nonlinear reaction diffusion (TNRD) model which has proven an extremely fast image restoration approach with performance surpassing recent state-of-the-arts. However, the straightforward direct gradient descent employed in the original TNRD-based denoising task is not applicable in this paper. To solve this problem, we resort to the proximal gradient descent method. We retrain the model parameters, including the linear filters and influence functions by taking into account the Poisson noise statistics, and end up with a well-trained nonlinear diffusion model specialized for Poisson denoising. The trained model provides strongly competitive results against state-of-the-art approaches, meanwhile bearing the properties of simple structure and high efficiency. Furthermore, our proposed model comes along with an additional advantage, that the diffusion process is well-suited for parallel computation on graphics processing units (GPUs). For images of size , our GPU implementation takes less than 0.1 s to produce state-of-the-art Poisson denoising performance.
Thermal diffusion of water vapour in porous materials: fact or fiction?
DEFF Research Database (Denmark)
Janssen, Hans
2011-01-01
diffusion. Thermal diffusion opponents, on the other hand, assert that these thermal transports are negligibly small. This paper resolves that contradiction. A critical analysis of the investigations supporting the occurrence of thermal diffusion reveals that all are flawed. A correct reinterpretation...... its negligible magnitude. It can in conclusion be stated that thermal diffusion is of no importance for building science applications, leaving vapour pressure as the sole significant transport potential for the diffusion of water vapour in porous materials. (C) 2010 Elsevier Ltd. All rights reserved....
Directory of Open Access Journals (Sweden)
M. Farooq
Full Text Available This research article investigates the squeezing flow of Newtonian fluid with variable viscosity over a stretchable sheet inserted in Darcy porous medium. Cattaneo-Christov double diffusion models are implemented to scrutinize the characteristics of heat and mass transfer via variable thermal conductivity and variable mass diffusivity. These models are the modification of conventional laws of Fourier’s and Fick’s via thermal and solutal relaxation times respectively. The homotopy analysis Method (HAM is being utilized to provide the solution of highly nonlinear system of coupled partial differential equations after converted into dimensionless governing equations. The behavior of flow parameters on velocity, concentration, and temperature distributions are sketched and analyzed physically. The result indicates that both concentration and temperature distributions decay for higher solutal and thermal relaxation parameters respectively. Keywords: Squeezing flow, Porous medium, Variable viscosity, Cattaneo-Christov heat and mass flux models, Variable thermal conductivity, Variable mass diffusivity
Numerical solution of non-linear diffusion problems
International Nuclear Information System (INIS)
Carmen, A. del; Ferreri, J.C.
1998-01-01
This paper presents a method for the numerical solution of non-linear diffusion problems using finite-differences in moving grids. Due to the presence of steep fronts in the solution domain and to the presence of advective terms originating in the grid movement, an implicit TVD scheme, first order in time and second order in space has been developed. Some algebraic details of the derivation are given. Results are shown for the pure advection of a scalar as a test case and an example dealing with the slow spreading of viscous fluids over plane surfaces. The agreement between numerical and analytical solutions is excellent. (author). 8 refs., 3 figs
Thermal diffusion in nanostructured porous InP
Indian Academy of Sciences (India)
Nanostructured porous InP samples were prepared by electrochemical anodic dissolution of InP for various current densities and etching periods. The samples were characterized by SEM and photoluminescence (PL) where a blue shift was observed in PL. Thermal properties studied by photoacoustic (PA) spectroscopy ...
Energy Technology Data Exchange (ETDEWEB)
Bennacer, R. [Neuville sur Oise, LEEVAM 5 mail Gay Lussac, Cergy-Pontoise Cedex (France); Mohamad, A.A. [CEERE University of Calgary, Department of Mechanical and Manufacturing Engineering, Calgary, Alberta (Canada); Ganaoui, M.El [Faculte des Sciences et Techniques de Limoges, Limoges (France)
2005-02-01
Double-diffusive natural convection within a multilayer anisotropic porous medium is studied numerically and analytically. The domain composed of two horizontal porous layers is subjected to a uniform horizontal heat flux and a vertical mass flux, where only the lower one is thermally anisotropic. Darcy model with classical Boussinesq approximation is used in formulating the mathematical model. The effect of thermal anisotropy and the relative width of the two layers on the flow and transfers is illustrated with characterising the transitions from the diffusive to the convective solution. Results were well compared with respect to a developed analytical approach, based on a parallel flow approximation for thermally anisotropic multilayer media. (orig.)
Moderately nonlinear diffuse-charge dynamics under an ac voltage.
Stout, Robert F; Khair, Aditya S
2015-09-01
The response of a symmetric binary electrolyte between two parallel, blocking electrodes to a moderate amplitude ac voltage is quantified. The diffuse charge dynamics are modeled via the Poisson-Nernst-Planck equations for a dilute solution of point-like ions. The solution to these equations is expressed as a Fourier series with a voltage perturbation expansion for arbitrary Debye layer thickness and ac frequency. Here, the perturbation expansion in voltage proceeds in powers of V_{o}/(k_{B}T/e), where V_{o} is the amplitude of the driving voltage and k_{B}T/e is the thermal voltage with k_{B} as Boltzmann's constant, T as the temperature, and e as the fundamental charge. We show that the response of the electrolyte remains essentially linear in voltage amplitude at frequencies greater than the RC frequency of Debye layer charging, D/λ_{D}L, where D is the ion diffusivity, λ_{D} is the Debye layer thickness, and L is half the cell width. In contrast, nonlinear response is predicted at frequencies below the RC frequency. We find that the ion densities exhibit symmetric deviations from the (uniform) equilibrium density at even orders of the voltage amplitude. This leads to the voltage dependence of the current in the external circuit arising from the odd orders of voltage. For instance, the first nonlinear contribution to the current is O(V_{o}^{3}) which contains the expected third harmonic but also a component oscillating at the applied frequency. We use this to compute a generalized impedance for moderate voltages, the first nonlinear contribution to which is quadratic in V_{o}. This contribution predicts a decrease in the imaginary part of the impedance at low frequency, which is due to the increase in Debye layer capacitance with increasing V_{o}. In contrast, the real part of the impedance increases at low frequency, due to adsorption of neutral salt from the bulk to the Debye layer.
Moderately nonlinear diffuse-charge dynamics under an ac voltage
Stout, Robert F.; Khair, Aditya S.
2015-09-01
The response of a symmetric binary electrolyte between two parallel, blocking electrodes to a moderate amplitude ac voltage is quantified. The diffuse charge dynamics are modeled via the Poisson-Nernst-Planck equations for a dilute solution of point-like ions. The solution to these equations is expressed as a Fourier series with a voltage perturbation expansion for arbitrary Debye layer thickness and ac frequency. Here, the perturbation expansion in voltage proceeds in powers of Vo/(kBT /e ) , where Vo is the amplitude of the driving voltage and kBT /e is the thermal voltage with kB as Boltzmann's constant, T as the temperature, and e as the fundamental charge. We show that the response of the electrolyte remains essentially linear in voltage amplitude at frequencies greater than the RC frequency of Debye layer charging, D /λDL , where D is the ion diffusivity, λD is the Debye layer thickness, and L is half the cell width. In contrast, nonlinear response is predicted at frequencies below the RC frequency. We find that the ion densities exhibit symmetric deviations from the (uniform) equilibrium density at even orders of the voltage amplitude. This leads to the voltage dependence of the current in the external circuit arising from the odd orders of voltage. For instance, the first nonlinear contribution to the current is O (Vo3) which contains the expected third harmonic but also a component oscillating at the applied frequency. We use this to compute a generalized impedance for moderate voltages, the first nonlinear contribution to which is quadratic in Vo. This contribution predicts a decrease in the imaginary part of the impedance at low frequency, which is due to the increase in Debye layer capacitance with increasing Vo. In contrast, the real part of the impedance increases at low frequency, due to adsorption of neutral salt from the bulk to the Debye layer.
Peppin, Stephen S. L.
2009-01-01
concentrations they form a nearly rigid porous glass through which the fluid permeates. The theoretically determined pressure drop is nonlinear in the diffusion regime and linear in the permeation regime, in quantitative agreement with experimental measurements
Preisach hysteresis model for non-linear 2D heat diffusion
International Nuclear Information System (INIS)
Jancskar, Ildiko; Ivanyi, Amalia
2006-01-01
This paper analyzes a non-linear heat diffusion process when the thermal diffusivity behaviour is a hysteretic function of the temperature. Modelling this temperature dependence, the discrete Preisach algorithm as general hysteresis model has been integrated into a non-linear multigrid solver. The hysteretic diffusion shows a heating-cooling asymmetry in character. The presented type of hysteresis speeds up the thermal processes in the modelled systems by a very interesting non-linear way
Katherine McCulloh; John S. Sperry; Barbara Lachenbruch; Frederick D. Meinzer; Peter B. Reich; Steven Voelker
2010-01-01
Coniferous, diffuse-porous and ring-porous trees vary in their xylem anatomy, but the functional consequences of these differences are not well understood from the scale of the conduit to the individual. Hydraulic and anatomical measurements were made on branches and trunks from 16 species from temperate and tropical areas, representing all three wood types. Scaling of...
Impact of local diffusion on macroscopic dispersion in three-dimensional porous media
Dartois, Arthur; Beaudoin, Anthony; Huberson, Serge
2018-02-01
While macroscopic longitudinal and transverse dispersion in three-dimensional porous media has been simulated previously mostly under purely advective conditions, the impact of diffusion on macroscopic dispersion in 3D remains an open question. Furthermore, both in 2D and 3D, recurring difficulties have been encountered due to computer limitation or analytical approximation. In this work, we use the Lagrangian velocity covariance function and the temporal derivative of second-order moments to study the influence of diffusion on dispersion in highly heterogeneous 2D and 3D porous media. The first approach characterizes the correlation between the values of Eulerian velocity components sampled by particles undergoing diffusion at two times. The second approach allows the estimation of dispersion coefficients and the analysis of their behaviours as functions of diffusion. These two approaches allowed us to reach new results. The influence of diffusion on dispersion seems to be globally similar between highly heterogeneous 2D and 3D porous media. Diffusion induces a decrease in the dispersion in the direction parallel to the flow direction and an increase in the dispersion in the direction perpendicular to the flow direction. However, the amplification of these two effects with the permeability variance is clearly different between 2D and 3D. For the direction parallel to the flow direction, the amplification is more important in 3D than in 2D. It is reversed in the direction perpendicular to the flow direction.
International Nuclear Information System (INIS)
Ferreri, J. C.; Carmen, A. del
1998-01-01
A numerical study of the dynamics of pattern evolution in reaction-diffusion systems is performed, although limited to one spatial dimension. The diffusion coefficients are nonlinear, based on powers of the scalar variables. The system keeps the dynamics of previous studies in the literature, but the presence of nonlinear diffusion generates a field of strong nonlinear interactions due to the presence of receding travelling waves. This field is limited by the plane of symmetry of the space domain and the last born outgoing travelling wave. These effects are discussed. (author). 10 refs., 7 figs
Global-local nonlinear model reduction for flows in heterogeneous porous media
AlOtaibi, Manal; Calo, Victor M.; Efendiev, Yalchin R.; Galvis, Juan; Ghommem, Mehdi
2015-01-01
In this paper, we combine discrete empirical interpolation techniques, global mode decomposition methods, and local multiscale methods, such as the Generalized Multiscale Finite Element Method (GMsFEM), to reduce the computational complexity associated with nonlinear flows in highly-heterogeneous porous media. To solve the nonlinear governing equations, we employ the GMsFEM to represent the solution on a coarse grid with multiscale basis functions and apply proper orthogonal decomposition on a coarse grid. Computing the GMsFEM solution involves calculating the residual and the Jacobian on a fine grid. As such, we use local and global empirical interpolation concepts to circumvent performing these computations on the fine grid. The resulting reduced-order approach significantly reduces the flow problem size while accurately capturing the behavior of fully-resolved solutions. We consider several numerical examples of nonlinear multiscale partial differential equations that are numerically integrated using fully-implicit time marching schemes to demonstrate the capability of the proposed model reduction approach to speed up simulations of nonlinear flows in high-contrast porous media.
Global-local nonlinear model reduction for flows in heterogeneous porous media
AlOtaibi, Manal
2015-08-01
In this paper, we combine discrete empirical interpolation techniques, global mode decomposition methods, and local multiscale methods, such as the Generalized Multiscale Finite Element Method (GMsFEM), to reduce the computational complexity associated with nonlinear flows in highly-heterogeneous porous media. To solve the nonlinear governing equations, we employ the GMsFEM to represent the solution on a coarse grid with multiscale basis functions and apply proper orthogonal decomposition on a coarse grid. Computing the GMsFEM solution involves calculating the residual and the Jacobian on a fine grid. As such, we use local and global empirical interpolation concepts to circumvent performing these computations on the fine grid. The resulting reduced-order approach significantly reduces the flow problem size while accurately capturing the behavior of fully-resolved solutions. We consider several numerical examples of nonlinear multiscale partial differential equations that are numerically integrated using fully-implicit time marching schemes to demonstrate the capability of the proposed model reduction approach to speed up simulations of nonlinear flows in high-contrast porous media.
Study of porous bed diffusion using the frequency response method
International Nuclear Information System (INIS)
Billy, J.
1967-11-01
The flow of an inert mixture of two gases across a catalytic bed is accompanied by diffusion phenomena in the inter-particulate space and inside the particles themselves, and adsorption phenomena at the surface of the particles. These phenomena are analyzed in turn and three coefficients which characterize each of them are defined. With a view to carrying out an experimental study by the frequency response method, the differential system deduced from the preceding analysis is then resolved with the help of two simplifying hypotheses; two relationships are given which make it possible to calculate the two diffusion coefficients and the absorption coefficient. (author) [fr
Markowich, Peter
2010-06-01
We study the system ct + u · ∇c = ∇c -nf(c) nt + u · ∇n = ∇n m - ∇ · (n×(c) ∇c) ut + u·∇u + ∇P - η∇u + n∇φ/ = 0 ∇·u = 0. arising in the modelling of the motion of swimming bacteria under the effect of diffusion, oxygen-taxis and transport through an incompressible fluid. The novelty with respect to previous papers in the literature lies in the presence of nonlinear porous-medium-like diffusion in the equation for the density n of the bacteria, motivated by a finite size effect. We prove that, under the constraint m ε (3/2, 2] for the adiabatic exponent, such system features global in time solutions in two space dimensions for large data. Moreover, in the case m = 2 we prove that solutions converge to constant states in the large-time limit. The proofs rely on standard energy methods and on a basic entropy estimate which cannot be achieved in the case m = 1. The case m = 2 is very special as we can provide a Lyapounov functional. We generalize our results to the three-dimensional case and obtain a smaller range of exponents m ε (m*, 2] with m* > 3/2, due to the use of classical Sobolev inequalities.
Robust and fast nonlinear optimization of diffusion MRI microstructure models.
Harms, R L; Fritz, F J; Tobisch, A; Goebel, R; Roebroeck, A
2017-07-15
Advances in biophysical multi-compartment modeling for diffusion MRI (dMRI) have gained popularity because of greater specificity than DTI in relating the dMRI signal to underlying cellular microstructure. A large range of these diffusion microstructure models have been developed and each of the popular models comes with its own, often different, optimization algorithm, noise model and initialization strategy to estimate its parameter maps. Since data fit, accuracy and precision is hard to verify, this creates additional challenges to comparability and generalization of results from diffusion microstructure models. In addition, non-linear optimization is computationally expensive leading to very long run times, which can be prohibitive in large group or population studies. In this technical note we investigate the performance of several optimization algorithms and initialization strategies over a few of the most popular diffusion microstructure models, including NODDI and CHARMED. We evaluate whether a single well performing optimization approach exists that could be applied to many models and would equate both run time and fit aspects. All models, algorithms and strategies were implemented on the Graphics Processing Unit (GPU) to remove run time constraints, with which we achieve whole brain dataset fits in seconds to minutes. We then evaluated fit, accuracy, precision and run time for different models of differing complexity against three common optimization algorithms and three parameter initialization strategies. Variability of the achieved quality of fit in actual data was evaluated on ten subjects of each of two population studies with a different acquisition protocol. We find that optimization algorithms and multi-step optimization approaches have a considerable influence on performance and stability over subjects and over acquisition protocols. The gradient-free Powell conjugate-direction algorithm was found to outperform other common algorithms in terms of
Diffusion and saponification inside porous cellulose triacetate fibers.
Braun, Jennifer L; Kadla, John F
2005-01-01
Cellulose triacetate (CTA) fibers were partially hydrolyzed in 0.054 N solutions of NaOH/H(2)O and NaOMe/MeOH. The surface concentration of acetyl groups was determined using ATR-FTIR. Total acetyl content was determined by the alkaline hydrolysis method. Fiber cross-sections were stained with Congo red in order to examine the interface between reacted and unreacted material; these data were used to estimate the rate constant k and effective diffusivity D(B) for each reagent during the early stages of reaction by means of a volume-based unreacted core model. For NaOH/H(2)O, k = 0.37 L mol(-1) min(-1) and D(B) = 6.2 x 10(-7) cm(2)/sec; for NaOMe/MeOH, k = 4.0 L mol(-1) min(-1) and D(B) = 5.7 x 10(-6) cm(2)/sec. The NaOMe/MeOH reaction has a larger rate constant due to solvent effects and the greater nucleophilicity of MeO(-) as compared to OH(-); the reaction has a larger effective diffusivity because CTA swells more in MeOH than it does in water. Similarities between calculated concentration profiles for each case indicate that the relatively diffuse interface seen in fibers from the NaOMe/MeOH reaction results from factors not considered in the model; shrinkage of stained fiber cross-sections suggests that increased disruption of intermolecular forces may be the cause.
Non-linear diffusion and pattern formation in vortex matter
Wijngaarden, Rinke J.; Surdeanu, R.; Huijbregtse, J. M.; Rector, J. H.; Dam, B.; Griessen, R.; Einfeld, J.; Woerdenweber, R.
2000-03-01
Penetration of magnetic flux in YBa_2Cu_3O7 superconducting thin films and crystals in externally applied magnetic fields is visualized with a magneto-optical technique. A variety of flux patterns due to non-linear vortex behavior is observed: 1. Roughening of the flux front^1 with scaling exponents identical to those observed in burning paper^2. Two regimes are found where respectively spatial disorder and temporal disorder dominate. In the latter regime Kardar-Parisi-Zhang behavior is found. 2. Roughening of the flux profile similar to the Oslo model for rice-piles. 3. Fractal penetration of flux^3 with Hausdorff dimension depending on the critical current anisotropy. 4. Penetration as 'flux-rivers'. 5. The occurrence of commensurate and incommensurate channels in films with anti-dots as predicted in numerical simulations by Reichhardt, Olson and Nori^4. By comparison with numerical simulations, it is shown that most of the observed behavior can be explained in terms of non-linear diffusion of vortices. ^1R. Surdeanu, R.J. Wijngaarden, E. Visser, J.M. Huijbregtse, J.H. Rector, B. Dam and R. Griessen, Phys.Rev. Lett. 83 (1999) 2054 ^2J. Maunuksela, M. Myllys, O.-P. Kähkönen, J. Timonen, N. Provatas, M.J. Alava, T. Ala-Nissila, Phys. Rev. Lett. 79, 1515 (1997) ^3R. Surdeanu, R.J. Wijngaarden, B. Dam, J. Rector, R. Griessen, C. Rossel, Z.F. Ren and J.H. Wang, Phys Rev B 58 (1998) 12467 ^4C. Reichhardt, C.J. Olson and F. Nori, Phys. Rev. B 58, 6534 (1998)
A coupled deformation-diffusion theory for fluid-saturated porous solids
Henann, David; Kamrin, Ken; Anand, Lallit
2012-02-01
Fluid-saturated porous materials are important in several familiar applications, such as the response of soils in geomechanics, food processing, pharmaceuticals, and the biomechanics of living bone tissue. An appropriate constitutive theory describing the coupling of the mechanical behavior of the porous solid with the transport of the fluid is a crucial ingredient towards understanding the material behavior in these varied applications. In this work, we formulate and numerically implement in a finite-element framework a large-deformation theory for coupled deformation-diffusion in isotropic, fluid-saturated porous solids. The theory synthesizes the classical Biot theory of linear poroelasticity and the more-recent Coussy theory of poroplasticity in a large deformation framework. In this talk, we highlight several salient features of our theory and discuss representative examples of the application of our numerical simulation capability to problems of consolidation as well as deformation localization in granular materials.
Directory of Open Access Journals (Sweden)
R Mehdaoui
2016-09-01
Full Text Available Two-dimensional, double diffusion, natural convection in a partially porous cavity satured with a binary fluid is investigated numerically. Multiple motions are driven by the external temperature and concentration differences imposed across vertical walls. The wavy interface between fluid and porous layer is horizontal. The equations which describe the fluid flow and heat and mass transfer are described by the Navier-Stokes equations (fluid region, Darcy-Brinkman equation (porous region and energy and mass equations. The finite element method was applied to solve the governing equations. The fluid flow and heat and mass transfer has been investigated for different values of the amplitude and the wave number of the interface and the buoyancy ratio. The results obtained in the form of isotherms, stream lines, isoconcentrations and the Nusselt and Sherwood numbers; show that the wavy interface has a significant effect on the flow and heat and mass transfer.
Retention and effective diffusion of model metabolites on porous graphitic carbon.
Lunn, Daniel B; Yun, Young J; Jorgenson, James W
2017-12-29
The study of metabolites in biological samples is of high interest for a wide range of biological and pharmaceutical applications. Reversed phase liquid chromatography is a common technique used for the separation of metabolites, but it provides little retention for polar metabolites. An alternative to C18 bonded phases, porous graphitic carbon has the ability to provide significant retention for both non-polar and polar analytes. The goal of this work is to study the retention and effective diffusion properties of porous graphitic carbon, to see if it is suitable for the wide injection bands and long run times associated with long, packed capillary-scale separations. The retention of a set of standard metabolites was studied for both stationary phases over a wide range of mobile phase conditions. This data showed that porous graphitic carbon benefits from significantly increased retention (often >100 fold) under initial gradient conditions for these metabolites, suggesting much improved ability to focus a wide injection band at the column inlet. The effective diffusion properties of these columns were studied using peak-parking experiments with the standard metabolites under a wide range of retention conditions. Under the high retention conditions, which can be associated with retention after injection loading for gradient separations, D eff /D m ∼0.1 for both the C18-bonded and porous graphitic carbon columns. As C18 bonded particles are widely, and successfully utilized for long gradient separations without issue of increasing peak width from longitudinal diffusion, this suggests that porous graphitic carbon should be amenable for long runtime gradient separations as well. Copyright © 2017 Elsevier B.V. All rights reserved.
Liu, Ping; Shi, Junping
2018-01-01
The bifurcation of non-trivial steady state solutions of a scalar reaction-diffusion equation with nonlinear boundary conditions is considered using several new abstract bifurcation theorems. The existence and stability of positive steady state solutions are proved using a unified approach. The general results are applied to a Laplace equation with nonlinear boundary condition and bistable nonlinearity, and an elliptic equation with superlinear nonlinearity and sublinear boundary conditions.
Martelloni, Gianluca; Bagnoli, Franco
2016-04-01
Richardson's treatise on turbulent diffusion in 1926 [24] and today, the list of system displaying anomalous dynamical behavior is quite extensive. We only report some examples: charge carrier transport in amorphous semiconductors [25], porous systems [26], reptation dynamics in polymeric systems [27, 28], transport on fractal geometries [29], the long-time dynamics of DNA sequences [30]. In this scenario, the fractional calculus is used to generalized the Fokker-Planck linear equation -∂P (x,t)=D ∇2P (x,t), ∂t (3) where P (x,t) is the density of probability in the space x=[x1, x2, x3] and time t, while D >0 is the diffusion coefficient. Such processes are characterized by Eq. (1). An example of Eq. (3) generalization is ∂∂tP (x,t)=D∇ αP β(x,t) - ∞ - 1 , (4) where the fractional based-derivatives Laplacian Σ(∂α/∂xα)i, (i = 1, 2, 3), of non-linear term Pβ(x,t) is taken into account [31]. Another generalized form is represented by equation ∂∂tδδP(x,t)=D ∇ αP(x,t) δ > 0 α ≤ 2 , (5) that considers also the fractional time-derivative [32]. These fractional-described processes exhibit a power law patters as expressed by Eq. (2). This general introduction introduces the presented work, whose aim is to develop a theoretical model in order to forecast the triggering and propagation of landslides, using the techniques of fractional calculus. The latter is suitable for modeling the water infiltration (i.e., the pore water pressure diffusion in the soil) and the dynamical processes in the fractal media [33]. Alternatively the fractal representation of temporal and spatial derivative (the fractal order only appears in the denominator of the derivative) is considered and the results are compared to the fractional one. The prediction of landslides and the discovering of the triggering mechanism, is one of the challenging problems in earth science. Landslides can be triggered by different factors but in most cases the trigger is an intense or long rain
On the integrability of the generalized Fisher-type nonlinear diffusion equations
International Nuclear Information System (INIS)
Wang Dengshan; Zhang Zhifei
2009-01-01
In this paper, the geometric integrability and Lax integrability of the generalized Fisher-type nonlinear diffusion equations with modified diffusion in (1+1) and (2+1) dimensions are studied by the pseudo-spherical surface geometry method and prolongation technique. It is shown that the (1+1)-dimensional Fisher-type nonlinear diffusion equation is geometrically integrable in the sense of describing a pseudo-spherical surface of constant curvature -1 only for m = 2, and the generalized Fisher-type nonlinear diffusion equations in (1+1) and (2+1) dimensions are Lax integrable only for m = 2. This paper extends the results in Bindu et al 2001 (J. Phys. A: Math. Gen. 34 L689) and further provides the integrability information of (1+1)- and (2+1)-dimensional Fisher-type nonlinear diffusion equations for m = 2
Monte Carlo simulation of nonlinear reactive contaminant transport in unsaturated porous media
International Nuclear Information System (INIS)
Giacobbo, F.; Patelli, E.
2007-01-01
In the current proposed solutions of radioactive waste repositories, the protective function against the radionuclide water-driven transport back to the biosphere is to be provided by an integrated system of engineered and natural geologic barriers. The occurrence of several nonlinear interactions during the radionuclide migration process may render burdensome the classical analytical-numerical approaches. Moreover, the heterogeneity of the barriers' media forces approximations to the classical analytical-numerical models, thus reducing their fidelity to reality. In an attempt to overcome these difficulties, in the present paper we adopt a Monte Carlo simulation approach, previously developed on the basis of the Kolmogorov-Dmitriev theory of branching stochastic processes. The approach is here extended for describing transport through unsaturated porous media under transient flow conditions and in presence of nonlinear interchange phenomena between the liquid and solid phases. This generalization entails the determination of the functional dependence of the parameters of the proposed transport model from the water content and from the contaminant concentration, which change in space and time during the water infiltration process. The corresponding Monte Carlo simulation approach is verified with respect to a case of nonreactive transport under transient unsaturated flow and to a case of nonlinear reactive transport under stationary saturated flow. Numerical applications regarding linear and nonlinear reactive transport under transient unsaturated flow are reported
Diffusion processes in unsaturated porous media studied with nuclear magnetic resonance techniques
International Nuclear Information System (INIS)
Farrher, German David
2006-01-01
Unsaturated porous media form two-phase systems consisting of the liquid and its vapor. Molecular exchange between the two phases defines an effective diffusion coefficient which substantially deviates from the bulk value of the liquid. The objective of the present thesis is to study self-diffusion under such conditions by varying both the filling degree of the porous medium and the diffusion time. The main experimental tool was a combination of two different NMR field gradient diffusometry techniques. For comparison, diffusion in a porous medium was modeled with the aid of Monte Carlo simulations. The NMR diffusometry techniques under consideration were the pulsed gradient stimulated echo (PGStE) method, the fringe field stimulated echo (FFStE) method, and the magnetization grid rotating frame imaging (MAGROFI) method. As liquids, water and cyclohexane were chosen as representatives of polar and nonpolar species. The porous glasses examined were Vycor with a mean pore size of 4 nm and VitraPor 5, with a pore size ranging from 1 to 1.6 μm. Using a combination of the FFStE and the MAGROFI technique permits one to cover four decades of the diffusion time from 100 μs to 1 s. The time dependences acquired in this way were compared with Monte Carlo simulations of a model structure in a time window of eight decades, from 125 ps up to 12.5 ms. NMR microscopy of VitraPor5 partially filled with water or cyclohexane reveals heterogeneous distributions of the liquid on a length scale much longer than the pore dimension. As a consequence of the inhomogeneous filling degree, the effective transverse relaxation time varies, which in turn leads to NMR imaging contrasts. The NMR methods employed, that is, a combination of FFStE and MAGROFI diffusometry, provide effective diffusion coefficients not affected by spatial variations of the transverse relaxation time, in contrast to the PGStE method: The FFStE and MAGROFI techniques render the effective diffusion coefficient averaged
Frank, T. D.
2008-02-01
We discuss two central claims made in the study by Bassler et al. [K.E. Bassler, G.H. Gunaratne, J.L. McCauley, Physica A 369 (2006) 343]. Bassler et al. claimed that Green functions and Langevin equations cannot be defined for nonlinear diffusion equations. In addition, they claimed that nonlinear diffusion equations are linear partial differential equations disguised as nonlinear ones. We review bottom-up and top-down approaches that have been used in the literature to derive Green functions for nonlinear diffusion equations and, in doing so, show that the first claim needs to be revised. We show that the second claim as well needs to be revised. To this end, we point out similarities and differences between non-autonomous linear Fokker-Planck equations and autonomous nonlinear Fokker-Planck equations. In this context, we raise the question whether Bassler et al.’s approach to financial markets is physically plausible because it necessitates the introduction of external traders and causes. Such external entities can easily be eliminated when taking self-organization principles and concepts of nonextensive thermostatistics into account and modeling financial processes by means of nonlinear Fokker-Planck equations.
Asymptotic behaviour of a nonlinear model for the geographic diffusion of infections diseases
International Nuclear Information System (INIS)
Kirane, M.; Kouachi, S.
1994-01-01
In this paper a nonlinear diffusion model for the geographical spread of infective diseases is studied. In addition to proving well-posedness of the associated initial-boundary value problem, the large time behaviour is analyzed. (author). 4 refs
Immiscible three-dimensional fingering in porous media: A weakly nonlinear analysis
Brandão, Rodolfo; Dias, Eduardo O.; Miranda, José A.
2018-03-01
We present a weakly nonlinear theory for the development of fingering instabilities that arise at the interface between two immiscible viscous fluids flowing radially outward in a uniform three-dimensional (3D) porous medium. By employing a perturbative second-order mode-coupling scheme, we investigate the linear stability of the system as well as the emergence of intrinsically nonlinear finger branching events in this 3D environment. At the linear stage, we find several differences between the 3D radial fingering and its 2D counterpart (usual Saffman-Taylor flow in radial Hele-Shaw cells). These include the algebraic growth of disturbances and the existence of regions of absolute stability for finite values of viscosity contrast and capillary number in the 3D system. On the nonlinear level, our main focus is to get analytical insight into the physical mechanism resulting in the occurrence of finger tip-splitting phenomena. In this context, we show that the underlying mechanism leading to 3D tip splitting relies on the coupling between the fundamental interface modes and their first harmonics. However, we find that in three dimensions, in contrast to the usual 2D fingering structures normally encountered in radial Hele-Shaw flows, tip splitting into three branches can also be observed.
In situ bioremediation: A network model of diffusion and flow in granular porous media
Energy Technology Data Exchange (ETDEWEB)
Griffiths, S.K.; Nilson, R.H.; Bradshaw, R.W.
1997-04-01
In situ bioremediation is a potentially expedient, permanent and cost- effective means of waste site decontamination. However, permeability reductions due to the transport and deposition of native fines or due to excessive microorganism populations may severely inhibit the injection of supplemental oxygen in the contamination zone. To help understand this phenomenon, we have developed a micro-mechanical network model of flow, diffusion and particle transport in granular porous materials. The model differs from most similar models in that the network is defined by particle positions in a numerically-generated particle array. The model is thus widely applicable to computing effective transport properties for both ordered and realistic random porous media. A laboratory-scale apparatus to measure permeability reductions has also been designed, built and tested.
Speciation of copper diffused in a bi-porous molecular sieve
International Nuclear Information System (INIS)
Huang, C.-H.; Paul Wang, H.; Wei, Y.-L.; Chang, J.-E.
2010-01-01
To better understand diffusion of copper in the micro- and mesopores, speciation of copper in a bi-porous molecular sieve (BPMS) possessing inter-connecting 3-D micropores (0.50-0.55 nm) and 2-D mesopores (4.1 nm) has been studied by X-ray absorption near edge structure (XANES) spectroscopy. It is found that about 77% (16% of CuO nanoparticles and 61% of CuO clusters) and 23% (CuO ads ) of copper can be diffused into the meso- and micropores, respectively, in the BPMS. At least two diffusion steps in the BPMS may be involved: (i) free diffusion of copper in the mesopores and (ii) diffusion-controlled copper migrating into the micropores of the BPMS. The XANES data also indicate that diffusion rate of copper in the BPMS (4.68x10 -5 g/s) is greater than that in the ZSM-5 (1.11x10 -6 g/s) or MCM-41 (1.17x10 -5 g/s).
Energy Technology Data Exchange (ETDEWEB)
Galinsky, M.; Breitkopf, C. [Technische Univ. Dresden (Germany). Inst. fuer Energietechnik
2011-07-01
Sulfated zirconias have attracted an interest as catalysts due to their ability to isomerize alkanes at low temperatures, e.g., under thermodynamically favored conditions. However, the fast deactivation during the reaction remains a problem. To improve the catalytic performance of such porous catalysts, it is necessary to understand all steps in the catalytic cycle, namely diffusion and adsorption in more detail. The transient TAP method was applied to investigate sorption and diffusion phenomena of different alkanes in three different morphologically structured sulfated zirconias to elucidate their catalytic performances in the n-butane isomerization. New theoretical models were developed to describe the experimental results of TAP single-pulse experiments. The application of these models to pulse response curves allowed the extraction of adsorption and desorption rate constants as well as diffusion coefficients. Via introducing a second sorption center, the new adsorption model is able to reproduce the sorption behavior for larger alkanes quantitatively better than former models, especially in the low-temperature region. Moreover, the heterogeneous distribution of active centers was taken into account. Temperature dependent measurements have been performed to calculate heats of adsorption for various alkanes at the two assumed adsorption sites. The impact of these values on the catalytic properties is discussed. With the help of the new diffusion model, the diffusion coefficients for the inter- and intrapellet volume could be determined. These values are used in a numerical simulation to check whether the reaction rate for the isomerization at the investigated sulfated zirconias is diffusion limited. (orig.)
Speciation of copper diffused in a bi-porous molecular sieve
Huang, C.-H.; Paul Wang, H.; Wei, Y.-L.; Chang, J.-E.
2010-07-01
To better understand diffusion of copper in the micro- and mesopores, speciation of copper in a bi-porous molecular sieve (BPMS) possessing inter-connecting 3-D micropores (0.50-0.55 nm) and 2-D mesopores (4.1 nm) has been studied by X-ray absorption near edge structure (XANES) spectroscopy. It is found that about 77% (16% of CuO nanoparticles and 61% of CuO clusters) and 23% (CuO ads) of copper can be diffused into the meso- and micropores, respectively, in the BPMS. At least two diffusion steps in the BPMS may be involved: (i) free diffusion of copper in the mesopores and (ii) diffusion-controlled copper migrating into the micropores of the BPMS. The XANES data also indicate that diffusion rate of copper in the BPMS (4.68×10 -5 g/s) is greater than that in the ZSM-5 (1.11×10 -6 g/s) or MCM-41 (1.17×10 -5 g/s).
DEFF Research Database (Denmark)
Zhelezny, Petr; Shapiro, Alexander
2006-01-01
The present work describes a new experimental method that makes it possible to investigate diffusion coefficients in a porous medium. The method is based on application of X-ray computed tomography (CT). The general applicability of this method for the determination of diffusion coefficients...
Hedin, Niklas; DeMartin, Gregory J.; Reyes, Sebastián C.
2006-03-01
In studies of gas diffusion in porous solids with nuclear magnetic resonance (NMR) spectroscopy the sample preparation procedure becomes very important. An apparatus is presented here that pretreats the sample ex situ and accurately sets the desired pressure and temperature within the NMR tube prior to its introduction in the spectrometer. The gas manifold that supplies the NMR tube is also connected to a microbalance containing another portion of the same sample, which is kept at the same temperature as the sample in the NMR tube. This arrangement permits the simultaneous measurement of the adsorption loading on the sample, which is required for the interpretation of the NMR diffusion experiments. Furthermore, to ensure a good seal of the NMR tube, a hybrid valve design composed of titanium, a Teflon® seat, and Kalrez® O-rings is utilized. A computer controlled algorithm ensures the accuracy and reproducibility of all the procedures, enabling the NMR diffusion experiments to be performed at well controlled conditions of pressure, temperature, and amount of gas adsorbed on the porous sample.
International Nuclear Information System (INIS)
Wen, Zijuan; Fu, Shengmao
2016-01-01
This paper deals with a strongly coupled reaction-diffusion system modeling a competitor-competitor-mutualist three-species model with diffusion, self-diffusion and nonlinear cross-diffusion and subject to Neumann boundary conditions. First, we establish the persistence of a corresponding reaction-diffusion system without self- and cross-diffusion. Second, the global asymptotic stability of the unique positive equilibrium for weakly coupled PDE system is established by using a comparison method. Moreover, under certain conditions about the intra- and inter-species effects, we prove that the uniform positive steady state is linearly unstable for the cross-diffusion system when one of the cross-diffusions is large enough. The results indicate that Turing instability can be driven solely from strong diffusion effect of the first species (or the second species or the third species) due to the pressure of the second species (or the first species).
Directory of Open Access Journals (Sweden)
Md. Nur Alam
2016-06-01
Full Text Available In this article, we apply the exp(-Φ(ξ-expansion method to construct many families of exact solutions of nonlinear evolution equations (NLEEs via the nonlinear diffusive predator–prey system and the Bogoyavlenskii equations. These equations can be transformed to nonlinear ordinary differential equations. As a result, some new exact solutions are obtained through the hyperbolic function, the trigonometric function, the exponential functions and the rational forms. If the parameters take specific values, then the solitary waves are derived from the traveling waves. Also, we draw 2D and 3D graphics of exact solutions for the special diffusive predator–prey system and the Bogoyavlenskii equations by the help of programming language Maple.
An approximate method for nonlinear diffusion applied to enzyme inactivation during drying
Liou, J.K.
1982-01-01
An approximate model was developed for nonlinear diffusion with a power-function variation of the diffusion coefficient with concentration. This model may serve for the computation of desorption times and concentration profiles in non-shrinking or shrinking slabs, cylinders or spheres, under
Nonlinear diffusion in the presence of a time-dependent external electric field
International Nuclear Information System (INIS)
Lima e Silva, T. de; Galvao, R.M.O.
1987-09-01
The influence of a time-dependent external electric field on the nonlinear diffusion process of weakly ionized plasmas is investigated. A new solution of the diffusion equation is obtained for the case when electron-ion collisions can be neglected. (author) [pt
Polyanin, A. D.; Sorokin, V. G.
2017-12-01
The paper deals with nonlinear reaction-diffusion equations with one or several delays. We formulate theorems that allow constructing exact solutions for some classes of these equations, which depend on several arbitrary functions. Examples of application of these theorems for obtaining new exact solutions in elementary functions are provided. We state basic principles of construction, selection, and use of test problems for nonlinear partial differential equations with delay. Some test problems which can be suitable for estimating accuracy of approximate analytical and numerical methods of solving reaction-diffusion equations with delay are presented. Some examples of numerical solutions of nonlinear test problems with delay are considered.
The nonlinear interaction of convection modes in a box of a saturated porous medium
Florio, Brendan J.; Bassom, Andrew P.; Fowkes, Neville; Judd, Kevin; Stemler, Thomas
2015-05-01
A plethora of convection modes may occur within a confined box of porous medium when the associated dimensionless Rayleigh number R is above some critical value dependent on the geometry. In many cases the crucial Rayleigh number Rc for onset is different for each mode, and in practice the mode with the lowest associated Rc is likely to be the dominant one. For particular sizes of box, however, it is possible for multiple modes (typically three) to share a common Rc. For box shapes close to these special geometries the modes interact and compete nonlinearly near the onset of convection. Here this mechanism is explored and it is shown that generically the dynamics of the competition takes on one of two possible structures. A specific example of each is described, while the general properties of the system enables us to compare our results with some previous calculations for particular box dimensions.
Simulations of fluid flow through porous media based on cellular automata and non-linear dynamics
Energy Technology Data Exchange (ETDEWEB)
Paulson, K V
1992-05-15
A study is being carried out to apply cellular automata and non-linear dynamics in the construction of efficient and accurate computer simulations of multiphase fluid flow through porous media, with the objective of application to reservoir modelling for hydrocarbon recovery. An algorithm based on Boolean operations has been developed which transforms a PC clone into a highly efficient vector processor capable of cellular automata simulation of single fluid flow through two-dimensional rock matrix models of varying porosities. Macroscopic flow patterns have been established through spatial and temporal averaging with no floating point operations. Permeabilities of the different models have been calculated. Hardware allows the algorithm to function on dual processors on a PC platform using a video recording and editing facility. Very encouraging results have been obtained. 4 figs.
Malkyarenko, Dariya I; Chenevert, Thomas L
2014-12-01
To describe an efficient procedure to empirically characterize gradient nonlinearity and correct for the corresponding apparent diffusion coefficient (ADC) bias on a clinical magnetic resonance imaging (MRI) scanner. Spatial nonlinearity scalars for individual gradient coils along superior and right directions were estimated via diffusion measurements of an isotropicic e-water phantom. Digital nonlinearity model from an independent scanner, described in the literature, was rescaled by system-specific scalars to approximate 3D bias correction maps. Correction efficacy was assessed by comparison to unbiased ADC values measured at isocenter. Empirically estimated nonlinearity scalars were confirmed by geometric distortion measurements of a regular grid phantom. The applied nonlinearity correction for arbitrarily oriented diffusion gradients reduced ADC bias from 20% down to 2% at clinically relevant offsets both for isotropic and anisotropic media. Identical performance was achieved using either corrected diffusion-weighted imaging (DWI) intensities or corrected b-values for each direction in brain and ice-water. Direction-average trace image correction was adequate only for isotropic medium. Empiric scalar adjustment of an independent gradient nonlinearity model adequately described DWI bias for a clinical scanner. Observed efficiency of implemented ADC bias correction quantitatively agreed with previous theoretical predictions and numerical simulations. The described procedure provides an independent benchmark for nonlinearity bias correction of clinical MRI scanners.
Theory and simulation of time-fractional fluid diffusion in porous media
International Nuclear Information System (INIS)
Carcione, José M; Sanchez-Sesma, Francisco J; Gavilán, Juan J Perez; Luzón, Francisco
2013-01-01
We simulate a fluid flow in inhomogeneous anisotropic porous media using a time-fractional diffusion equation and the staggered Fourier pseudospectral method to compute the spatial derivatives. A fractional derivative of the order of 0 < ν < 2 replaces the first-order time derivative in the classical diffusion equation. It implies a time-dependent permeability tensor having a power-law time dependence, which describes memory effects and accounts for anomalous diffusion. We provide a complete analysis of the physics based on plane waves. The concepts of phase, group and energy velocities are analyzed to describe the location of the diffusion front, and the attenuation and quality factors are obtained to quantify the amplitude decay. We also obtain the frequency-domain Green function. The time derivative is computed with the Grünwald–Letnikov summation, which is a finite-difference generalization of the standard finite-difference operator to derivatives of fractional order. The results match the analytical solution obtained from the Green function. An example of the pressure field generated by a fluid injection in a heterogeneous sandstone illustrates the performance of the algorithm for different values of ν. The calculation requires storing the whole pressure field in the computer memory since anomalous diffusion ‘recalls the past’. (paper)
Kluijtmans, Sebastiaan G. J. M.; de Hoog, Els H. A.; Philipse, Albert P.
1998-05-01
The influence of charge on diffusion in porous media was studied for fluorescent colloidal silica spheres diffusing in a porous glass medium. The bicontinuous porous silica glasses were optically matched with an organic solvent mixture in which both glass and tracers are negatively charged. Using fluorescence recovery after photobleaching, the long-time self-diffusion coefficient DSL of the confined silica particles was monitored in situ as a function of the ionic strength and particle to pore size ratio. At high salt concentration DSL reaches a relatively high plateau value, which depends on the particle to pore size ratio. This plateau value is unexpectedly higher than the value found for uncharged silica spheres in these porous glasses, but still significantly smaller than the free particle bulk diffusion coefficient of the silica spheres. At low salt concentration DSL reduces markedly, up to the point where colloids are nearly immobilized. This peculiar retardation probably originates from potential traps and barriers at pore intersections due to deviations from cylinder symmetry in the double layer interactions between tracers and pore walls. This indicates that diffusion of charged particles in tortuous porous media may be very different from transport in long capillaries without such intersections.
Nonlinear variational models for reaction and diffusion systems
International Nuclear Information System (INIS)
Tanyi, G.E.
1983-08-01
There exists a natural metric w.r.t. which the density dependent diffusion operator is harmonic in the sense of Eells and Sampson. A physical corollary of this statement is the property that any two regular points on the orbit of a reaction or diffusion operator can be connected by a path along which the reaction rate is constant. (author)
International Nuclear Information System (INIS)
Rios Perez, Carlos A.; Biegalski, Steve R.; Deinert, Mark R.
2012-01-01
Highlights: ► Prompt gamma activation analysis is used to study gas diffusion in a porous system. ► Diffusion coefficients are determined using prompt gamma activation analysis. ► Predictions concentrations fit experimental measurements with an R 2 of 0.98. - Abstract: Diffusion plays a critical role in determining the rate at which gases migrate through porous systems. Accurate estimates of diffusion coefficients are essential if gas transport is to be accurately modeled and better techniques are needed that can be used to measure these coefficients non-invasively. Here we present a novel method for using prompt gamma activation analysis to determine the binary diffusion coefficients of a gas in a porous system. Argon diffusion experiments were conducted in a 1 m long, 10 cm diameter, horizontal column packed with a SiO 2 sand. The temporal variation of argon concentration within the system was measured using prompt gamma activation analysis. The binary diffusion coefficient was obtained by comparing the experimental data with the predictions from a numerical model in which the diffusion coefficient was varied until the sum of square errors between experiment and model data was minimized. Predictions of argon concentration using the optimal diffusivity fit experimental measurements with an R 2 of 0.983.
Schwartz, L M; Bergman, D J; Dunn, K J; Mitra, P P
1996-01-01
Random walk computer simulations are an important tool in understanding magnetic resonance measurements in porous media. In this paper we focus on the description of pulsed field gradient spin echo (PGSE) experiments that measure the probability, P(R,t), that a diffusing water molecule will travel a distance R in a time t. Because PGSE simulations are often limited by statistical considerations, we will see that valuable insight can be gained by working with simple periodic geometries and comparing simulation data to the results of exact eigenvalue expansions. In this connection, our attention will be focused on (1) the wavevector, k, and time dependent magnetization, M(k, t); and (2) the normalized probability, Ps(delta R, t), that a diffusing particle will return to within delta R of the origin after time t.
Directory of Open Access Journals (Sweden)
MENKA PETKOVSKA
2000-12-01
Full Text Available The concept of higher order frequency response functions (FRFs is used for the analysis of non-linear adsorption kinetics on a particle scale, for the case of non-isothermal micropore diffusion with variable diffusivity. Six series of FRFs are defined for the general non-isothermal case. A non-linerar mathematical model is postulated and the first and second order FRFs derived and simulated. A variable diffusivity influences the shapes of the second order FRFs relating the sorbate concentration in the solid phase and t he gas pressure significantly, but they still keep their characteristics which can be used for discrimination of this from other kinetic mechanisms. It is also shown that first and second order particle FRFs offter sufficient information for an easy and fast estimation of all model parameters, including those defining the system non-linearity.
Hibi, Yoshihiko; Kashihara, Ayumi
2018-03-01
A previous study has reported that Knudsen diffusion coefficients obtained by tracer experiments conducted with a binary gas system and a porous medium are consistently smaller than those obtained by permeability experiments conducted with a single-gas system and a porous medium. To date, however, that study is the only one in which tracer experiments have been conducted with a binary gas system. Therefore, to confirm this difference in Knudsen diffusion coefficients, we used a method we had developed previously to conduct tracer experiments with a binary carbon dioxide-nitrogen gas system and five porous media with permeability coefficients ranging from 10-13 to 10-11 m2. The results showed that the Knudsen diffusion coefficient of N2 (DN2) (cm2/s) was related to the effective permeability coefficient ke (m2) as DN2 = 7.39 × 107ke0.767. Thus, the Knudsen diffusion coefficients of N2 obtained by our tracer experiments were consistently 1/27 of those obtained by permeability experiments conducted with many porous media and air by other researchers. By using an inversion simulation to fit the advection-diffusion equation to the distribution of concentrations at observation points calculated by mathematically solving the equation, we confirmed that the method used to obtain the Knudsen diffusion coefficient in this study yielded accurate values. Moreover, because the Knudsen diffusion coefficient did not differ when columns with two different lengths, 900 and 1500 mm, were used, this column property did not influence the flow of gas in the column. The equation of the dusty gas model already includes obstruction factors for Knudsen diffusion and molecular diffusion, which relate to medium heterogeneity and tortuosity and depend only on the structure of the porous medium. Furthermore, there is no need to take account of any additional correction factor for molecular diffusion except the obstruction factor because molecular diffusion is only treated in a multicomponent
A Nonlinear Diffusion Equation-Based Model for Ultrasound Speckle Noise Removal
Zhou, Zhenyu; Guo, Zhichang; Zhang, Dazhi; Wu, Boying
2018-04-01
Ultrasound images are contaminated by speckle noise, which brings difficulties in further image analysis and clinical diagnosis. In this paper, we address this problem in the view of nonlinear diffusion equation theories. We develop a nonlinear diffusion equation-based model by taking into account not only the gradient information of the image, but also the information of the gray levels of the image. By utilizing the region indicator as the variable exponent, we can adaptively control the diffusion type which alternates between the Perona-Malik diffusion and the Charbonnier diffusion according to the image gray levels. Furthermore, we analyze the proposed model with respect to the theoretical and numerical properties. Experiments show that the proposed method achieves much better speckle suppression and edge preservation when compared with the traditional despeckling methods, especially in the low gray level and low-contrast regions.
Malyarenko, Dariya I; Ross, Brian D; Chenevert, Thomas L
2014-03-01
Gradient nonlinearity of MRI systems leads to spatially dependent b-values and consequently high non-uniformity errors (10-20%) in apparent diffusion coefficient (ADC) measurements over clinically relevant field-of-views. This work seeks practical correction procedure that effectively reduces observed ADC bias for media of arbitrary anisotropy in the fewest measurements. All-inclusive bias analysis considers spatial and time-domain cross-terms for diffusion and imaging gradients. The proposed correction is based on rotation of the gradient nonlinearity tensor into the diffusion gradient frame where spatial bias of b-matrix can be approximated by its Euclidean norm. Correction efficiency of the proposed procedure is numerically evaluated for a range of model diffusion tensor anisotropies and orientations. Spatial dependence of nonlinearity correction terms accounts for the bulk (75-95%) of ADC bias for FA = 0.3-0.9. Residual ADC non-uniformity errors are amplified for anisotropic diffusion. This approximation obviates need for full diffusion tensor measurement and diagonalization to derive a corrected ADC. Practical scenarios are outlined for implementation of the correction on clinical MRI systems. The proposed simplified correction algorithm appears sufficient to control ADC non-uniformity errors in clinical studies using three orthogonal diffusion measurements. The most efficient reduction of ADC bias for anisotropic medium is achieved with non-lab-based diffusion gradients. Copyright © 2013 Wiley Periodicals, Inc.
Chaotic behaviour of nonlinear coupled reaction–diffusion system in ...
Indian Academy of Sciences (India)
chaos in four-dimensional space by the generalized definitions of spatial ... according to nonlinear noise in the real physical world, f(φ(x),ψ(x)) and g(φ(x) ... tion in ecological system, where φm,n(s) is the host density in generations s and s + 1,.
Diffusion-controlled cementation experiments in porous rock analogues using potash alum and halite
Energy Technology Data Exchange (ETDEWEB)
Hufe, A.; Hilgers, C. [RWTH Aachen Univ. (Germany). Inst. of Reservoir-Petrology; Stanjek, H. [RWTH Aachen Univ. (Germany). Inst. of Interface and Clay Mineralogy
2013-08-01
A good understanding of cementation is critical for reservoir quality predictions. However, studies of core material have shown that cementation may be driven by variations in pore size of the host rock. To better understand the underlying process, we developed a transparent microreactor for diffusion-controlled cementation experiments under the microscope. We studied the effect of different pore sizes and surface charges of solid material at different pH, using rock analogs. High-resolution videos allowed to analyze the nucleation from solution, pore cementation and growth rates of cements. Diffusion - considered the major mass transport during burial diagenesis - was driven along a temperature gradient across the microreactor. Pores were cemented with salt, which is well known to form pore-size dependent seals in silicilastic reservoirs. While halite precipitated primarily in pores bigger than 200 {mu}m, alum nucleated in smaller pores. The growth rate of alum (10{sup -5} mm/s) was one order of magnitude higher than that of halite. However, the dissolution rates of both minerals was similar at about 10{sup -6} mm/s. Authigenic euhdral halite migrated against the bulk diffusion transport and towards the higher-temperature reservoir. Halite growth rates increased by one order of magnitude to 1.8 x 10{sup -5} mm/s, if the phase boundary was vapor-liquid. A comparison nucleation in a 2-phase porous rock analog showed no difference in cementation pattern at a pH 7. However, at a pH of 10.5 the surface energies of the two different solids are altered, and porosity was reduced 60% more by cements in the phase-1 porous layers. Our experiments showed that pore size dependent nucleation and cementation is a process, which may also take place in complex reservoirs. With the successful pore clogging of halite we can now bring our experimental setup to reservoir conditions and establish the processes at elevated p-T conditions. (orig.)
Directory of Open Access Journals (Sweden)
Palle Kiran
2016-03-01
Full Text Available A weak nonlinear oscillatory mode of thermal instability is investigated while deriving a non autonomous complex Ginzburg–Landau equation. Darcy porous medium is considered in the presence of vertical throughflow and time periodic thermal boundaries. Only infinitesimal disturbances are considered. The disturbances in velocity, temperature and solutal fields are treated by a perturbation expansion in powers of amplitude of applied temperature field. The effect of throughflow has either to stabilize or to destabilize the system for stress free and isothermal boundary conditions. Nusselt and Sherwood numbers are obtained numerically and presented the results on heat and mass transfer. It is found that, throughflow and thermal modulation can be used alternatively to control the heat and mass transfer. Further, it is also found that oscillatory flow enhances the heat and mass transfer than stationary flow. Effect of modulation frequency and phase angle on mean Nusselt number is also discussed.
NMR diffusion and relaxation measurements of organic molecules adsorbed in porous media
International Nuclear Information System (INIS)
Gjerdaaker, Lars
2002-01-01
The work in this thesis can be divided into two parts. The first part is focused on dynamic investigations of plastic crystals, both in bulk phases but also confined in porous materials (paper 1-3). This part was done together with professor Liudvikas Kimtys, Vilnius, Lithuania. The second part, with emphasis on diffusion, employed PFG NMR to measure the true intra-crystalline diffusivity, including development of a new pulse sequence with shorter effective diffusion time. This work was performed in collaboration with Dr. Geir H. Soerland, Trondheim, Norway and has resulted in three papers (paper 4-6). Paper 1-3: In these papers the dynamics of three organic compounds confined within mesoporous silica have been studied, and the results are discussed with reference to the bulk material. The three investigated compounds form disordered (plastic) phases of high symmetry on solidification (solid I). Thus, bulk cyclohexane exhibits a disordered phase between the solid-solid phase transition at 186 K and the melting point at 280 K. X-ray diffraction measurements have shown that solid I is face-centred cubic (Z=4, a=0.861 nm at 195 K), while the ordered solid II is monoclinic. Tert-butyl cyanide exhibits a plastic phase between the solid-solid transition point at 233 K and the melting point at 292 K. Neutron scattering techniques have established that solid I is tetragonal (Z=2, a=b=0.683 nm, c=0.674 nm, beta=90 deg at 234 K), while solid II is monoclinic. Finally, the disordered phase of pivalic acid melts at 310 K and undergoes a solid-solid phase transition at 280 K. The disordered phase is face-centred cubic, (Z=4, a=0.887 nm), while the low temperature phase (solid II) is triclinic. Paper 4-6; If one is aiming to measure true intra-crystallite diffusivities in porous media the distance travelled by the molecules during the pulse must be shorter than the size of the crystallite. The length of the diffusion time is therefore important. Working with heterogeneous media
A mixed-order nonlinear diffusion compressed sensing MR image reconstruction.
Joy, Ajin; Paul, Joseph Suresh
2018-03-07
Avoid formation of staircase artifacts in nonlinear diffusion-based MR image reconstruction without compromising computational speed. Whereas second-order diffusion encourages the evolution of pixel neighborhood with uniform intensities, fourth-order diffusion considers smooth region to be not necessarily a uniform intensity region but also a planar region. Therefore, a controlled application of fourth-order diffusivity function is used to encourage second-order diffusion to reconstruct the smooth regions of the image as a plane rather than a group of blocks, while not being strong enough to introduce the undesirable speckle effect. Proposed method is compared with second- and fourth-order nonlinear diffusion reconstruction, total variation (TV), total generalized variation, and higher degree TV using in vivo data sets for different undersampling levels with application to dictionary learning-based reconstruction. It is observed that the proposed technique preserves sharp boundaries in the image while preventing the formation of staircase artifacts in the regions of smoothly varying pixel intensities. It also shows reduced error measures compared with second-order nonlinear diffusion reconstruction or TV and converges faster than TV-based methods. Because nonlinear diffusion is known to be an effective alternative to TV for edge-preserving reconstruction, the crucial aspect of staircase artifact removal is addressed. Reconstruction is found to be stable for the experimentally determined range of fourth-order regularization parameter, and therefore not does not introduce a parameter search. Hence, the computational simplicity of second-order diffusion is retained. © 2018 International Society for Magnetic Resonance in Medicine.
Ground state solutions for diffusion system with superlinear nonlinearity
Directory of Open Access Journals (Sweden)
Zhiming Luo
2015-03-01
where $z=(u,v\\colon\\mathbb{R}\\times\\mathbb{R}^{N}\\rightarrow\\mathbb{R}^{2}$, $b\\in C^{1}(\\mathbb{R}\\times\\mathbb{R}^{N}, \\mathbb{R}^{N}$ and $V(x\\in C(\\mathbb{R}^{N},\\mathbb{R}$. Under suitable assumptions on the nonlinearity, we establish the existence of ground state solutions by the generalized Nehari manifold method developed recently by Szulkin and Weth.
Solitary wave solutions of selective nonlinear diffusion-reaction ...
Indian Academy of Sciences (India)
An auto-Bäcklund transformation derived in the homogeneous balance method is employed to obtain several new exact solutions of certain kinds of nonlin- ear diffusion-reaction (D-R) equations. These equations arise in a variety of problems in physical, chemical, biological, social and ecological sciences. Keywords.
Directory of Open Access Journals (Sweden)
M.M. Bhatti
2017-06-01
Full Text Available Biologically-inspired propulsion systems are currently receiving significant interest in the aerospace sector. Since many spacecraft propulsion systems operate at high temperatures, thermal radiation is important as a mode of heat transfer. Motivated by these developments, in the present article, the influence of nonlinear thermal radiation (via the Rosseland diffusion flux model has been studied on the laminar, incompressible, dissipative EMHD (Electro-magneto-hydrodynamic peristaltic propulsive flow of a non-Newtonian (Jefferys viscoelastic dusty fluid containing solid particles through a porous planar channel. The fluid is electrically-conducting and a constant static magnetic field is applied transverse to the flow direction (channel walls. Slip effects are also included. Magnetic induction effects are neglected. The mathematical formulation is based on continuity, momentum and energy equations with appropriate boundary conditions, which are simplified by neglecting the inertial forces and taking the long wavelength and lubrication approximations. The boundary value problem is then rendered non-dimensional with appropriate variables and the resulting system of reduced ordinary differential equations is solved analytically. The impact of various emerging parameters dictating the non-Newtonian propulsive flow i.e. Prandtl number, radiation parameter, Hartmann number, permeability parameter, Eckert number, particle volume fraction, electric field and slip parameter are depicted graphically. Increasing particle volume fraction is observed to suppress temperature magnitudes. Furthermore the computations demonstrate that an increase in particle volume fraction reduces the pumping rate in retrograde pumping region whereas it causes the opposite effect in the co-pumping region. The trapping mechanism is also visualized with the aid of streamline contour plots. Increasing thermal radiation elevates temperatures. Increasing Hartmann (magnetic body
Yang, Haijian
2016-07-26
Fully implicit methods are drawing more attention in scientific and engineering applications due to the allowance of large time steps in extreme-scale simulations. When using a fully implicit method to solve two-phase flow problems in porous media, one major challenge is the solution of the resultant nonlinear system at each time step. To solve such nonlinear systems, traditional nonlinear iterative methods, such as the class of the Newton methods, often fail to achieve the desired convergent rate due to the high nonlinearity of the system and/or the violation of the boundedness requirement of the saturation. In the paper, we reformulate the two-phase model as a variational inequality that naturally ensures the physical feasibility of the saturation variable. The variational inequality is then solved by an active-set reduced-space method with a nonlinear elimination preconditioner to remove the high nonlinear components that often causes the failure of the nonlinear iteration for convergence. To validate the effectiveness of the proposed method, we compare it with the classical implicit pressure-explicit saturation method for two-phase flow problems with strong heterogeneity. The numerical results show that our nonlinear solver overcomes the often severe limits on the time step associated with existing methods, results in superior convergence performance, and achieves reduction in the total computing time by more than one order of magnitude.
Yang, Haijian; Yang, Chao; Sun, Shuyu
2016-01-01
Fully implicit methods are drawing more attention in scientific and engineering applications due to the allowance of large time steps in extreme-scale simulations. When using a fully implicit method to solve two-phase flow problems in porous media, one major challenge is the solution of the resultant nonlinear system at each time step. To solve such nonlinear systems, traditional nonlinear iterative methods, such as the class of the Newton methods, often fail to achieve the desired convergent rate due to the high nonlinearity of the system and/or the violation of the boundedness requirement of the saturation. In the paper, we reformulate the two-phase model as a variational inequality that naturally ensures the physical feasibility of the saturation variable. The variational inequality is then solved by an active-set reduced-space method with a nonlinear elimination preconditioner to remove the high nonlinear components that often causes the failure of the nonlinear iteration for convergence. To validate the effectiveness of the proposed method, we compare it with the classical implicit pressure-explicit saturation method for two-phase flow problems with strong heterogeneity. The numerical results show that our nonlinear solver overcomes the often severe limits on the time step associated with existing methods, results in superior convergence performance, and achieves reduction in the total computing time by more than one order of magnitude.
Analytical Solutions of Ionic Diffusion and Heat Conduction in Multilayered Porous Media
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Yu Bai
2015-01-01
Full Text Available Ionic diffusion and heat conduction in a multiple layered porous medium have many important engineering applications. One of the examples is the chloride ions from deicers penetrating into concrete structures such as bridge decks. Different overlays can be placed on top of concrete surface to slowdown the chloride penetration. In this paper, the chloride ion diffusion equations were established for concrete structures with multiple layers of protective system. By using Laplace transformation, an analytical solution was developed first for chloride concentration profiles in two-layered system and then extended to multiple layered systems with nonconstant boundary conditions, including the constant boundary and linear boundary conditions. Because ionic diffusion in saturated media and heat conduction are governed by the same form of partial differential equations with different materials parameters, the analytical solution was further extended to handle heat conduction in a multiple layered system under nonconstant boundary conditions. The numerical results were compared with available test data. The basic trends of the analytical solution and the test data agreed quite well.
Diffusion Geometry Based Nonlinear Methods for Hyperspectral Change Detection
2010-05-12
for matching biological spectra across a data base of hyperspectral pathology slides acquires with different instruments in different conditions, as...generalizing wavelets and similar scaling mechanisms. Plain Sight Systems, Inc. -7- Proprietary and Confidential To be specific, let the bi-Markov...remarkably well. Conventional nearest neighbor search , compared with a diffusion search. The data is a pathology slide ,each pixel is a digital
Directory of Open Access Journals (Sweden)
H. Kaviani
2007-09-01
Full Text Available Band structure of porous alumina photonic crystal in the Γ X direction was calculated using order-N method . In a comparison of calculated results with experimental data of reflective and absorptive index, the variation of refractive index of alumina in the external region of oxide layer, around the pores were studied. A Gaussian distribution function was adopted for phosphate anions in the external oxide layer and the variation of refractive index and diffusion depth were determined. The structure of the first four bands was calculated using the obtained distribution of refractive index in the external oxide layer for both TE and TM mode. This results show a narrow full band gap in the TM mode.
Cherniha, Roman
2017-01-01
This book presents several fundamental results in solving nonlinear reaction-diffusion equations and systems using symmetry-based methods. Reaction-diffusion systems are fundamental modeling tools for mathematical biology with applications to ecology, population dynamics, pattern formation, morphogenesis, enzymatic reactions and chemotaxis. The book discusses the properties of nonlinear reaction-diffusion systems, which are relevant for biological applications, from the symmetry point of view, providing rigorous definitions and constructive algorithms to search for conditional symmetry (a nontrivial generalization of the well-known Lie symmetry) of nonlinear reaction-diffusion systems. In order to present applications to population dynamics, it focuses mainly on two- and three-component diffusive Lotka-Volterra systems. While it is primarily a valuable guide for researchers working with reaction-diffusion systems and those developing the theoretical aspects of conditional symmetry conception,...
Tan, Xiaoyu
2016-01-01
way to fabricate defect-free and thin ZIF-8 membranes on porous polymeric supports showing high selectivity and high gas permeance. The ZIF-8 layers were produced via a contra-diffusion method. Several polymeric membranes were employed as support
PFG NMR Study of Liquid n-Hexane Self-Diffusion in the Bed of Porous Glass Beads
Czech Academy of Sciences Publication Activity Database
Peksa, M.; Lang, J.; Kočiřík, Milan
2009-01-01
Roč. 11, č. 36 (2009), s. 1-2 ISSN 1862-4138 R&D Projects: GA ČR GA203/09/1353 Institutional research plan: CEZ:AV0Z40400503 Keywords : PFG NMR Study * porous glass beads Subject RIV: CF - Physical ; Theoretical Chemistry http://www.uni-leipzig.de/diffusion/journal/index.html
Zanden, van der A.J.J.; Taher, A.
2014-01-01
A new procedure is presented with which the diffusion coefficient of water in partially saturated porous materials can be measured. The first step in the procedure is the creation of a non-equilibrium situation inside a sample by placing it into a centrifuge. In the second step, the mass of the
International Nuclear Information System (INIS)
Guzman, Juan; Maximov, Serguei; Escarela-Perez, Rafael; López-García, Irvin; Moranchel, Mario
2015-01-01
The diffusion and distribution coefficients are important parameters in the design of barrier systems used in radioactive repositories. These coefficients can be determined using a two-reservoir configuration, where a saturated porous medium is allocated between two reservoirs filled by stagnant water. One of the reservoirs contains a high concentration of radioisotopes. The goal of this work is to obtain an analytical solution for the concentration of all radioisotopes in the decay chain of a two-reservoir configuration. The analytical solution must be obtained by taking into account the diffusion and sorption processes. Concepts such as overvalued concentration, diffusion and decay factors are employed to this end. It is analytically proven that a factor of the solution is identical for all chains (considering a time scaling factor), if certain parameters do not change. In addition, it is proven that the concentration sensitivity, due to the distribution coefficient variation, depends of the porous medium thickness, which is practically insensitive for small porous medium thicknesses. The analytical solution for the radioisotope concentration is compared with experimental and numerical results available in literature. - Highlights: • Saturated porous media allocated between two reservoirs. • Analytical solution of the isotope transport equation. • Transport considers diffusion, sorption and decay chain
Fukao, Takeshi; Kurima, Shunsuke; Yokota, Tomomi
2018-05-01
This paper develops an abstract theory for subdifferential operators to give existence and uniqueness of solutions to the initial-boundary problem (P) for the nonlinear diffusion equation in an unbounded domain $\\Omega\\subset\\mathbb{R}^N$ ($N\\in{\\mathbb N}$), written as \\[ \\frac{\\partial u}{\\partial t} + (-\\Delta+1)\\beta(u) = g \\quad \\mbox{in}\\ \\Omega\\times(0, T), \\] which represents the porous media, the fast diffusion equations, etc., where $\\beta$ is a single-valued maximal monotone function on $\\mathbb{R}$, and $T>0$. Existence and uniqueness for (P) were directly proved under a growth condition for $\\beta$ even though the Stefan problem was excluded from examples of (P). This paper completely removes the growth condition for $\\beta$ by confirming Cauchy's criterion for solutions of the following approximate problem (P)$_{\\varepsilon}$ with approximate parameter $\\varepsilon>0$: \\[ \\frac{\\partial u_{\\varepsilon}}{\\partial t} + (-\\Delta+1)(\\varepsilon(-\\Delta+1)u_{\\varepsilon} + \\beta(u_{\\varepsilon}) + \\pi_{\\varepsilon}(u_{\\varepsilon})) = g \\quad \\mbox{in}\\ \\Omega\\times(0, T), \\] which is called the Cahn--Hilliard system, even if $\\Omega \\subset \\mathbb{R}^N$ ($N \\in \\mathbb{N}$) is an unbounded domain. Moreover, it can be seen that the Stefan problem is covered in the framework of this paper.
Energy Technology Data Exchange (ETDEWEB)
Schunert, Sebastian; Hammer, Hans; Lou, Jijie; Wang, Yaqi; Ortensi, Javier; Gleicher, Frederick; Baker, Benjamin; DeHart, Mark; Martineau, Richard
2016-11-01
The common definition of the diffusion coeffcient as the inverse of three times the transport cross section is not compat- ible with voids. Morel introduced a non-local tensor diffusion coeffcient that remains finite in voids[1]. It can be obtained by solving an auxiliary transport problem without scattering or fission. Larsen and Trahan successfully applied this diffusion coeffcient for enhancing the accuracy of diffusion solutions of very high temperature reactor (VHTR) problems that feature large, optically thin channels in the z-direction [2]. It is demonstrated that a significant reduction of error can be achieved in particular in the optically thin region. Along the same line of thought, non-local diffusion tensors are applied modeling the TREAT reactor confirming the findings of Larsen and Trahan [3]. Previous work of the authors have introduced a flexible Nonlinear-Diffusion Acceleration (NDA) method for the first order S N equations discretized with the discontinuous finite element method (DFEM), [4], [5], [6]. This NDA method uses a scalar diffusion coeffcient in the low-order system that is obtained as the flux weighted average of the inverse transport cross section. Hence, it su?ers from very large and potentially unbounded diffusion coeffcients in the low order problem. However, it was noted that the choice of the diffusion coeffcient does not influence consistency of the method at convergence and hence the di?usion coeffcient is essentially a free parameter. The choice of the di?usion coeffcient does, however, affect the convergence behavior of the nonlinear di?usion iterations. Within this work we use Morel’s non-local di?usion coef- ficient in the aforementioned NDA formulation in lieu of the flux weighted inverse of three times the transport cross section. The goal of this paper is to demonstrate that significant en- hancement of the spectral properties of NDA can be achieved in near void regions. For testing the spectral properties of the NDA
Some applications of nonlinear diffusion to processing of dynamic evolution images
International Nuclear Information System (INIS)
Goltsov, Alexey N.; Nikishov, Sergey A.
1997-01-01
Model nonlinear diffusion equation with the most simple Landau-Ginzburg free energy functional was applied to locate boundaries between meaningful regions of low-level images. The method is oriented to processing images of objects that are a result of dynamic evolution: images of different organs and tissues obtained by radiography and NMR methods, electron microscope images of morphogenesis fields, etc. In the methods developed by us, parameters of the nonlinear diffusion model are chosen on the basis of the preliminary treatment of the images. The parameters of the Landau-Ginzburg free energy functional are extracted from the structure factor of the images. Owing to such a choice of the model parameters, the image to be processed is located in the vicinity of the steady-state of the diffusion equation. The suggested method allows one to separate distinct structures having specific space characteristics from the whole image. The method was applied to processing X-ray images of the lung
Diffusion and Clustering of Carbon Dioxide on Non-porous Amorphous Solid Water
Energy Technology Data Exchange (ETDEWEB)
He, Jiao; Emtiaz, Shahnewaj M.; Vidali, Gianfranco, E-mail: jhe08@syr.edu, E-mail: gvidali@syr.edu [Physics Department, Syracuse University, Syracuse, NY 13244 (United States)
2017-03-01
Observations by ISO and Spitzer toward young stellar objects showed that CO{sub 2} segregates in the icy mantles covering dust grains. Thermal processing of the ice mixture was proposed as being responsible for the segregation. Although several laboratories studied thermally induced segregation, a satisfying quantification is still missing. We propose that the diffusion of CO{sub 2} along pores inside water ice is the key to quantify segregation. We combined Temperature Programmed Desorption and Reflection Absorption InfraRed Spectroscopy to study how CO{sub 2} molecules interact on a non-porous amorphous solid water (np-ASW) surface. We found that CO{sub 2} diffuses significantly on an np-ASW surface above 65 K and clusters are formed at well below one monolayer. A simple rate equation simulation finds that the diffusion energy barrier of CO{sub 2} on np-ASW is 2150 ± 50 K, assuming a diffusion pre-exponential factor of 10{sup 12} s{sup −1}. This energy should also apply to the diffusion of CO{sub 2} on the wall of pores. The binding energy of CO{sub 2} from CO{sub 2} clusters and CO{sub 2} from H{sub 2}O ice has been found to be 2415 ± 20 K and 2250 ± 20 K, respectively, assuming the same prefactor for desorption. CO{sub 2}–CO{sub 2} interaction is stronger than CO{sub 2}–H{sub 2}O interaction, in agreement with the experimental finding that CO{sub 2} does not wet the np-ASW surface. For comparison, we carried out similar experiments with CO on np-ASW, and found that the CO–CO interaction is always weaker than CO–H{sub 2}O. As a result, CO wets the np-ASW surface. This study should be of help to uncover the thermal history of CO{sub 2} on the icy mantles of dust grains.
A nonlinear equation for ionic diffusion in a strong binary electrolyte
Ghosal, Sandip; Chen, Zhen
2010-01-01
The problem of the one-dimensional electro-diffusion of ions in a strong binary electrolyte is considered. The mathematical description, known as the Poisson–Nernst–Planck (PNP) system, consists of a diffusion equation for each species augmented by transport owing to a self-consistent electrostatic field determined by the Poisson equation. This description is also relevant to other important problems in physics, such as electron and hole diffusion across semiconductor junctions and the diffusion of ions in plasmas. If concentrations do not vary appreciably over distances of the order of the Debye length, the Poisson equation can be replaced by the condition of local charge neutrality first introduced by Planck. It can then be shown that both species diffuse at the same rate with a common diffusivity that is intermediate between that of the slow and fast species (ambipolar diffusion). Here, we derive a more general theory by exploiting the ratio of the Debye length to a characteristic length scale as a small asymptotic parameter. It is shown that the concentration of either species may be described by a nonlinear partial differential equation that provides a better approximation than the classical linear equation for ambipolar diffusion, but reduces to it in the appropriate limit. PMID:21818176
Nonlinear waves in reaction-diffusion systems: The effect of transport memory
International Nuclear Information System (INIS)
Manne, K. K.; Hurd, A. J.; Kenkre, V. M.
2000-01-01
Motivated by the problem of determining stress distributions in granular materials, we study the effect of finite transport correlation times on the propagation of nonlinear wave fronts in reaction-diffusion systems. We obtain results such as the possibility of spatial oscillations in the wave-front shape for certain values of the system parameters and high enough wave-front speeds. We also generalize earlier known results concerning the minimum wave-front speed and shape-speed relationships stemming from the finiteness of the correlation times. Analytic investigations are made possible by a piecewise linear representation of the nonlinearity. (c) 2000 The American Physical Society
Nonlinear waves in reaction-diffusion systems: The effect of transport memory
Manne, K. K.; Hurd, A. J.; Kenkre, V. M.
2000-04-01
Motivated by the problem of determining stress distributions in granular materials, we study the effect of finite transport correlation times on the propagation of nonlinear wave fronts in reaction-diffusion systems. We obtain results such as the possibility of spatial oscillations in the wave-front shape for certain values of the system parameters and high enough wave-front speeds. We also generalize earlier known results concerning the minimum wave-front speed and shape-speed relationships stemming from the finiteness of the correlation times. Analytic investigations are made possible by a piecewise linear representation of the nonlinearity.
2016 CIME Course on Nonlocal and Nonlinear Diffusions and Interactions : New Methods and Directions
Grillo, Gabriele
2017-01-01
Presenting a selection of topics in the area of nonlocal and nonlinear diffusions, this book places a particular emphasis on new emerging subjects such as nonlocal operators in stationary and evolutionary problems and their applications, swarming models and applications to biology and mathematical physics, and nonlocal variational problems. The authors are some of the most well-known mathematicians in this innovative field, which is presently undergoing rapid development. The intended audience includes experts in elliptic and parabolic equations who are interested in extending their expertise to the nonlinear setting, as well as Ph.D. or postdoctoral students who want to enter into the most promising research topics in the field.
Marin, D.; Ribeiro, M. A.; Ribeiro, H. V.; Lenzi, E. K.
2018-07-01
We investigate the solutions for a set of coupled nonlinear Fokker-Planck equations coupled by the diffusion coefficient in presence of external forces. The coupling by the diffusion coefficient implies that the diffusion of each species is influenced by the other and vice versa due to this term, which represents an interaction among them. The solutions for the stationary case are given in terms of the Tsallis distributions, when arbitrary external forces are considered. We also use the Tsallis distributions to obtain a time dependent solution for a linear external force. The results obtained from this analysis show a rich class of behavior related to anomalous diffusion, which can be characterized by compact or long-tailed distributions.
A Fully Discrete Galerkin Method for a Nonlinear Space-Fractional Diffusion Equation
Directory of Open Access Journals (Sweden)
Yunying Zheng
2011-01-01
Full Text Available The spatial transport process in fractal media is generally anomalous. The space-fractional advection-diffusion equation can be used to characterize such a process. In this paper, a fully discrete scheme is given for a type of nonlinear space-fractional anomalous advection-diffusion equation. In the spatial direction, we use the finite element method, and in the temporal direction, we use the modified Crank-Nicolson approximation. Here the fractional derivative indicates the Caputo derivative. The error estimate for the fully discrete scheme is derived. And the numerical examples are also included which are in line with the theoretical analysis.
Analysis of nonlinear parabolic equations modeling plasma diffusion across a magnetic field
International Nuclear Information System (INIS)
Hyman, J.M.; Rosenau, P.
1984-01-01
We analyse the evolutionary behavior of the solution of a pair of coupled quasilinear parabolic equations modeling the diffusion of heat and mass of a magnetically confined plasma. The solutions's behavior, due to the nonlinear diffusion coefficients, exhibits many new phenomena. In short time, the solution converges into a highly organized symmetric pattern that is almost completely independent of initial data. The asymptotic dynamics then become very simple and take place in a finite dimensional space. These conclusions are backed by extensive numerical experimentation
Frost fatigue and spring recovery of xylem vessels in three diffuse-porous trees in situ.
Christensen-Dalsgaard, Karen K; Tyree, Melvin T
2014-05-01
Frost has been shown to cause frost fatigue (reduced cavitation resistance) in branch segments in the lab. Here, we studied the change in cavitation resistance and percent loss of conductivity (PLC) from fall to spring over 2 consecutive years in three diffuse-porous species in situ. We used the cavitron technique to measure P25 , P50 and P90 (the xylem pressure causing a 25, 50 and 90% conductivity loss) and PLC and stained functioning vessels. Cavitation resistance was reduced by 64-87% (in terms of P50 ), depending on the species and year. P25 was impacted the most and P90 the least, changing the vulnerability curves from s- to r-shaped over the winter in all three species. The branches suffered an almost complete loss of conductivity, but frost fatigue did not necessarily occur concurrently with increases in PLC. In two species, there was a trade-off between conduit size and vulnerability. Spring recovery occurred by growth of new vessels, and in two species by partial refilling of embolized conduits. Although newly grown and functioning conduits appeared more vulnerable to cavitation than year-old vessels, cavitation resistance generally improved in spring, suggesting other mechanisms for partial frost fatigue repair. © 2013 John Wiley & Sons Ltd.
Cheung, Perry; Fairweather, Joseph D.; Schwartz, Daniel T.
2012-09-01
Simple laboratory methods for determining liquid water distribution in polymer electrolyte membrane fuel cell gas diffusion layers (GDLs) are needed to engineer better GDL materials. Capillary pressure vs. liquid saturation measurements are attractive, but lack the ability to probe the hydraulic interconnectivity and distribution within the pore structure. Hydraulic admittance measurements of simple capillary bundles have recently been shown to nicely measure characteristics of the free-interfaces and hydraulic path. Here we examine the use of hydraulic admittance with a succession of increasingly complex porous media, starting with a laser-drilled sample with 154 asymmetric pores and progress to the behavior of Toray TGP-H090 carbon papers. The asymmetric laser-drilled sample clearly shows hydraulic admittance measurements are sensitive to sample orientation, especially when examined as a function of saturation state. Finite element modeling of the hydraulic admittance is consistent with experimental measurements. The hydraulic admittance spectra from GDL samples are complex, so we examine trends in the spectra as a function of wet proofing (0% and 40% Teflon loadings) as well as saturation state of the GDL. The presence of clear peaks in the admittance spectra for both GDL samples suggests a few pore types are largely responsible for transporting liquid water.
The influence of transverse diffusion/dispersion on the migration of radionuclides in porous media
International Nuclear Information System (INIS)
Schmocker, U.
1980-07-01
Repositories in geological formations are planned for the final disposal of radioactive wastes produced by nuclear power. Generally, water entry leading to leaching of the waste matrix is considered as the critical process which can result in release of radionuclides from a waste repository. Consequently, radionuclide transport through the geosphere is of crucial importance, because the geological medium acts as the last barrier to the biosphere. The influence of the transverse diffusion/dispersion effect on the migration of radionuclides through the geosphere is dealt with. Migration in porous media only is considered which is the standard approach of most existing transport models. The present study shows that it is only for homogeneous-isotropic media that the three-dimensional time-dependent transport equation can be solved analytically - provided that only simple source geometries and leach processes are taken into account. For heterogeneous layered media only the two-dimensional quasi-stationary transport equation can be solved; the only time dependent process which can be handled is simple radioactive decay excluding extended decay chains. The study shows moreover that only for an idealized three-layer geology can analytical solutions be found. In particular the solutions for multi-layered media cannot be derived from single-layer solutions; each problem with special source and boundary conditions has to be solved directly. The numerical results from the present study show a relatively strong influence of the transverse dispersion effect in the case of homogeneous-isotropic media. (Auth.)
International Nuclear Information System (INIS)
Gladden, Lynn F; Mitchell, Jonathan
2011-01-01
Magnetic resonance (MR) techniques are increasingly used to improve our understanding of the multi-component, multi-phase processes encountered in chemical engineering. This review brings together many of the MR techniques used, and often developed specifically, to study chemical engineering systems and, in particular, processes occurring within porous media. Pulse sequences for relaxometry, pulsed field gradient measurements of diffusion, imaging and velocimetry measurements are described. Recent applications of these MR pulse sequences to microporous, mesoporous and macroporous structures are then reviewed. Considering the microporous and mesoporous systems, we focus attention on studies of rock cores, manufactured materials such as cement and gypsum plaster, and catalysts. When considering macroporous structures, the transport through packed beds of particles typical of fixed-bed catalytic reactors is reviewed; a brief overview of the increasing research interest in gas-solid fluidized beds is also presented. We highlight the field of sparse k-space sampling as an area that is in its infancy and suggest that, combined with Bayesian methods, it will offer new opportunities in both extending the application of high-field MR techniques to chemical engineering and increasing the range of measurements that can be carried out using low-field hardware.
Fagioli, Simone; Radici, Emanuela
2018-01-01
We investigate the existence of weak type solutions for a class of aggregation-diffusion PDEs with nonlinear mobility obtained as large particle limit of a suitable nonlocal version of the follow-the-leader scheme, which is interpreted as the discrete Lagrangian approximation of the target continuity equation. We restrict the analysis to nonnegative initial data in $L^{\\infty} \\cap BV$ away from vacuum and supported in a closed interval with zero-velocity boundary conditions. The main novelti...
A strongly nonlinear reaction-diffusion model for a deterministic diffusive epidemic
International Nuclear Information System (INIS)
Kirane, M.; Kouachi, S.
1992-10-01
In the present paper the mathematical validity of a model on the spread of an infectious disease is proved. This model was proposed by Bailey. The mathematical validity is proved by means of a positivity, uniqueness and existence theorem. In spite of the apparent simplicity of the problem, the solution requires a delicate set of techniques. It seems very difficult to extend these techniques to a model in more than one dimension without imposing conditions on the diffusivities. (author). 7 refs
Directory of Open Access Journals (Sweden)
Zhixin Yang
Full Text Available The onset of double diffusive convection in a viscoelastic fluid-saturated porous layer is studied when the fluid and solid phase are not in local thermal equilibrium. The modified Darcy model is used for the momentum equation and a two-field model is used for energy equation each representing the fluid and solid phases separately. The effect of thermal non-equilibrium on the onset of double diffusive convection is discussed. The critical Rayleigh number and the corresponding wave number for the exchange of stability and over-stability are obtained, and the onset criterion for stationary and oscillatory convection is derived analytically and discussed numerically.
Directory of Open Access Journals (Sweden)
Estelle Arbellay
Full Text Available Vessels of broad-leaved trees have been analyzed to study how trees deal with various environmental factors. Cambial injury, in particular, has been reported to induce the formation of narrower conduits. Yet, little or no effort has been devoted to the elaboration of vessel sampling strategies for retrospective injury detection based on vessel lumen size reduction. To fill this methodological gap, four wounded individuals each of grey alder (Alnus incana (L. Moench and downy birch (Betula pubescens Ehrh. were harvested in an avalanche path. Earlywood vessel lumina were measured and compared for each tree between the injury ring built during the growing season following wounding and the control ring laid down the previous year. Measurements were performed along a 10 mm wide radial strip, located directly next to the injury. Specifically, this study aimed at (i investigating the intra-annual duration and local extension of vessel narrowing close to the wound margin and (ii identifying an adequate sample of earlywood vessels (number and intra-ring location of cells attesting to cambial injury. Based on the results of this study, we recommend analyzing at least 30 vessels in each ring. Within the 10 mm wide segment of the injury ring, wound-induced reduction in vessel lumen size did not fade with increasing radial and tangential distances, but we nevertheless advise favoring early earlywood vessels located closest to the injury. These findings, derived from two species widespread across subarctic, mountainous, and temperate regions, will assist retrospective injury detection in Alnus, Betula, and other diffuse-porous species as well as future related research on hydraulic implications after wounding.
A clutter removal method for the Doppler ultrasound signal based on a nonlinear diffusion equation
International Nuclear Information System (INIS)
Li Peng; Xin Pengcheng; Bian Zhengzhong; Yu Gang
2008-01-01
Strong clutter components produced by stationary and slow-moving tissue structures render the lower frequency part of the spectrogram useless and degrade the accuracy of clinical ultrasound indices. An adaptive method based on the nonlinear forward-and-backward diffusion equation (FAB-DE) is proposed to remove strong clutter components from the contaminated Doppler signal. The clutter signal is extracted first by the FAB-DE accurately, in which the nonlinear diffusion coefficient function of the FAB-DE locally adjusts according to signal features and the diffusion adaptively switches between forward and backward mode. The present method has been validated by simulated and realistic pulse wave Doppler signals, and compared with the conventional high pass filter and the matching pursuit method. The simulation results, including spectrogram, mean velocity error, standard deviation of mean velocity and signal-to-clutter ratio of a decontaminated signal, demonstrate that the present FAB-DE method can remove clutter sufficiently and retain more low blood components simultaneously as compared with the other two methods. Results of the realistic Doppler blood signal, including spectrogram and low-frequency part of the spectrum, support the conclusion drawn from simulation cases
Existence of weak solutions to a nonlinear reaction-diffusion system with singular sources
Directory of Open Access Journals (Sweden)
Ida de Bonis
2017-09-01
Full Text Available We discuss the existence of a class of weak solutions to a nonlinear parabolic system of reaction-diffusion type endowed with singular production terms by reaction. The singularity is due to a potential occurrence of quenching localized to the domain boundary. The kind of quenching we have in mind is due to a twofold contribution: (i the choice of boundary conditions, modeling in our case the contact with an infinite reservoir filled with ready-to-react chemicals and (ii the use of a particular nonlinear, non-Lipschitz structure of the reaction kinetics. Our working techniques use fine energy estimates for approximating non-singular problems and uniform control on the set where singularities are localizing.
International Nuclear Information System (INIS)
Liu, Y.; Ecke, R.E.
1999-01-01
We present experimental measurements of a sidewall traveling wave in rotating Rayleigh-Bacute enard convection. The fluid, water with Prandtl number about 6.3, was confined in a 1-cm-high cylindrical cell with radius-to-height ratio Γ=5. We used simultaneous optical-shadowgraph, heat-transport, and local temperature measurements to determine the stability and characteristics of the traveling-wave state for dimensionless rotation rates 60<Ω<420. The state is well described by the one-dimensional complex Ginzburg-Landau (CGL) equation for which the linear and nonlinear coefficients were determined for Ω=274. The Eckhaus-Benjamin-Feir-stability boundary was established and the phase-diffusion coefficient and nonlinear group velocity were determined in the stable regime. Higher-order corrections to the CGL equation were also investigated. copyright 1999 The American Physical Society
Bourg, Ian C; Sposito, Garrison
2010-03-15
In this paper, we address the manner in which the continuum-scale diffusive properties of smectite-rich porous media arise from their molecular- and pore-scale features. Our starting point is a successful model of the continuum-scale apparent diffusion coefficient for water tracers and cations, which decomposes it as a sum of pore-scale terms describing diffusion in macropore and interlayer "compartments." We then apply molecular dynamics (MD) simulations to determine molecular-scale diffusion coefficients D(interlayer) of water tracers and representative cations (Na(+), Cs(+), Sr(2+)) in Na-smectite interlayers. We find that a remarkably simple expression relates D(interlayer) to the pore-scale parameter δ(nanopore) ≤ 1, a constrictivity factor that accounts for the lower mobility in interlayers as compared to macropores: δ(nanopore) = D(interlayer)/D(0), where D(0) is the diffusion coefficient in bulk liquid water. Using this scaling expression, we can accurately predict the apparent diffusion coefficients of tracers H(2)0, Na(+), Sr(2+), and Cs(+) in compacted Na-smectite-rich materials.
Brandt-Pollmann, U; Lebiedz, D; Diehl, M; Sager, S; Schlöder, J
2005-09-01
Theoretical and experimental studies related to manipulation of pattern formation in self-organizing reaction-diffusion processes by appropriate control stimuli become increasingly important both in chemical engineering and cellular biochemistry. In a model study, we demonstrate here exemplarily the application of an efficient nonlinear model predictive control (NMPC) algorithm to real-time optimal feedback control of pattern formation in a bacterial chemotaxis system modeled by nonlinear partial differential equations. The corresponding drift-diffusion model type is representative for many (bio)chemical systems involving nonlinear reaction dynamics and nonlinear diffusion. We show how the computed optimal feedback control strategy exploits the system inherent physical property of wave propagation to achieve desired control aims. We discuss various applications of our approach to optimal control of spatiotemporal dynamics.
Multi-level nonlinear diffusion acceleration method for multigroup transport k-Eigenvalue problems
International Nuclear Information System (INIS)
Anistratov, Dmitriy Y.
2011-01-01
The nonlinear diffusion acceleration (NDA) method is an efficient and flexible transport iterative scheme for solving reactor-physics problems. This paper presents a fast iterative algorithm for solving multigroup neutron transport eigenvalue problems in 1D slab geometry. The proposed method is defined by a multi-level system of equations that includes multigroup and effective one-group low-order NDA equations. The Eigenvalue is evaluated in the exact projected solution space of smallest dimensionality, namely, by solving the effective one- group eigenvalue transport problem. Numerical results that illustrate performance of the new algorithm are demonstrated. (author)
Nonlinear dynamics in flow through unsaturated fractured-porous media: Status and perspectives
Energy Technology Data Exchange (ETDEWEB)
Faybishenko, Boris
2002-11-27
The need has long been recognized to improve predictions of flow and transport in partially saturated heterogeneous soils and fractured rock of the vadose zone for many practical applications, such as remediation of contaminated sites, nuclear waste disposal in geological formations, and climate predictions. Until recently, flow and transport processes in heterogeneous subsurface media with oscillating irregularities were assumed to be random and were not analyzed using methods of nonlinear dynamics. The goals of this paper are to review the theoretical concepts, present the results, and provide perspectives on investigations of flow and transport in unsaturated heterogeneous soils and fractured rock, using the methods of nonlinear dynamics and deterministic chaos. The results of laboratory and field investigations indicate that the nonlinear dynamics of flow and transport processes in unsaturated soils and fractured rocks arise from the dynamic feedback and competition between various nonlinear physical processes along with complex geometry of flow paths. Although direct measurements of variables characterizing the individual flow processes are not technically feasible, their cumulative effect can be characterized by analyzing time series data using the models and methods of nonlinear dynamics and chaos. Identifying flow through soil or rock as a nonlinear dynamical system is important for developing appropriate short- and long-time predictive models, evaluating prediction uncertainty, assessing the spatial distribution of flow characteristics from time series data, and improving chemical transport simulations. Inferring the nature of flow processes through the methods of nonlinear dynamics could become widely used in different areas of the earth sciences.
Nonlinear dynamics in flow through unsaturated fractured porous media: Status and perspectives
International Nuclear Information System (INIS)
Faybishenko, Boris
2002-01-01
The need has long been recognized to improve predictions of flow and transport in partially saturated heterogeneous soils and fractured rock of the vadose zone for many practical applications, such as remediation of contaminated sites, nuclear waste disposal in geological formations, and climate predictions. Until recently, flow and transport processes in heterogeneous subsurface media with oscillating irregularities were assumed to be random and were not analyzed using methods of nonlinear dynamics. The goals of this paper are to review the theoretical concepts, present the results, and provide perspectives on investigations of flow and transport in unsaturated heterogeneous soils and fractured rock, using the methods of nonlinear dynamics and deterministic chaos. The results of laboratory and field investigations indicate that the nonlinear dynamics of flow and transport processes in unsaturated soils and fractured rocks arise from the dynamic feedback and competition between various nonlinear physical processes along with complex geometry of flow paths. Although direct measurements of variables characterizing the individual flow processes are not technically feasible, their cumulative effect can be characterized by analyzing time series data using the models and methods of nonlinear dynamics and chaos. Identifying flow through soil or rock as a nonlinear dynamical system is important for developing appropriate short- and long-time predictive models, evaluating prediction uncertainty, assessing the spatial distribution of flow characteristics from time series data, and improving chemical transport simulations. Inferring the nature of flow processes through the methods of nonlinear dynamics could become widely used in different areas of the earth sciences
Tuan, Nguyen Huy; Van Au, Vo; Khoa, Vo Anh; Lesnic, Daniel
2017-05-01
The identification of the population density of a logistic equation backwards in time associated with nonlocal diffusion and nonlinear reaction, motivated by biology and ecology fields, is investigated. The diffusion depends on an integral average of the population density whilst the reaction term is a global or local Lipschitz function of the population density. After discussing the ill-posedness of the problem, we apply the quasi-reversibility method to construct stable approximation problems. It is shown that the regularized solutions stemming from such method not only depend continuously on the final data, but also strongly converge to the exact solution in L 2-norm. New error estimates together with stability results are obtained. Furthermore, numerical examples are provided to illustrate the theoretical results.
Hu, Weiming; Hu, Ruiguang; Xie, Nianhua; Ling, Haibin; Maybank, Stephen
2014-04-01
In this paper, we propose saliency driven image multiscale nonlinear diffusion filtering. The resulting scale space in general preserves or even enhances semantically important structures such as edges, lines, or flow-like structures in the foreground, and inhibits and smoothes clutter in the background. The image is classified using multiscale information fusion based on the original image, the image at the final scale at which the diffusion process converges, and the image at a midscale. Our algorithm emphasizes the foreground features, which are important for image classification. The background image regions, whether considered as contexts of the foreground or noise to the foreground, can be globally handled by fusing information from different scales. Experimental tests of the effectiveness of the multiscale space for the image classification are conducted on the following publicly available datasets: 1) the PASCAL 2005 dataset; 2) the Oxford 102 flowers dataset; and 3) the Oxford 17 flowers dataset, with high classification rates.
International Nuclear Information System (INIS)
Spasennykh, M.Yu.; Apps, J.A.
1995-05-01
A model is developed describing one dimensional radionuclide transport in porous media coupled with locally reversible radionuclide water-mineral exchange reactions and radioactive decay. Problems are considered in which radionuclide transport by diffusion and infiltration processes occur in cases where radionuclide water-solid interaction are kinetically and thermodynamically controlled. The limits of Sr-90 and Cs-137 migration are calculated over a wide range of the problem variables (infiltration velocity, distribution coefficients, and rate constants of water-mineral radionuclide exchange reactions)
MHD heat and mass diffusion flow by natural convection past a surface embedded in a porous medium
Directory of Open Access Journals (Sweden)
Chaudhary R.C.
2009-01-01
Full Text Available This paper presents an analytical study of the transient hydromagnetic natural convection flow past a vertical plate embedded in a porous medium, taking account of the presence of mass diffusion and fluctuating temperature about time at the plate. The governing equations are solved in closed form by the Laplace-transform technique. The results are obtained for temperature, velocity, penetration distance, Nusselt number and skin-friction. The effects of various parameters are discussed on the flow variables and presented by graphs.
An artificial nonlinear diffusivity method for supersonic reacting flows with shocks
Fiorina, B.; Lele, S. K.
2007-03-01
A computational approach for modeling interactions between shocks waves, contact discontinuities and reactions zones with a high-order compact scheme is investigated. To prevent the formation of spurious oscillations around shocks, artificial nonlinear viscosity [A.W. Cook, W.H. Cabot, A high-wavenumber viscosity for high resolution numerical method, J. Comput. Phys. 195 (2004) 594-601] based on high-order derivative of the strain rate tensor is used. To capture temperature and species discontinuities a nonlinear diffusivity based on the entropy gradient is added. It is shown that the damping of 'wiggles' is controlled by the model constants and is largely independent of the mesh size and the shock strength. The same holds for the numerical shock thickness and allows a determination of the L2 error. In the shock tube problem, with fluids of different initial entropy separated by the diaphragm, an artificial diffusivity is required to accurately capture the contact surface. Finally, the method is applied to a shock wave propagating into a medium with non-uniform density/entropy and to a CJ detonation wave. Multi-dimensional formulation of the model is presented and is illustrated by a 2D oblique wave reflection from an inviscid wall, by a 2D supersonic blunt body flow and by a Mach reflection problem.
International Nuclear Information System (INIS)
Maldonado, G.I.; Turinsky, P.J.
1995-01-01
The determination of the family of optimum core loading patterns for pressurized water reactors (PWRs) involves the assessment of the core attributes for thousands of candidate loading patterns. For this reason, the computational capability to efficiently and accurately evaluate a reactor core's eigenvalue and power distribution versus burnup using a nodal diffusion generalized perturbation theory (GPT) model is developed. The GPT model is derived from the forward nonlinear iterative nodal expansion method (NEM) to explicitly enable the preservation of the finite difference matrix structure. This key feature considerably simplifies the mathematical formulation of NEM GPT and results in reduced memory storage and CPU time requirements versus the traditional response-matrix approach to NEM. In addition, a treatment within NEM GPT can account for localized nonlinear feedbacks, such as that due to fission product buildup and thermal-hydraulic effects. When compared with a standard nonlinear iterative NEM forward flux solve with feedbacks, the NEM GPT model can execute between 8 and 12 times faster. These developments are implemented within the PWR in-core nuclear fuel management optimization code FORMOSA-P, combining the robustness of its adaptive simulated annealing stochastic optimization algorithm with an NEM GPT neutronics model that efficiently and accurately evaluates core attributes associated with objective functions and constraints of candidate loading patterns
International Nuclear Information System (INIS)
Potemki, Valeri G.; Borisevich, Valentine D.; Yupatov, Sergei V.
1996-01-01
This paper describes the the next evolution step in development of the direct method for solving systems of Nonlinear Algebraic Equations (SNAE). These equations arise from the finite difference approximation of original nonlinear partial differential equations (PDE). This method has been extended on the SNAE with three variables. The solving SNAE bases on Reiterating General Singular Value Decomposition of rectangular matrix pencils (RGSVD-algorithm). In contrast to the computer algebra algorithm in integer arithmetic based on the reduction to the Groebner's basis that algorithm is working in floating point arithmetic and realizes the reduction to the Kronecker's form. The possibilities of the method are illustrated on the example of solving the one-dimensional diffusion equation for 3-component model isotope mixture in a ga centrifuge. The implicit scheme for the finite difference equations without simplifying the nonlinear properties of the original equations is realized. The technique offered provides convergence to the solution for the single run. The Toolbox SNAE is developed in the framework of the high performance numeric computation and visualization software MATLAB. It includes more than 30 modules in MATLAB language for solving SNAE with two and three variables. (author)
Basko, D M
2014-02-01
We study the discrete nonlinear Schröinger equation with weak disorder, focusing on the regime when the nonlinearity is, on the one hand, weak enough for the normal modes of the linear problem to remain well resolved but, on the other, strong enough for the dynamics of the normal mode amplitudes to be chaotic for almost all modes. We show that in this regime and in the limit of high temperature, the macroscopic density ρ satisfies the nonlinear diffusion equation with a density-dependent diffusion coefficient, D(ρ) = D(0)ρ(2). An explicit expression for D(0) is obtained in terms of the eigenfunctions and eigenvalues of the linear problem, which is then evaluated numerically. The role of the second conserved quantity (energy) in the transport is also quantitatively discussed.
International Nuclear Information System (INIS)
Wu Rui; Zhu Xun; Liao Qiang; Wang Hong; Ding Yudong; Li Jun; Ye Dingding
2010-01-01
In proton exchange membrane fuel cell (PEMFC) models, oxygen effective diffusivity is the most important parameter to characterize the oxygen transport in the gas diffusion layer (GDL). However, its determination is a challenge due to its complex dependency on GDL structure. In the present study, a three-dimensional network consisting of spherical pores and cylindrical throats is developed and used to investigate the effects of GDL structural parameters on oxygen effective diffusivity under the condition with/without water invasion process. Oxygen transport in the throat is described by Fick's law and water invasion process in the network is simulated using the invasion percolation with trapping algorithm. The simulation results reveal that oxygen effective diffusivity is slightly affected by network size but increases with decreasing the network heterogeneity and with increasing the pore connectivity. Impacts of network anisotropy on oxygen transport are also investigated in this paper. The anisotropic network is constructed by constricting the throats in the through-plane direction with a constriction factor. It is found that water invasion has a more severe negative influence on oxygen transport in an anisotropic network. Finally, two new correlations are introduced to determine the oxygen effective diffusivity for the Toray carbon paper GDLs.
DEFF Research Database (Denmark)
Rolle, Massimo; Muniruzzaman, Muhammad
water are cross-coupled due to the effects of Coulombic interactions. Such effects are illustrated in flow-through experiments in saturated porous media. Simple strong electrolytes (i.e., salts and strong acid solutions) were selected as tracers and their transport was studied under different advection......-dominated conditions in homogeneous and heterogeneous porous media [2-3]. The model-based interpretation of the experimental results is challenging since it requires a multicomponent ionic formulation with an accurate description of local hydrodynamic dispersion and explicitly accounting for the cross-coupling...
Yang, Haijian
2016-12-10
Most existing methods for solving two-phase flow problems in porous media do not take the physically feasible saturation fractions between 0 and 1 into account, which often destroys the numerical accuracy and physical interpretability of the simulation. To calculate the solution without the loss of this basic requirement, we introduce a variational inequality formulation of the saturation equilibrium with a box inequality constraint, and use a conservative finite element method for the spatial discretization and a backward differentiation formula with adaptive time stepping for the temporal integration. The resulting variational inequality system at each time step is solved by using a semismooth Newton algorithm. To accelerate the Newton convergence and improve the robustness, we employ a family of adaptive nonlinear elimination methods as a nonlinear preconditioner. Some numerical results are presented to demonstrate the robustness and efficiency of the proposed algorithm. A comparison is also included to show the superiority of the proposed fully implicit approach over the classical IMplicit Pressure-Explicit Saturation (IMPES) method in terms of the time step size and the total execution time measured on a parallel computer.
Yang, Haijian; Sun, Shuyu; Yang, Chao
2016-01-01
Most existing methods for solving two-phase flow problems in porous media do not take the physically feasible saturation fractions between 0 and 1 into account, which often destroys the numerical accuracy and physical interpretability of the simulation. To calculate the solution without the loss of this basic requirement, we introduce a variational inequality formulation of the saturation equilibrium with a box inequality constraint, and use a conservative finite element method for the spatial discretization and a backward differentiation formula with adaptive time stepping for the temporal integration. The resulting variational inequality system at each time step is solved by using a semismooth Newton algorithm. To accelerate the Newton convergence and improve the robustness, we employ a family of adaptive nonlinear elimination methods as a nonlinear preconditioner. Some numerical results are presented to demonstrate the robustness and efficiency of the proposed algorithm. A comparison is also included to show the superiority of the proposed fully implicit approach over the classical IMplicit Pressure-Explicit Saturation (IMPES) method in terms of the time step size and the total execution time measured on a parallel computer.
Directory of Open Access Journals (Sweden)
Shahid Hasnain
2017-07-01
Full Text Available This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.
Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman
2017-07-01
This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.
Steppe, Kathy; Lemeur, Raoul
2007-01-01
Calibration of a recently developed water flow and storage model based on experimental data for a young diffuse-porous beech tree (Fagus sylvatica L.) and a young ring-porous oak tree (Quercus robur L.) revealed that differences in stem wood anatomy between species strongly affect the calibrated values of the hydraulic model parameters. The hydraulic capacitance (C) of the stem storage tissue was higher in oak than in beech (939.8 versus 212.3 mg MPa(-1)). Model simulation of the elastic modulus (epsilon) revealed that this difference was linked to the higher elasticity of the stem storage tissue of oak compared with beech. Furthermore, the hydraulic resistance (R (x)) of beech was about twice that of oak (0.1829 versus 0.1072 MPa s mg(-1)). To determine the physiological meaning of the R (x) parameter identified by model calibration, we analyzed the stem wood anatomy of the beech and oak trees. Calculation of stem specific hydraulic conductivity (k (s)) of beech and oak with the Hagen-Poiseuille equation confirmed the differences in R (x) predicted by the model. The contributions of different vessel diameter classes to the total hydraulic conductivity of the xylem were calculated. As expected, the few big vessels contributed much more to total conductivity than the many small vessels. Compared with beech, the larger vessels of oak resulted in a higher k (s) (10.66 versus 4.90 kg m(-1) s(-1) MPa(-1)). The calculated ratio of k (s) of oak to beech was 2, confirming the R (x) ratio obtained by model calibration. Thus, validation of the R (x) parameter of the model led to identification of its physiological meaning.
Identification of Water Diffusivity of Inorganic Porous Materials Using Evolutionary Algorithms
Czech Academy of Sciences Publication Activity Database
Kočí, J.; Maděra, J.; Jerman, M.; Keppert, M.; Svora, Petr; Černý, R.
2016-01-01
Roč. 113, č. 1 (2016), s. 51-66 ISSN 0169-3913 Institutional support: RVO:61388980 Keywords : Evolutionary algorithms * Water transport * Inorganic porous materials * Inverse analysis Subject RIV: CA - Inorganic Chemistry Impact factor: 2.205, year: 2016
Carrillo, J. A.; Desvillettes, L.; Fellner, K.
2009-01-01
Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [5], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters. © Taylor & Francis Group, LLC.
Carrillo, J. A.
2009-10-30
Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [5], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters. © Taylor & Francis Group, LLC.
Energy Technology Data Exchange (ETDEWEB)
Tartakovsky, Daniel
2013-08-30
We developed new CDF and PDF methods for solving non-linear stochastic hyperbolic equations that does not rely on linearization approximations and allows for rigorous formulation of the boundary conditions.
Higher-order Solution of Stochastic Diffusion equation with Nonlinear Losses Using WHEP technique
El-Beltagy, Mohamed A.; Al-Mulla, Noah
2014-01-01
Using Wiener-Hermite expansion with perturbation (WHEP) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. The Wiener-Hermite expansion is the only known expansion that handles the white/colored noise exactly. The main statistics, such as the mean, covariance, and higher order statistical moments, can be calculated by simple formulae involving only the deterministic Wiener-Hermite coefficients. In this poster, the WHEP technique is used to solve the 2D diffusion equation with nonlinear losses and excited with white noise. The solution will be obtained numerically and will be validated and compared with the analytical solution that can be obtained from any symbolic mathematics package such as Mathematica.
Nonlinear drift-diffusion model of gating in K and nACh ion channels
Energy Technology Data Exchange (ETDEWEB)
Vaccaro, S.R. [Department of Physics, University of Adelaide, Adelaide, South Australia 5005 (Australia)], E-mail: svaccaro@physics.adelaide.edu.au
2007-09-03
The configuration of a sensor regulates the transition between the closed and open states of both voltage and ligand gated channels. The closed state dwell-time distribution f{sub c}(t) derived from a Fokker-Planck equation with a nonlinear diffusion coefficient is in good agreement with experimental data and can account for the power law approximation to f{sub c}(t) for a delayed rectifier K channel and a nicotinic acetylcholine (nACh) ion channel. The solution of a master equation which approximates the Fokker-Planck equation provides a better description of the small time behaviour of the dwell-time distribution and can account for the empirical rate-amplitude correlation for these ion channels.
Higher-order Solution of Stochastic Diffusion equation with Nonlinear Losses Using WHEP technique
El-Beltagy, Mohamed A.
2014-01-06
Using Wiener-Hermite expansion with perturbation (WHEP) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. The Wiener-Hermite expansion is the only known expansion that handles the white/colored noise exactly. The main statistics, such as the mean, covariance, and higher order statistical moments, can be calculated by simple formulae involving only the deterministic Wiener-Hermite coefficients. In this poster, the WHEP technique is used to solve the 2D diffusion equation with nonlinear losses and excited with white noise. The solution will be obtained numerically and will be validated and compared with the analytical solution that can be obtained from any symbolic mathematics package such as Mathematica.
A synchrotron radiation study of nonlinear diffusion in Cu-Au
International Nuclear Information System (INIS)
Menon, E.S.K.; Huang, P.; Kraitchman, M.; deFontaine, D.; Hoyt, J.J.; Chow, P.
1992-01-01
This paper reports a study in which alternate layers of pure copper and gold were vapor deposited on a sodium chloride substrate, the average concentration of the films being Cu-16 at% Au and the layering periodicity (modulation wavelength) being 3.31 nm. The composition modulation gives rise to satellite diffraction peaks around the (200) Bragg reelections. Synchrotron radiation at SSRL was able to detect u to third order satellite intensity the evolution of which was measured as a function of annealing time at 515 K. although the first order satellite intensity decayed as expected exponentially with time, intensities of both second and third order satellites decreased very rapidly at first, then increased before decaying exponentially. These results are in conformity with theoretical models of satellite evolution during annealing in a one-dimensional modulated system governed by a nonlinear diffusion equation
Umari, P; Marzari, Nicola
2009-09-07
We calculate the linear and nonlinear susceptibilities of periodic longitudinal chains of hydrogen dimers with different bond-length alternations using a diffusion quantum Monte Carlo approach. These quantities are derived from the changes in electronic polarization as a function of applied finite electric field--an approach we recently introduced and made possible by the use of a Berry-phase, many-body electric-enthalpy functional. Calculated susceptibilities and hypersusceptibilities are found to be in excellent agreement with the best estimates available from quantum chemistry--usually extrapolations to the infinite-chain limit of calculations for chains of finite length. It is found that while exchange effects dominate the proper description of the susceptibilities, second hypersusceptibilities are greatly affected by electronic correlations. We also assess how different approximations to the nodal surface of the many-body wave function affect the accuracy of the calculated susceptibilities.
International Nuclear Information System (INIS)
Leaf, G.K.; Minkoff, M.
1982-01-01
1 - Description of problem or function: DISPL1 is a software package for solving second-order nonlinear systems of partial differential equations including parabolic, elliptic, hyperbolic, and some mixed types. The package is designed primarily for chemical kinetics- diffusion problems, although not limited to these problems. Fairly general nonlinear boundary conditions are allowed as well as inter- face conditions for problems in an inhomogeneous medium. The spatial domain is one- or two-dimensional with rectangular Cartesian, cylindrical, or spherical (in one dimension only) geometry. 2 - Method of solution: The numerical method is based on the use of Galerkin's procedure combined with the use of B-Splines (C.W.R. de-Boor's B-spline package) to generate a system of ordinary differential equations. These equations are solved by a sophisticated ODE software package which is a modified version of Hindmarsh's GEAR package, NESC Abstract 592. 3 - Restrictions on the complexity of the problem: The spatial domain must be rectangular with sides parallel to the coordinate geometry. Cross derivative terms are not permitted in the PDE. The order of the B-Splines is at most 12. Other parameters such as the number of mesh points in each coordinate direction, the number of PDE's etc. are set in a macro table used by the MORTRAn2 preprocessor in generating the object code
Influence of radiation on double conjugate diffusion in a porous cavity
International Nuclear Information System (INIS)
Azeem,; Idris, Mohd Yamani Idna; Khan, T. M. Yunus; Badruddin, Irfan Anjum; Nik-Ghazali, N.
2016-01-01
The current work highlights the effect of radiation on the conjugate heat and mass transfer in a square porous cavity having a solid wall. The solid wall is placed at the center of cavity. The left surface of cavity is maintained at higher temperature T_w and concentration C_w whereas the right surface is maintained at T_c and C_c such that T_w>T_c and Cw>Cc. The top and bottom surfaces are adiabatic. The governing equations are solved with the help of finite element method by making use of triangular elements. The results are discussed with respect to two different heights of solid wall inside the porous medium along with the radiation parameter.
Influence of radiation on double conjugate diffusion in a porous cavity
Energy Technology Data Exchange (ETDEWEB)
Azeem,; Idris, Mohd Yamani Idna [Dept. of Computer System & Technology, University of Malaya, Kuala Lumpur (Malaysia); Khan, T. M. Yunus, E-mail: yunus.tatagar@gmail.com [Dept. of Mechanical Engineering, University of Malaya, Kuala Lumpur, 50603 (Malaysia); Dept. of Mechanical Engineering, BVB College of Engineering & Technology, Hubli (India); Badruddin, Irfan Anjum, E-mail: irfan-magami@Rediffmail.com; Nik-Ghazali, N. [Dept. of Mechanical Engineering, University of Malaya, Kuala Lumpur, 50603 (Malaysia)
2016-05-06
The current work highlights the effect of radiation on the conjugate heat and mass transfer in a square porous cavity having a solid wall. The solid wall is placed at the center of cavity. The left surface of cavity is maintained at higher temperature T{sub w} and concentration C{sub w} whereas the right surface is maintained at T{sub c} and C{sub c} such that T{sub w}>T{sub c} and Cw>Cc. The top and bottom surfaces are adiabatic. The governing equations are solved with the help of finite element method by making use of triangular elements. The results are discussed with respect to two different heights of solid wall inside the porous medium along with the radiation parameter.
Modeling and simulation of liquid diffusion through a porous finitely elastic solid
Zhao, Qiangsheng
2013-01-29
A new theory is proposed for the continuum modeling of liquid flow through a porous elastic solid. The solid and the voids are assumed to jointly constitute the macroscopic solid phase, while the liquid volume fraction is included as a separate state variable. A finite element implementation is employed to assess the predictive capacity of the proposed theory, with particular emphasis on the mechanical response of Nafion® membranes to the flow of water. © 2013 Springer-Verlag Berlin Heidelberg.
Directory of Open Access Journals (Sweden)
Goyal M.
2017-12-01
Full Text Available In this paper, triple diffusive natural convection under Darcy flow over an inclined plate embedded in a porous medium saturated with a binary base fluid containing nanoparticles and two salts is studied. The model used for the nanofluid is the one which incorporates the effects of Brownian motion and thermophoresis. In addition, the thermal energy equations include regular diffusion and cross-diffusion terms. The vertical surface has the heat, mass and nanoparticle fluxes each prescribed as a power law function of the distance along the wall. The boundary layer equations are transformed into a set of ordinary differential equations with the help of group theory transformations. A wide range of parameter values are chosen to bring out the effect of buoyancy ratio, regular Lewis number and modified Dufour parameters of both salts and nanofluid parameters with varying angle of inclinations. The effects of parameters on the velocity, temperature, solutal and nanoparticles volume fraction profiles, as well as on the important parameters of heat and mass transfer, i.e., the reduced Nusselt, regular and nanofluid Sherwood numbers, are discussed. Such problems find application in extrusion of metals, polymers and ceramics, production of plastic films, insulation of wires and liquid packaging.
Saito, Takahiro; Takahashi, Hiromi; Komatsu, Takashi
2006-02-01
The Retinex theory was first proposed by Land, and deals with separation of irradiance from reflectance in an observed image. The separation problem is an ill-posed problem. Land and others proposed various Retinex separation algorithms. Recently, Kimmel and others proposed a variational framework that unifies the previous Retinex algorithms such as the Poisson-equation-type Retinex algorithms developed by Horn and others, and presented a Retinex separation algorithm with the time-evolution of a linear diffusion process. However, the Kimmel's separation algorithm cannot achieve physically rational separation, if true irradiance varies among color channels. To cope with this problem, we introduce a nonlinear diffusion process into the time-evolution. Moreover, as to its extension to color images, we present two approaches to treat color channels: the independent approach to treat each color channel separately and the collective approach to treat all color channels collectively. The latter approach outperforms the former. Furthermore, we apply our separation algorithm to a high quality chroma key in which before combining a foreground frame and a background frame into an output image a color of each pixel in the foreground frame are spatially adaptively corrected through transformation of the separated irradiance. Experiments demonstrate superiority of our separation algorithm over the Kimmel's separation algorithm.
Fellner, Klemens; Tang, Bao Quoc
2018-06-01
The convergence to equilibrium for renormalised solutions to nonlinear reaction-diffusion systems is studied. The considered reaction-diffusion systems arise from chemical reaction networks with mass action kinetics and satisfy the complex balanced condition. By applying the so-called entropy method, we show that if the system does not have boundary equilibria, i.e. equilibrium states lying on the boundary of R_+^N, then any renormalised solution converges exponentially to the complex balanced equilibrium with a rate, which can be computed explicitly up to a finite-dimensional inequality. This inequality is proven via a contradiction argument and thus not explicitly. An explicit method of proof, however, is provided for a specific application modelling a reversible enzyme reaction by exploiting the specific structure of the conservation laws. Our approach is also useful to study the trend to equilibrium for systems possessing boundary equilibria. More precisely, to show the convergence to equilibrium for systems with boundary equilibria, we establish a sufficient condition in terms of a modified finite-dimensional inequality along trajectories of the system. By assuming this condition, which roughly means that the system produces too much entropy to stay close to a boundary equilibrium for infinite time, the entropy method shows exponential convergence to equilibrium for renormalised solutions to complex balanced systems with boundary equilibria.
Error estimates for the finite volume discretization for the porous medium equation
Pop, I.S.; Sepúlveda, M.; Radu, F.A.; Vera Villagrán, O.P.
2010-01-01
We analyze the convergence of a numerical scheme for a class of degenerate parabolic problems modelling reactions in porous media, and involving a nonlinear, possibly vanishing diffusion. The scheme involves the Kirchhoff transformation of the regularized nonlinearity, as well as an Euler implicit
International Nuclear Information System (INIS)
Grebenkov, Denis S.; Nguyen, Hang T.; Li, Jing-Rebecca
2013-01-01
A fast random walk (FRW) algorithm is adapted to compute diffusion-weighted NMR signals in a Menger sponge which is formed by multiple channels of broadly distributed sizes and often considered as a model for soils and porous materials. The self-similar structure of a Menger sponge allows for rapid simulations that were not feasible by other numerical techniques. The role of multiple length scales on diffusion-weighted NMR signals is investigated. (authors)
Directory of Open Access Journals (Sweden)
Pratibha Joshi
2014-12-01
Full Text Available In this paper, we have achieved high order solution of a three dimensional nonlinear diffusive-convective problem using modified variational iteration method. The efficiency of this approach has been shown by solving two examples. All computational work has been performed in MATHEMATICA.
Porous silicon used as an oxide diffusion mask to produce a periodic micro doped n{sup ++}/n regions
Energy Technology Data Exchange (ETDEWEB)
Dimassi, Wissem; Jafel, Hayet; Lajnef, Mohamed; Ali Kanzari, M.; Bouaicha, Mongi; Bessais, Brahim; Ezzaouia, Hatem [Laboratoire de Photovoltaique, Centre de Recherche et des Technologies de l' Energie, PB: 95, Hammam Lif 2050 (Tunisia)
2011-06-15
The realization of screen-printed contacts on silicon solar cells requires highly doped regions under the fingers and lowly doped and thin ones between them. In this work, we present a low-cost approach to fabricate selective emitter (n{sup ++}/n doped silicon regions), using oxidized porous silicon (ox-PS) as a mask. Micro-periodic fingers were opened on the porous silicon layer using a micro groove machining process. Optimized phosphorous diffusion through the micro grooved ox-PS let us obtain n{sup ++} doped regions in opened zones and n doped large regions underneath the ox-PS layer. The dark I-V characteristics of the obtained device and Fourier transform infrared (FTIR) spectroscopy investigations of the PS layer show the possibility to use PS as a dielectric layer. The Light Beam Induced Current (LBIC) mapping of the realized device, confirm the presence of a micro periodic n{sup ++}/n type structure. (copyright 2011 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Directory of Open Access Journals (Sweden)
Bég Anwar O.
2014-01-01
Full Text Available A mathematical model is presented for viscous hydromagnetic flow through a hybrid non-Darcy porous media rotating generator. The system is simulated as steady, incompressible flow through a nonlinear porous regime intercalated between parallel plates of the generator in a rotating frame of reference in the presence of a strong, inclined magnetic field A pressure gradient term is included which is a function of the longitudinal coordinate. The general equations for rotating viscous magnetohydrodynamic flow are presented and neglecting convective acceleration effects, the two-dimensional viscous flow equations are derived incorporating current density components, porous media drag effects, Lorentz drag force components and Hall current effects. Using an appropriate group of dimensionless variables, the momentum equations for primary and secondary flow are rendered nondimensional and shown to be controlled by six physical parameters-Hartmann number (Ha, Hall current parameter (Nh, Darcy number (Da, Forchheimer number (Fs, Ekman number (Ek and dimensionless pressure gradient parameter (Np, in addition to one geometric parameter-the orientation of the applied magnetic field (θ . Several special cases are extracted from the general model, including the non-porous case studied earlier by Ghosh and Pop (2006. A numerical solution is presented to the nonlinear coupled ordinary differential equations using both the Network Simulation Method and Finite Element Method, achieving excellent agreement. Additionally very good agreement is also obtained with the earlier analytical solutions of Ghosh and Pop (2006. for selected Ha, Ek and Nh values. We examine in detail the effects of magnetic field, rotation, Hall current, bulk porous matrix drag, second order porous impedance, pressure gradient and magnetic field inclination on primary and secondary velocity distributions and also frictional shear stresses at the plates. Primary velocity is seen to decrease
Qin, C.; Hassanizadeh, S.M.; van Oosterhout, L.M.
2016-01-01
In the cathode side of a polymer electrolyte fuel cell (PEFC), a micro porous layer (MPL) added between the catalyst layer (CL) and the gas diffusion layer (GDL) plays an important role in water management. In this work, by using both quasi-static and dynamic pore-network models, water and vapor
Nonlinear optical susceptibilities in the diffusion modified AlxGa1-xN/GaN single quantum well
Das, T.; Panda, S.; Panda, B. K.
2018-05-01
Under thermal treatment of the post growth AlGaN/GaN single quantum well, the diffusion of Al and Ga atoms across the interface is expected to form the diffusion modified quantum well with diffusion length as a quantitative parameter for diffusion. The modification of confining potential and position-dependent effective mass in the quantum well due to diffusion is calculated taking the Fick's law. The built-in electric field which arises from spontaneous and piezoelectric polarizations in the wurtzite structure is included in the effective mass equation. The electronic states are calculated from the effective mass equation using the finite difference method for several diffusion lengths. Since the effective well width decreases with increasing diffusion length, the energy levels increase with it. The intersubband energy spacing in the conduction band decreases with diffusion length due to built-in electric field and reduction of effective well width. The linear susceptibility for first-order and the nonlinear second-order and third-order susceptibilities are calculated using the compact density matrix approach taking only two levels. The calculated susceptibilities are red shifted with increase in diffusion lengths due to decrease in intersubband energy spacing.
Transient diffusion from a waste solid into water-saturated, fractured porous rock
International Nuclear Information System (INIS)
Ahn, J.; Chambre, P.L.; Pigford, T.H.; Lee, W.W.-L.
1989-09-01
Numerical illustrations for transient mass transfer from an infinitely long cylinder intersected by a planar fracture are shown based on Chambre's exact analytical solutions. The concentration at the cylinder surface is maintained at the solubility. In the fracture contaminant diffuses in the radial direction. In the rock matrix three-dimensional diffusion is assumed in the cylindrical coordinate. No advection is assumed. Radioactive decay and sorption equilibrium are included. Radioactive decay enhances the mass transfer from the cylinder. Due to the presence of the fracture, the mass flux from the cylinder to the rock matrix becomes smaller, but the fracture effect is limited in the vicinity of the fracture in early times. Even though the fracture is assumed to be a faster diffusion path than the rock matrix, the larger waste surface exposed to the matrix and the greater assumed matrix sorption result in greater release rate to the matrix than to the fracture. 8 refs., 4 figs
Energy Technology Data Exchange (ETDEWEB)
Lee, Shiu-Hang; Kamae, Tuneyoshi; Ellison, Donald C.
2008-07-02
We present a 3-dimensional model of supernova remnants (SNRs) where the hydrodynamical evolution of the remnant is modeled consistently with nonlinear diffusive shock acceleration occurring at the outer blast wave. The model includes particle escape and diffusion outside of the forward shock, and particle interactions with arbitrary distributions of external ambient material, such as molecular clouds. We include synchrotron emission and cooling, bremsstrahlung radiation, neutral pion production, inverse-Compton (IC), and Coulomb energy-loss. Boardband spectra have been calculated for typical parameters including dense regions of gas external to a 1000 year old SNR. In this paper, we describe the details of our model but do not attempt a detailed fit to any specific remnant. We also do not include magnetic field amplification (MFA), even though this effect may be important in some young remnants. In this first presentation of the model we don't attempt a detailed fit to any specific remnant. Our aim is to develop a flexible platform, which can be generalized to include effects such as MFA, and which can be easily adapted to various SNR environments, including Type Ia SNRs, which explode in a constant density medium, and Type II SNRs, which explode in a pre-supernova wind. When applied to a specific SNR, our model will predict cosmic-ray spectra and multi-wavelength morphology in projected images for instruments with varying spatial and spectral resolutions. We show examples of these spectra and images and emphasize the importance of measurements in the hard X-ray, GeV, and TeV gamma-ray bands for investigating key ingredients in the acceleration mechanism, and for deducing whether or not TeV emission is produced by IC from electrons or pion-decay from protons.
Stability, diffusion and interactions of nonlinear excitations in a many body system
Coste, Christophe; Jean, Michel Saint; Dessup, Tommy
2017-04-01
When repelling particles are confined in a quasi-one-dimensional trap by a transverse potential, a configurational phase transition happens. All particles are aligned along the trap axis at large confinement, but below a critical transverse confinement they adopt a staggered row configuration (zigzag phase). This zigzag transition is a subcritical pitchfork bifurcation in extended systems and in systems with cyclic boundary conditions in the longitudinal direction. Among many evidences, phase coexistence is exhibited by localized nonlinear patterns made of a zigzag phase embedded in otherwise aligned particles. We give the normal form at the bifurcation and we show that these patterns can be described as solitary wave envelopes that we call bubbles. They are stable in a large temperature range and can diffuse as quasi-particles, with a diffusion coefficient that may be deduced from the normal form. The potential energy of a bubble is found to be lower than that of the homogeneous bifurcated phase, which explains their stability. We observe also metastable states, that are pairs of solitary wave envelopes which spontaneously evolve toward a stable single bubble. We evidence a strong effect of the discreteness of the underlying particles system and introduce the concept of topological frustration of a bubble pair. A configuration is frustrated when the particles between the two bubbles are not organized in a modulated staggered row. For a nonfrustrated (NF) bubble pair configuration, the bubbles interaction is attractive so that the bubbles come closer and eventually merge as a single bubble. In contrast, the bubbles interaction is found to be repulsive for a frustrated (F) configuration. We describe a model of interacting solitary wave that provides all qualitative characteristics of the interaction force: it is attractive for NF-systems, repulsive for F-systems, and decreases exponentially with the bubbles distance.
Application of nonlinear nodal diffusion method for a small research reactor
International Nuclear Information System (INIS)
Jaradat, Mustafa K.; Alawneh, Luay M.; Park, Chang Je; Lee, Byungchul
2014-01-01
Highlights: • We applied nonlinear unified nodal method for 10 MW IAEA MTR benchmark problem. • TRITION–NEWT system was used to obtain two-group burnup dependent cross sections. • The criticality and power distribution compared with reference (IAEA-TECDOC-233). • Comparison between different fuel materials was conducted. • Satisfactory results were provided using UNM for MTR core calculations. - Abstract: Nodal diffusion methods are usually used for LWR calculations and rarely used for research reactor calculations. A unified nodal method with an implementation of the coarse mesh finite difference acceleration was developed for use in plate type research reactor calculations. It was validated for two PWR benchmark problems and then applied for IAEA MTR benchmark problem for static calculations to check the validity and accuracy of the method. This work was conducted to investigate the unified nodal method capability to treat material testing reactor cores. A 10 MW research reactor core is considered with three calculation cases for low enriched uranium fuel depending on the core burnup status of fresh, beginning-of-life, and end-of-life cores. The validation work included criticality calculations, flux distribution, and power distribution; in addition, a comparison between different fuel materials with the same uranium content was conducted. The homogenized two-group cross sections were generated using the TRITON–NEWT system. The results were compared with a reference, which was taken from IAEA-TECDOC-233. The unified nodal method provides satisfactory results for an all-rod out case, and the three-dimensional, two-group diffusion model can be considered accurate enough for MTR core calculations
International Nuclear Information System (INIS)
Basko, D.M.
2011-01-01
Research highlights: → In a one-dimensional disordered chain of oscillators all normal modes are localized. → Nonlinearity leads to chaotic dynamics. → Chaos is concentrated on rare chaotic spots. → Chaotic spots drive energy exchange between oscillators. → Macroscopic transport coefficients are obtained. - Abstract: The subject of this study is the long-time equilibration dynamics of a strongly disordered one-dimensional chain of coupled weakly anharmonic classical oscillators. It is shown that chaos in this system has a very particular spatial structure: it can be viewed as a dilute gas of chaotic spots. Each chaotic spot corresponds to a stochastic pump which drives the Arnold diffusion of the oscillators surrounding it, thus leading to their relaxation and thermalization. The most important mechanism of equilibration at long distances is provided by random migration of the chaotic spots along the chain, which bears analogy with variable-range hopping of electrons in strongly disordered solids. The corresponding macroscopic transport equations are obtained.
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Inci Cilingir Sungu
2015-01-01
Full Text Available A new application of the hybrid generalized differential transform and finite difference method is proposed by solving time fractional nonlinear reaction-diffusion equations. This method is a combination of the multi-time-stepping temporal generalized differential transform and the spatial finite difference methods. The procedure first converts the time-evolutionary equations into Poisson equations which are then solved using the central difference method. The temporal differential transform method as used in the paper takes care of stability and the finite difference method on the resulting equation results in a system of diagonally dominant linear algebraic equations. The Gauss-Seidel iterative procedure then used to solve the linear system thus has assured convergence. To have optimized convergence rate, numerical experiments were done by using a combination of factors involving multi-time-stepping, spatial step size, and degree of the polynomial fit in time. It is shown that the hybrid technique is reliable, accurate, and easy to apply.
International Nuclear Information System (INIS)
Chierice, G.O.
1974-01-01
The diffusion coefficient is one of the parameters necessary for the obtention of the extraction exponential coefficients, that are contained within the H.T.U. (height of transfer unity) calculation expression, when operating with continuous organic phase. The organic phase used was tri-n-butyl-phosphate (TBP) and varsol in the 35% and 65% proportions respectively. After each experiment, the uranium content present in each compartment was spectrophotometrically determined and the quantities contained in the aqueous phases were determined by means of volumetric titration. It was found out that the uranyl ion diffusion coefficient is two and one half times less in organic phase, this just being attributed to the greater interactions of the uranyl ions in organic than in aqueous medium
El-Amin, Mohamed
2017-08-29
Purpose In this paper, we introduce modeling, numerical simulation, and convergence analysis of the problem nanoparticles transport carried by a two-phase flow in a porous medium. The model consists of equations of pressure, saturation, nanoparticles concentration, deposited nanoparticles concentration on the pore-walls, and entrapped nanoparticles concentration in pore-throats. Design/methodology/approach Nonlinear iterative IMPES-IMC (IMplicit Pressure Explicit Saturation–IMplicit Concentration) scheme is used to solve the problem under consideration. The governing equations are discretized using the cell-centered finite difference (CCFD) method. The pressure and saturation equations are coupled to calculate the pressure, then the saturation is updated explicitly. Therefore, the equations of nanoparticles concentration, the deposited nanoparticles concentration on the pore walls and the entrapped nanoparticles concentration in pore throats are computed implicitly. Then, the porosity and the permeability variations are updated. Findings We stated and proved three lemmas and one theorem for the convergence of the iterative method under the natural conditions and some continuity and boundedness assumptions. The theorem is proved by induction states that after a number of iterations the sequences of the dependent variables such as saturation and concentrations approach solutions on the next time step. Moreover, two numerical examples are introduced with convergence test in terms of Courant–Friedrichs–Lewy (CFL) condition and a relaxation factor. Dependent variables such as pressure, saturation, concentration, deposited concentrations, porosity and permeability are plotted as contours in graphs, while the error estimations are presented in table for different values of number of time steps, number of iterations and mesh size. Research limitations/implications The domain of the computations is relatively small however, it is straightforward to extend this method
International Nuclear Information System (INIS)
Fichot, Floriana; Duval, Fabiena; Garcia, Aureliena; Belloni, Julien; Quintard, Michel
2005-01-01
Full text of publication follows: In the framework of its research programme on severe nuclear reactor accidents, IRSN investigates the water flooding of an overheated porous bed, where complex two-phase flows are likely to exist. The goal is to describe the flow with a general model, covering rods and debris beds regions in the vessel. A better understanding of the flow at the pore level appears to be necessary in order to justify and improve closure laws of macroscopic models. Although the Direct Numerical Simulation (DNS) of two-phase flows is possible with several methods, applications are now limited to small computational domains, typically of the order of a few centimeters. Therefore, numerical solutions at the reactor scale can only be obtained by using averaged models. Volume averaging is the most traditional way of deriving such models. For nuclear safety codes, a control volume must include a few rods or a few debris particles, with a characteristic dimension of a few centimeters. The difficulty usually met with averaged models is the closure of several transport or source terms which appear in the averaged conservation equations (for example the interfacial drag or the heat transfers between phases) [2]. In the past, the closure of these terms was obtained, when possible, from one-dimensional experiments that allowed measurements of heat flux or pressure drops. For more complex flows, the experimental measurement of local parameters is often impossible and the effective properties cannot be determined easily. An alternative way is to perform 'numerical experiments' with numerical simulations of the local flow. As mentioned above, the domain of application of DNS corresponds to the size of control volumes necessary to derive averaged models. Therefore DNS appears as a powerful tool to investigate the local features of a two-phase flow in complex geometries. Diffuse interface methods provide a way to model flows with interfacial phenomena through an
International Nuclear Information System (INIS)
Kontorovich, V.M.; Kochanov, A.E.
1980-01-01
It is demonstrated that in the case of hard injection of relativistic electrons accompanied by the joint action of synchrotron (Compton) losses and energy-dependent spatial diffusion, a spectrum with 'breaks' is formed containing universal (with index γ = 2) and diffusion regions, both independent of the injection spectrum. The effect from non-linearity of the electron spectrum is considered in averaged electromagnetic spectra for various geometries of sources (sphere, disk, arm). It is shown that an universal region (with index α = 0.5) can occur in the radiation spectrum. (orig.)
International Nuclear Information System (INIS)
Vu, T.H.
2009-10-01
This thesis documents the relationship between the porous microstructure of cement based materials and theirs gaseous diffusivity properties relative to the aqueous phase location and the global saturation level of the material. The materials studied are cement pastes and mortars. To meet the thesis objective, the materials are characterized in detail by means of several experimental methods: mercury intrusion porosimetry, water porosimetry, thermo-poro-metry, nitrogen sorption and water desorption. In addition, diffusion tests realized on materials maintained in controlled humidity chambers allow obtaining the effective hydrogen diffusivity as function of the microstructure and the saturation state of material with a gas chromatography. The experimental results are then used as a data base that is compared to a modeling approach. The model developed consists of a combination of ordinary diffusion (Fick regime) and Knudsen diffusion of hydrogen. The model also accounts for the effects of the liquid curtains, the impact of tortuosity on gas diffusion, and the saturation level of the porous system. (author)
Xia, Ya-Rong; Zhang, Shun-Li; Xin, Xiang-Peng
2018-03-01
In this paper, we propose the concept of the perturbed invariant subspaces (PISs), and study the approximate generalized functional variable separation solution for the nonlinear diffusion-convection equation with weak source by the approximate generalized conditional symmetries (AGCSs) related to the PISs. Complete classification of the perturbed equations which admit the approximate generalized functional separable solutions (AGFSSs) is obtained. As a consequence, some AGFSSs to the resulting equations are explicitly constructed by way of examples.
Tan, Xiaoyu
2016-05-18
In the last decade, many attempts were made to put metal organic frameworks (MOFs) in industrial applications, but most of these efforts weren’t successfully. As one of the few MOFs produced on industrial scale, ZIF-8 has interesting pore size, huge internal surface area and great thermal and chemical stability. Therefore, ZIF-8 might become the first MOF, which will be applied in industrial separation processes. In this thesis, a synthesis study is presented, which leads to a cheap and convenient way to fabricate defect-free and thin ZIF-8 membranes on porous polymeric supports showing high selectivity and high gas permeance. The ZIF-8 layers were produced via a contra-diffusion method. Several polymeric membranes were employed as support in this study, such as PAN, PEI, PSU, PA and PTSC. We studied the influence of the polymeric support properties for the ZIF-8 membrane preparation and optimized the ZIF-8 preparation conditions. The ZIF-8 membranes were characterized via scanning electron microscopy (SEM) and X-ray diffraction (XRD). For gas permeation test, we chose a Wicke-Kallenbach apparatus to measure membrane’s gas permeance and selectivity. One of the best ZIF-8 membranes exhibited a hydrogen permeance of 3.45 × 10-8 mol m-2 s-1 Pa-1 and an ideal selectivity of hydrogen over propane of about 500.
Growth of fingers at an unstable diffusing interface in a porous medium or hele-shaw cell
Energy Technology Data Exchange (ETDEWEB)
Wooding, R A
1969-11-27
Waves at an unstable horizontal interface, between 2 fluids moving vertically through a saturated porous medium, are observed to grow rapidly to become fingers (i.e., the amplitude greatly exceeds the wavelength). For a diffusing interface, in experiments using a Hele-Shaw cell, the mean amplitude taken over many fingers grows approx. as (time)U2D, followed by a transition to a growth proportional to time. Correspondingly, the mean wave number decreases approx. as (time)U-1/2D. Because of the rapid increase in amplitude, longitudinal dispersion ultimately becomes negligible relative to wave growth. To represent the observed quantities at large time, the transport equation is suitably weighted and averaged over the horizontal plane. Hyperbolic equations result, and the ascending and descending zones containing the fronts of the fingers are replaced by discontinuities. These averaged equations form an open set, but closure is achieved by assuming a law for the mean wave number based on similarity. (22 refs.)
International Nuclear Information System (INIS)
Chagneau, Aurelie; Claret, Francis; Made, Benoit; Tuckermann, Juergen; Enzmann, Frieder; Schaefer, Thorsten
2012-01-01
Document available in extended abstract form only. The main objective of the present study is to characterize the evolution of diffusion properties of porous materials as influenced by porosity changes. When under geochemical perturbation, the rocks porosity evolves with dissolution/precipitation processes. The impact of changes in porosity on the diffusion phenomena are implemented in most geochemical models using Archie's law: D e /D 0 = ε m where D e and D 0 are the effective diffusivity and the diffusivity of the element in water in m 2 s -1 , respectively, e is the overall porosity and m is the cementation factor. The factor m is a function of pores geometry and compaction. Depending on the rock considered, its value ranges from 1 to 3. Moreover, as the porosity decreases the connectivity of pores changes. At low overall porosity, the effective porosity is the determining parameter affecting effective diffusivity. Therefore, the Archie's law needs to be modified to accurately predict geochemical migration of pollutants such as radio-elements in a dynamic system. Our experimental approach is divided in two complementary parts: (i) diffusion experiments conducted in hot-laboratory using radiotracers and (ii) time-dependant monitoring of porosity evolution in three dimensions using computed tomography (CT). For the two approaches, simplified systems are used to define the co-evolution of porosity and diffusivity using a minimum number of parameters, in order to optimize the understanding of the basics and determining processes. For this purpose, three materials are used in diffusion columns: (i) rods of porous ceramic, (ii) artificial silica beads of different particle sizes (SiLi R ) and (iii) purified sea sand (Merck R ). The precipitation of simple salts, celestite (SrSO 4 ) and strontianite (SrCO 3 ), is forced in the porous material once placed in diffusion columns. Celestite and strontianite were chosen for their fast precipitation kinetics, and because
Anomalous water absorption in porous materials
Lockington, D A
2003-01-01
The absorption of fluid by unsaturated, rigid porous materials may be characterized by the sorptivity. This is a simple parameter to determine and is increasingly being used as a measure of a material's resistance to exposure to fluids (especially moisture and reactive solutes) in aggressive environments. The complete isothermal absorption process is described by a nonlinear diffusion equation, with the hydraulic diffusivity being a strongly nonlinear function of the degree of saturation of the material. This diffusivity can be estimated from the sorptivity test. In a typical test the cumulative absorption is proportional to the square root of time. However, a number of researchers have observed deviation from this behaviour when the infiltrating fluid is water and there is some potential for chemo-mechanical interaction with the material. In that case the current interpretation of the test and estimation of the hydraulic diffusivity is no longer appropriate. Kuentz and Lavallee (2001) discuss the anomalous b...
Directory of Open Access Journals (Sweden)
Ali Izadi
2015-10-01
Full Text Available In this study, substrates concentration profile has been studied in a porous matrix containing immobilized amyloglucosidase for glucose production. This analysis has been performed by using of an analytical method called Least Square Method and results have been compared with numerical solution. Effects of effective diffusivity (, Michael's constant (, maximum reaction rate ( and initial substrate concentration ( are studied on Soluble Starch and Dextrin concentration in the spherical support. Outcomes reveal that Least Square Method has an excellent agreement with numerical solution and in the center of support, substrate concentration is minimum and increasing of effective diffusivity and Michael's constant reduce the Soluble Starch and Dextrin profile gradient.
Diffusion and sorption in particles and two-dimensional dispersion in a porous media
International Nuclear Information System (INIS)
Rasmuson, A.
1980-01-01
A solution of the two-dimensional differential equation of dispersion from a disk source, coupled with a differential equation of diffusion and sorption in particles, is developed. The solution is obtained by the successive use of the Laplace and the Hankel transforms and is given in the form of an infinite double-integral. If the lateral dispersion is negligible, the solution is shown to simplify to a solution presented earlier. Dimensionless quantities are introduced. A steady-state condition is obtained after long time. This is investigated in some detail. An expression is derived for the highest concentration which may be expected at a point in space. An important relation is obtained when longitudinal dispersion is neglected. The solution for any value of the lateral dispersion coefficient and radial distance from the source is then obtained by simple multiplication of a solution for no lateral dispersion with the steady-state value. A method for integrating the infinite double integral is given. Some typical examples are shown. (Auth.)
International Nuclear Information System (INIS)
Kubaschewski, O.
1983-01-01
The diffusion rate values of titanium, its compounds and alloys are summarized and tabulated. The individual chemical diffusion coefficients and self-diffusion coefficients of certain isotopes are given. Experimental methods are listed which were used for the determination of diffusion coefficients. Some values have been taken over from other studies. Also given are graphs showing the temperature dependences of diffusion and changes in the diffusion coefficient with concentration changes
Ginzburg, Irina; Vikhansky, Alexander
2018-05-01
The extended method of moments (EMM) is elaborated in recursive algorithmic form for the prediction of the effective diffusivity, the Taylor dispersion dyadic and the associated longitudinal high-order coefficients in mean-concentration profiles and residence-time distributions. The method applies in any streamwise-periodic stationary d-dimensional velocity field resolved in the piecewise continuous heterogeneous porosity field. It is demonstrated that EMM reduces to the method of moments and the volume-averaging formulation in microscopic velocity field and homogeneous soil, respectively. The EMM simultaneously constructs two systems of moments, the spatial and the temporal, without resorting to solving of the high-order upscaled PDE. At the same time, the EMM is supported with the reconstruction of distribution from its moments, allowing to visualize the deviation from the classical ADE solution. The EMM can be handled by any linear advection-diffusion solver with explicit mass-source and diffusive-flux jump condition on the solid boundary and permeable interface. The prediction of the first four moments is decisive in the optimization of the dispersion, asymmetry, peakedness and heavy-tails of the solute distributions, through an adequate design of the composite materials, wetlands, chemical devices or oil recovery. The symbolic solutions for dispersion, skewness and kurtosis are constructed in basic configurations: diffusion process and Darcy flow through two porous blocks in "series", straight and radial Poiseuille flow, porous flow governed by the Stokes-Brinkman-Darcy channel equation and a fracture surrounded by penetrable diffusive matrix or embedded in porous flow. We examine the moments dependency upon porosity contrast, aspect ratio, Péclet and Darcy numbers, but also for their response on the effective Brinkman viscosity applied in flow modeling. Two numerical Lattice Boltzmann algorithms, a direct solver of the microscopic ADE in heterogeneous
Directory of Open Access Journals (Sweden)
O. Anwar Bég
2016-03-01
Full Text Available A theoretical and numerical study is presented to analyze the nonlinear, non-isothermal, magnetohydrodynamic (MHD free convection boundary layer flow and heat transfer in a non-Darcian, isotropic, homogenous porous medium, in the presence of Hall currents, Ionslip currents, viscous heating and Joule heating. A power-law variation is used for the temperature at the wall. The governing nonlinear coupled partial differential equations for momentum conservation in the x and z directions and heat conservation, in the flow regime are transformed from an (x, y, z coordinate system to a (ξ,η coordinate system in terms of dimensionless x-direction velocity (∂F/∂η and z-direction velocity (G and dimensionless temperature function (H under appropriate boundary conditions. Both Darcian and Forchheimer porous impedances are incorporated in both momentum equations. Computations are also provided for the variation of the x and z direction shear stress components and also local Nusselt number. Excellent correlation is achieved with a Nakamura tridiagonal finite difference scheme (NTM. The model finds applications in magnetic materials processing, MHD power generators and purification of crude oils.
International Nuclear Information System (INIS)
Boher, C.
2012-01-01
This work documents the relationship that exists between the transfer properties of a material (pore size distribution, total porosity accessible to water, water saturation degree), and its diffusion coefficient. For this sake, materials having a quasi mono modal porosity are used: Vycor glasses and geo-polymers. We also use materials having a complex porosity: CEM V cement pastes. The use of Vycor glasses and geo-polymers allows quantifying the gas diffusion coefficient through materials having known pores size, as a function of their water saturation degree. The use of cement pastes allows checking if it is possible to decompose the diffusion coefficient of a complex porosity material, in an assembling of diffusion coefficients of quasi mono modal porosity materials. For this sake, the impact of pore network arrangement on the diffusion coefficient is studied in great details. This study is divided into three parts:1)Measurement of the geometric characteristics of materials porous network by means of the mercury intrusion porosimetry, water porosimetry, isotherms of nitrogen sorption / desorption, and water desorption tests. 2) Measurement of the materials diffusion coefficient, as a function of their relative humidity storage, and their water saturation degree. 3) Modeling the diffusion coefficient of the materials, and study the impact of the pore network (tortuosity, pores connection). (author) [fr
International Nuclear Information System (INIS)
Chambarel, A.; Pumborios, M.
1992-01-01
This paper reports that many engineering problems concern the determination of a steady state solution in the case with strong thermal gradients, and results obtained using the finite-element technique are sometimes inaccurate, particularly for nonlinear problems with unadapted meshes. Building on previous results in linear problems, we propose an autoadaptive technique for nonlinear cases that uses quasi-Newtonian iterations to reevaluate an interpolation error estimation. The authors perfected an automatic refinement technique to solve the nonlinear thermal problem of temperature calculus in a cast-iron cylinder head of a diesel engine
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Kumar Hitesh
2016-01-01
Full Text Available The present paper analyzes the chemically reacting free convection MHD micropolar flow, heat and mass transfer in porous medium past an infinite vertical plate with radiation and viscous dissipation. The non-linear coupled partial differential equations are solved numerically using an implicit finite difference scheme known as Keller-box method. The results for concentration, transverse velocity, angular velocity and temperature are obtained and effects of various parameters on these functions are presented graphically. The numerical discussion with physical interpretations for the influence of various parameters also presented.
Peppin, Stephen S. L.
2009-01-01
Diffusion and permeation are discussed within the context of irreversible thermodynamics. A new expression for the generalized Stokes-Einstein equation is obtained which links the permeability to the diffusivity of a two-component solution and contains the poroelastic Biot-Willis coefficient. The theory is illustrated by predicting the concentration and pressure profiles during the filtration of a protein solution. At low concentrations the proteins diffuse independently while at higher concentrations they form a nearly rigid porous glass through which the fluid permeates. The theoretically determined pressure drop is nonlinear in the diffusion regime and linear in the permeation regime, in quantitative agreement with experimental measurements. © 2009 Walter de Gruyter, Berlin, New York.
Energy Technology Data Exchange (ETDEWEB)
Tinturier, B [Commissariat a l' Energie Atomique, Fontenay-Aux-Roses (France). Centre d' Etudes Nucleaires
1966-12-01
The study of the leaching of heaped uranium ore can be considered theoretically as the problem of the diffusion of liquids in porous bodies and in particular as that of its influence on the chemical reaction rates of conventional uranium oxides. Below a certain value of the pore diameter, it is diffusion which is responsible for mass transfer. The porous structure can be characterized by various physical constants which modify the free diffusion equation and, as long as the pores have a diameter greater than a few microns, it can be shown that the pore walls have a negligible effect on the diffusion. The diffusion coefficients for the nitrate, the sulfate, the chloride, the acetate and the perchlorate of uranium have been determined. In the case of the reaction of uranium trioxide with acids in a porous body, the reaction kinetics are governed by the arrival of the reagent by diffusion. The attack of uranium dioxide by an acid ferric iron solution has been studied under the same conditions and it has been found that the diffusion modifies the influence of the ferrous and ferric iron concentrations on the reaction kinetics. The same is true for the oxide U{sub 3}O{sub 8}. All the results concerning these reactions studied in the absence of the influence of diffusion should be modified to take this factor into account when it intervenes in an extraction process. (authors) [French] L'etude de la lixiviation en tas d'un minerai d'uranium peut se ramener theoriquement au probleme de la diffusion des liquides dans les corps poreux et en particulier a celui de son influence sur les vitesses de reaction chimique des oxydes classiques de l'uranium. En dessous d'une certaine limite de diametre des pores la diffusion est responsable du transfert de masse. La structure poreuse peut se caracteriser par differentes constantes physiques qui modifient l'equation de la diffusion libre et tant que les pores ont un diametre superieur a quelques microns, on a montre que l
DEFF Research Database (Denmark)
Johannesson, Björn; Hosokawa, Yoshifumi; Yamada, Kazuo
2009-01-01
A method to analyse and calculate concentration profiles of different types of ions in the pore solution of porous materials such as concrete subjected to external wetting and drying is described. The equations in use have a solid theoretical meaning and are derived from a porous media technique......, which is a special branch of the more general mixture theory. The effect of chemical action is ignored making the presented model suitable to be implemented into codes dealing solely with chemical equilibrium. The coupled set of equations for diffusion of ionic species, the internal electrical potential...... of the model should be judged from the assumptions made when developing the balance laws and the constitutive equations and the assumptions made in obtaining a working numerical calculation scheme....
International Nuclear Information System (INIS)
Aurangzeb; Ali, Zulqurnain; Gurmani, Samia Faiz; Maqsood, Asghari
2006-01-01
Thermal conductivity, thermal diffusivity and heat capacity per unit volume of porous consolidated igneous rocks have been measured, simultaneously by Gustafsson's probe at room temperature and normal pressure using air as saturant. Data are presented for eleven samples of dunite, ranging in porosity from 0.130 to 0.665% by volume, taken from Chillas near Gilgit, Pakistan. The porosity and density parameters have been measured using American Society of Testing and Materials (ASTM) standards at ambient conditions. The mineral composition of samples has been analysed from their thin sections (petrography). An empirical model to predict the thermal conductivity of porous consolidated igneous rocks is also proposed. The thermal conductivities are predicted by some of the existing models along with the proposed one. It is observed that the values of effective thermal conductivity predicted by the proposed model are in agreement with the experimental thermal conductivity data within 6%
Malyarenko, Dariya I; Pang, Yuxi; Senegas, Julien; Ivancevic, Marko K; Ross, Brian D; Chenevert, Thomas L
2015-12-01
Spatially non-uniform diffusion weighting bias due to gradient nonlinearity (GNL) causes substantial errors in apparent diffusion coefficient (ADC) maps for anatomical regions imaged distant from magnet isocenter. Our previously-described approach allowed effective removal of spatial ADC bias from three orthogonal DWI measurements for mono-exponential media of arbitrary anisotropy. The present work evaluates correction feasibility and performance for quantitative diffusion parameters of the two-component IVIM model for well-perfused and nearly isotropic renal tissue. Sagittal kidney DWI scans of a volunteer were performed on a clinical 3T MRI scanner near isocenter and offset superiorly. Spatially non-uniform diffusion weighting due to GNL resulted both in shift and broadening of perfusion-suppressed ADC histograms for off-center DWI relative to unbiased measurements close to isocenter. Direction-average DW-bias correctors were computed based on the known gradient design provided by vendor. The computed bias maps were empirically confirmed by coronal DWI measurements for an isotropic gel-flood phantom. Both phantom and renal tissue ADC bias for off-center measurements was effectively removed by applying pre-computed 3D correction maps. Comparable ADC accuracy was achieved for corrections of both b -maps and DWI intensities in presence of IVIM perfusion. No significant bias impact was observed for IVIM perfusion fraction.
International Nuclear Information System (INIS)
Uedono, Akira; Armini, Silvia; Zhang, Yu; Kakizaki, Takeaki; Krause-Rehberg, Reinhard; Anwand, Wolfgang; Wagner, Andreas
2016-01-01
Graphical abstract: - Highlights: • Pores with cubic pore side lengths of 1.1 and 3.1 nm coexisted in the low-k film. • For the sample without the SAM sealing process, metal atoms diffused from the top Cu/MnN layer into the OSG film and were trapped by the pores. Almost all pore interiors were covered by those metals. • For the sample damaged by a plasma etch treatment before the SAM sealing process, self-assembled molecules diffused into the OSG film, and they were preferentially trapped by larger pores. - Abstract: Surface sealing effects on the diffusion of metal atoms in porous organosilicate glass (OSG) films were studied by monoenergetic positron beams. For a Cu(5 nm)/MnN(3 nm)/OSG(130 nm) sample fabricated with pore stuffing, C_4F_8 plasma etch, unstuffing, and a self-assembled monolayer (SAM) sealing process, it was found that pores with cubic pore side lengths of 1.1 and 3.1 nm coexisted in the OSG film. For the sample without the SAM sealing process, metal (Cu and Mn) atoms diffused from the top Cu/MnN layer into the OSG film and were trapped by the pores. As a result, almost all pore interiors were covered with those metals. For the sample damaged by an Ar/C_4F_8 plasma etch treatment before the SAM sealing process, SAMs diffused into the OSG film, and they were preferentially trapped by larger pores. The cubic pore side length in these pores containing self-assembled molecules was estimated to be 0.7 nm. Through this work, we have demonstrated that monoenergetic positron beams are a powerful tool for characterizing capped porous films and the trapping of atoms and molecules by pores.
Directory of Open Access Journals (Sweden)
Olivier Millet
2008-03-01
Full Text Available In this paper, we propose a macroscopic migration model for cementitious porous media obtained from periodic homogenization technique. The dimensional analysis of Nernst-Planck equation leads to dimensionless numbers characterizing the problem. According to the order of magnitude of the dimensionless numbers, the homogenization of Nernst-Planck equation leads at the leading order to a macroscopic model where several rates can be coupled or not. For a large applied electrical field accelerating the transfer of ionic species, we obtain a macroscopic model only involving migration. A simple experimental procedure of measurement of the homogenized chlorides diffusivity is then proposed for cement-based materials.
Improvement of nonlinear diffusion equation using relaxed geometric mean filter for low PSNR images
DEFF Research Database (Denmark)
Nadernejad, Ehsan
2013-01-01
A new method to improve the performance of low PSNR image denoising is presented. The proposed scheme estimates edge gradient from an image that is regularised with a relaxed geometric mean filter. The proposed method consists of two stages; the first stage consists of a second order nonlinear an...
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.
Cluster Synchronization of Diffusively Coupled Nonlinear Systems: A Contraction-Based Approach
Aminzare, Zahra; Dey, Biswadip; Davison, Elizabeth N.; Leonard, Naomi Ehrich
2018-04-01
Finding the conditions that foster synchronization in networked nonlinear systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in nonlinear systems with linear coupling, such as has been used to model neuronal networks, are in general not strict enough to accurately determine the system behavior. We leverage contraction theory to derive new sufficient conditions for cluster synchronization in terms of the network structure, for a network where the intrinsic nonlinear dynamics of each node may differ. Our result requires that network connections satisfy a cluster-input-equivalence condition, and we explore the influence of this requirement on network dynamics. For application to networks of nodes with FitzHugh-Nagumo dynamics, we show that our new sufficient condition is tighter than those found in previous analyses that used smooth or nonsmooth Lyapunov functions. Improving the analytical conditions for when cluster synchronization will occur based on network configuration is a significant step toward facilitating understanding and control of complex networked systems.
Concentration fluctuations in non-isothermal reaction-diffusion systems. II. The nonlinear case
Bedeaux, D.; Ortiz de Zárate, J.M.; Pagonabarraga, I.; Sengers, J.V.; Kjelstrup, S.
2011-01-01
In this paper, we consider a simple reaction-diffusion system, namely, a binary fluid mixture with an association-dissociation reaction between two species. We study fluctuations at hydrodynamic spatiotemporal scales when this mixture is driven out of equilibrium by the presence of a temperature
Duval, J.F.L.
2005-01-01
In a previous study (Langmuir 2004, 20, 10324), the electrokinetic properties of diffuse soft layers were theoretically investigated within the framework of the Debye-H¿ckel approximation valid in the limit of sufficiently low values for the Donnan potential. In the current paper, the
DEFF Research Database (Denmark)
Rolle, Massimo
2015-01-01
to multicomponent ionic dispersion: the dispersive fluxes of the different ions are cross-coupled due to the effects of Coulombic interactions. Such effects are illustrated in flow-through experiments in saturated porous media. Simple strong electrolytes were selected as tracers and their transport was studied...... under different advection-dominated conditions and in homogeneous and heterogeneous porous media. The interpretation of the experimental results requires a multicomponent modeling approach with an accurate description of local hydrodynamic dispersion and explicitly accounting for the cross-coupling...
International Nuclear Information System (INIS)
Paraschiv, I.; Bauer, B. S.; Lindemuth, I. R.; Makhin, V.
2010-01-01
The effect of sheared axial flow on the Z-pinch sausage instability has been examined with two-dimensional magnetohydrodynamic simulations. Diffuse Bennett equilibria in the presence of axial flows with parabolic and linear radial profiles have been considered, and a detailed study of the linear and nonlinear development of small perturbations from these equilibria has been performed. The consequences of both single-wavelength and random-seed perturbations were calculated. It was found that sheared flows changed the internal m=0 mode development by reducing the linear growth rates, decreasing the saturation amplitude, and modifying the instability spectrum. High spatial frequency modes were stabilized to small amplitudes and only long wavelengths continued to grow. Full stability was obtained for supersonic plasma flows.
Sahmani, Saeid; Aghdam, Mohammad Mohammadi; Rabczuk, Timon
2018-04-01
By gradually changing of the porosity across a specific direction, functionally graded porous materials (FGPMs) are produced which can impart desirable mechanical properties. To enhance these properties, it is common to reinforce FGPMs with nanofillers. The main aim of the current study is to investigate the size-dependent nonlinear axial postbuckling characteristics of FGPM micro/nano-plates reinforced with graphene platelets. For this purpose, the theory of nonlocal strain gradient elasticity incorporating the both stiffness reduction and stiffness enhancement mechanisms of size effects is applied to the refined exponential shear deformation plate theory. Three different patterns of porosity dispersion across the plate thickness in conjunction with the uniform one are assumed for FGPM as an open-cell metal foam is utilized associated with the coefficients of the relative density and porosity. With the aid of the virtual work’s principle, the non-classical governing differential equations are constructed. Thereafter, an improved perturbation technique is employed to capture the size dependencies in the nonlinear load-deflection and load-shortening responses of the reinforced FGPM micro/nano-plates with and without initial geometric imperfection. It is indicated that by increasing the value of porosity coefficient, the size-dependent critical buckling loads of reinforced FGPM micro/nano-plates with all types of porosity dispersion pattern reduce, but the associated shortening may increase or decrease which depends on the type of dispersion pattern.
Non-linear diffusion of charged particles due to stochastic electromagnetic fields
International Nuclear Information System (INIS)
Martins, A.M.; Balescu, R.; Mendonca, J.T.
1989-01-01
It is well known that the energy confinement times observed in tokamak cannot be explained by the classical or neo-classical transport theory. The alternative explanations are based on the existence of various kinds of micro-instabilities, or on the stochastic destruction of the magnetic surfaces, due to the interaction of magnetic islands of different helicities. In the absence of a well established theory of anomalous transport it is perhaps important to study in some detail the diffusion coefficient of single charged particles in the presence of electromagnetic fluctuation, because it can provide the physical grounds for more complete and self-consistent calculations. In the present work we derive a general expression for the transverse diffusion coefficient of electrons and ions in a constant magnetic field and in the presence of space and time dependent electromagnetic fluctuation. We neglect macroscopic drifts due to inhomogeneity and field curvatures, but retain finite Larmor radius effects. (author) 3 refs
Markowich, Peter; Lorz, Alexander; Francesco, Marco
2010-01-01
We study the system ct + u · ∇c = ∇c -nf(c) nt + u · ∇n = ∇n m - ∇ · (n×(c) ∇c) ut + u·∇u + ∇P - η∇u + n∇φ/ = 0 ∇·u = 0. arising in the modelling of the motion of swimming bacteria under the effect of diffusion, oxygen-taxis and transport through
On an adaptive time stepping strategy for solving nonlinear diffusion equations
International Nuclear Information System (INIS)
Chen, K.; Baines, M.J.; Sweby, P.K.
1993-01-01
A new time step selection procedure is proposed for solving non- linear diffusion equations. It has been implemented in the ASWR finite element code of Lorenz and Svoboda [10] for 2D semiconductor process modelling diffusion equations. The strategy is based on equi-distributing the local truncation errors of the numerical scheme. The use of B-splines for interpolation (as well as for the trial space) results in a banded and diagonally dominant matrix. The approximate inverse of such a matrix can be provided to a high degree of accuracy by another banded matrix, which in turn can be used to work out the approximate finite difference scheme corresponding to the ASWR finite element method, and further to calculate estimates of the local truncation errors of the numerical scheme. Numerical experiments on six full simulation problems arising in semiconductor process modelling have been carried out. Results show that our proposed strategy is more efficient and better conserves the total mass. 18 refs., 6 figs., 2 tabs
Directory of Open Access Journals (Sweden)
Xuehui Yin
2015-01-01
Full Text Available The traditional integer-order partial differential equations and gradient regularization based image denoising techniques often suffer from staircase effect, speckle artifacts, and the loss of image contrast and texture details. To address these issues, in this paper, a difference curvature driven fractional anisotropic diffusion for image noise removal is presented, which uses two new techniques, fractional calculus and difference curvature, to describe the intensity variations in images. The fractional-order derivatives information of an image can deal well with the textures of the image and achieve a good tradeoff between eliminating speckle artifacts and restraining staircase effect. The difference curvature constructed by the second order derivatives along the direction of gradient of an image and perpendicular to the gradient can effectively distinguish between ramps and edges. Fourier transform technique is also proposed to compute the fractional-order derivative. Experimental results demonstrate that the proposed denoising model can avoid speckle artifacts and staircase effect and preserve important features such as curvy edges, straight edges, ramps, corners, and textures. They are obviously superior to those of traditional integral based methods. The experimental results also reveal that our proposed model yields a good visual effect and better values of MSSIM and PSNR.
Malyarenko, Dariya I; Wilmes, Lisa J; Arlinghaus, Lori R; Jacobs, Michael A; Huang, Wei; Helmer, Karl G; Taouli, Bachir; Yankeelov, Thomas E; Newitt, David; Chenevert, Thomas L
2016-12-01
Previous research has shown that system-dependent gradient nonlinearity (GNL) introduces a significant spatial bias (nonuniformity) in apparent diffusion coefficient (ADC) maps. Here, the feasibility of centralized retrospective system-specific correction of GNL bias for quantitative diffusion-weighted imaging (DWI) in multisite clinical trials is demonstrated across diverse scanners independent of the scanned object. Using corrector maps generated from system characterization by ice-water phantom measurement completed in the previous project phase, GNL bias correction was performed for test ADC measurements from an independent DWI phantom (room temperature agar) at two offset locations in the bore. The precomputed three-dimensional GNL correctors were retrospectively applied to test DWI scans by the central analysis site. The correction was blinded to reference DWI of the agar phantom at magnet isocenter where the GNL bias is negligible. The performance was evaluated from changes in ADC region of interest histogram statistics before and after correction with respect to the unbiased reference ADC values provided by sites. Both absolute error and nonuniformity of the ADC map induced by GNL (median, 12%; range, -35% to +10%) were substantially reduced by correction (7-fold in median and 3-fold in range). The residual ADC nonuniformity errors were attributed to measurement noise and other non-GNL sources. Correction of systematic GNL bias resulted in a 2-fold decrease in technical variability across scanners (down to site temperature range). The described validation of GNL bias correction marks progress toward implementation of this technology in multicenter trials that utilize quantitative DWI.
Directory of Open Access Journals (Sweden)
Evgeny G. Bugaev
2011-01-01
Full Text Available Geological, geophysical and seismogeological studies are now conducted in a more detail and thus provide for determining seismic sources with higher accuracy, from the first meters to first dozens of meters [Waldhauser, Schaff, 2008]. It is now possible to consider uncertainty ellipses of earthquake hypocenters, that are recorded in the updated Earthquake Catalogue, as surfaces of earthquake focus generators. In our article, it is accepted that a maximum horizontal size of an uncertainty ellipse corresponds to an area of a focus generator, and seismic events are thus classified into two groups, earthquakes with nonstiff and stiff foci. Criteria of such a classification are two limits of elastic strain and brittle strain in case of uniaxial (3⋅10–5 or omnidirectional (10–6 compression. The criteria are established from results of analyses of parameters of seismic dislocations and earthquake foci with regard to studies of surface parameters and deformation parameters of fault zones. It is recommendable that the uniaxial compression criterion shall be applied to zones of interaction between tectonic plates, and the unilateral compression criterion shall be applied to low active (interplate areas. Sample cases demonstrate the use of data sets on nonstiff and stiff foci for separate evaluation of magnitude reoccurrence curves, analyses of structured and dissipated seismicity, review of the physical nature of nonlinearity of recurrence curves and conditions of preparation of strong earthquakes. Changes of parameters of the recurrence curves with changes of data collection square areas are considered. Reviewed are changes of parameters of the recurrence curves during preparation for the Japan major earthquake of 11 March 2011 prior to and after the major shock. It is emphasized that it is important to conduct even more detailed geological and geophysical studies and to improve precision and sensitivity of local seismological monitoring networks
International Nuclear Information System (INIS)
Chang-Jian, C.-W.; Chen, C.-K.
2008-01-01
This study presents a dynamic analysis of a flexible rotor supported by two porous squeeze couple stress fluid film journal bearings with non-linear suspension. The dynamics of the rotor center and bearing center are studied. The analysis of the rotor-bearing system is investigated under the assumptions of non-Newtonian fluid and a short bearing approximation. The spatial displacements in the horizontal and vertical directions are considered for various non-dimensional speed ratios. The dynamic equations are solved using the Runge-Kutta method. The analysis methods employed in this study is inclusive of the dynamic trajectories of the rotor center and bearing center, power spectra, Poincare maps and bifurcation diagrams. The maximum Lyapunov exponent analysis is also used to identify the onset of chaotic motion. The numerical results show that the stability of the system varies with the non-dimensional speed ratios, the non-dimensional parameter l* and the permeability. The modeling results thus obtained by using the method proposed in this paper can be employed to predict the stability of the rotor-bearing system and the undesirable behavior of the rotor and bearing center can be avoided
Czech Academy of Sciences Publication Activity Database
Šolcová, Olga; Soukup, Karel; Schneider, Petr
2006-01-01
Roč. 91, 1-3 (2006), s. 100-106 ISSN 1387-1811 R&D Projects: GA AV ČR(CZ) IAA4072404 Institutional research plan: CEZ:AV0Z40720504 Keywords : chromatography * diffusion * mass transfer Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 2.796, year: 2006
Directory of Open Access Journals (Sweden)
Isaac Lare Animasaun
2016-06-01
Full Text Available The problem of unsteady convective with thermophoresis, chemical reaction and radiative heat transfer in a micropolar fluid flow past a vertical porous surface moving through binary mixture considering temperature dependent dynamic viscosity and constant vortex viscosity has been investigated theoretically. For proper and correct analysis of fluid flow along vertical surface with a temperature lesser than that of the free stream, Boussinesq approximation and temperature dependent viscosity model were modified and incorporated into the governing equations. The governing equations are converted to systems of ordinary differential equations by applying suitable similarity transformations and solved numerically using fourth-order Runge–Kutta method along with shooting technique. The results of the numerical solution are presented graphically and in tabular forms for different values of parameters. Velocity profile increases with temperature dependent variable fluid viscosity parameter. Increase of suction parameter corresponds to an increase in both temperature and concentration within the thin boundary layer.
Fractional Diffusion Equations and Anomalous Diffusion
Evangelista, Luiz Roberto; Kaminski Lenzi, Ervin
2018-01-01
Preface; 1. Mathematical preliminaries; 2. A survey of the fractional calculus; 3. From normal to anomalous diffusion; 4. Fractional diffusion equations: elementary applications; 5. Fractional diffusion equations: surface effects; 6. Fractional nonlinear diffusion equation; 7. Anomalous diffusion: anisotropic case; 8. Fractional Schrödinger equations; 9. Anomalous diffusion and impedance spectroscopy; 10. The Poisson–Nernst–Planck anomalous (PNPA) models; References; Index.
Directory of Open Access Journals (Sweden)
Eitzinger Bernhard
2015-09-01
Full Text Available La distribution de la taille des pores détermine la perméabilité d’air et la capacité de diffusion d’un papier à cigarettes, et par conséquent elle a une influence signifiante sur les échanges gazeux à travers le papier à cigarettes, non seulement d’une cigarette allumée, mais aussi d’une cigarette qui s’éteint. Pour le dessin des cigarettes, et notamment des papiers à cigarettes, il faut comprendre comment la distribution de la taille des pores du papier à cigarettes est influencée par la structure et les qualités du papier, ainsi que comment la distribution de la taille des pores influence la perméabilité d’air et la capacité de diffusion.
Kang, Jia-Jhen; Yang, Tsung-Yu; Lan, Yi-Kang; Wu, Wei-Ru; Su, Chun-Jen; Weng, Shih-Chang; Yamada, Norifumi L; Su, An-Chung; Jeng, U-Ser
2018-04-01
Cathode buffer layers (CBLs) can effectively further the efficiency of polymer solar cells (PSCs), after optimization of the active layer. Hidden between the active layer and cathode of the inverted PSC device configuration is the critical yet often unattended vertical diffusion of the active layer components across CBL. Here, a novel methodology of contrast variation with neutron and anomalous X-ray reflectivity to map the multicomponent depth compositions of inverted PSCs, covering from the active layer surface down to the bottom of the ZnO-based CBL, is developed. Uniquely revealed for a high-performance model PSC are the often overlooked porosity distributions of the ZnO-based CBL and the differential diffusions of the polymer PTB7-Th and fullerene derivative PC 71 BM of the active layer into the CBL. Interface modification of the ZnO-based CBL with fullerene derivative PCBEOH for size-selective nanochannels can selectively improve the diffusion of PC 71 BM more than that of the polymer. The deeper penetration of PC 71 BM establishes a gradient distribution of fullerene derivatives over the ZnO/PCBE-OH CBL, resulting in markedly improved electron mobility and device efficiency of the inverted PSC. The result suggests a new CBL design concept of progressive matching of the conduction bands. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Transport and sorption of volatile organic compounds and water vapor in porous media
Energy Technology Data Exchange (ETDEWEB)
Lin, Tsair-Fuh [Univ. of California, Berkeley, CA (United States)
1995-07-01
To gain insight on the controlling mechanisms for VOC transport in porous media, the relations among sorbent properties, sorption equilibrium and intraparticle diffusion processes were studied at the level of individual sorbent particles and laboratory columns for soil and activated carbon systems. Transport and sorption of VOCs and water vapor were first elucidated within individual dry soil mineral grains. Soil properties, sorption capacity, and sorption rates were measured for 3 test soils; results suggest that the soil grains are porous, while the sorption isotherms are nonlinear and adsorption-desorption rates are slow and asymmetric. An intragranular pore diffusion model coupled with the nonlinear Freundlich isotherm was developed to describe the sorption kinetic curves. Transport of benzene and water vapor within peat was studied; partitioning and sorption kinetics were determined with an electrobalance. A dual diffusion model was developed. Transport of benzene in dry and moist soil columns was studied, followed by gaseous transport and sorption in activated carbon. The pore diffusion model provides good fits to sorption kinetics for VOCs to soil and VOC to granular activated carbon and activated carbon fibers. Results of this research indicate that: Intraparticle diffusion along with a nonlinea sorption isotherm are responsible for the slow, asymmetric sorption-desorption. Diffusion models are able to describe results for soil and activated carbon systems; when combined with mass transfer equations, they predict column breakthrough curves for several systems. Although the conditions are simplified, the mechanisms should provide insight on complex systems involving transport and sorption of vapors in porous media.
Slug flow model for infiltration into fractured porous media
International Nuclear Information System (INIS)
Martinez, M.J.
1999-01-01
A model for transient infiltration into a periodically fractured porous layer is presented. The fracture is treated as a permeable-walled slot and the moisture distribution is in the form of a slug being an advancing meniscus. The wicking of moisture from the fracture to the unsaturated porous matrix is a nonlinear diffusion process and is approximately by self-similar solutions. The resulting model is a nonlinear Volterra integral equation with a weakly singular kernel. Numerical analysis provides solutions over a wide range of the parameter space and reveals the asymptotic forms of the penetration of this slug in terms of dimensionless variables arising in the model. The numerical solutions corroborate asymptotic results given earlier by Nitao and Buscheck (1991), and by Martinez (1988). Some implications for the transport of liquid in fractured rock are discussed
Suresh, P V; Jayanti, Sreenivas
2016-10-01
Adoption of hydrogen economy by means of using hydrogen fuel cells is one possible solution for energy crisis and climate change issues. Polymer electrolyte membrane (PEM) fuel cell, which is an important type of fuel cells, suffers from the problem of water management. Cross-flow is induced in some flow field designs to enhance the water removal. The presence of cross-flow in the serpentine and interdigitated flow fields makes them more effective in proper distribution of the reactants on the reaction layer and evacuation of water from the reaction layer than diffusion-based conventional parallel flow fields. However, too much of cross-flow leads to flow maldistribution in the channels, higher pressure drop, and membrane dehydration. In this study, an attempt has been made to quantify the amount of cross-flow required for effective distribution of reactants and removal of water in the gas diffusion layer. Unit cells containing two adjacent channels with gas diffusion layer (GDL) and catalyst layer at the bottom have been considered for the parallel, interdigitated, and serpentine flow patterns. Computational fluid dynamics-based simulations are carried out to study the reactant transport in under-the-rib area with cross-flow in the GDL. A new criterion based on the Peclet number is presented as a quantitative measure of cross-flow in the GDL. The study shows that a cross-flow Peclet number of the order of 2 is required for effective removal of water from the GDL. Estimates show that this much of cross-flow is not usually produced in the U-bends of Serpentine flow fields, making these areas prone to flooding.
Electrochemical Impedance Imaging via the Distribution of Diffusion Times
Song, Juhyun; Bazant, Martin Z.
2018-03-01
We develop a mathematical framework to analyze electrochemical impedance spectra in terms of a distribution of diffusion times (DDT) for a parallel array of random finite-length Warburg (diffusion) or Gerischer (reaction-diffusion) circuit elements. A robust DDT inversion method is presented based on complex nonlinear least squares regression with Tikhonov regularization and illustrated for three cases of nanostructured electrodes for energy conversion: (i) a carbon nanotube supercapacitor, (ii) a silicon nanowire Li-ion battery, and (iii) a porous-carbon vanadium flow battery. The results demonstrate the feasibility of nondestructive "impedance imaging" to infer microstructural statistics of random, heterogeneous materials.
Macías-Díaz, J E; Macías, Siegfried; Medina-Ramírez, I E
2013-12-01
In this manuscript, we present a computational model to approximate the solutions of a partial differential equation which describes the growth dynamics of microbial films. The numerical technique reported in this work is an explicit, nonlinear finite-difference methodology which is computationally implemented using Newton's method. Our scheme is compared numerically against an implicit, linear finite-difference discretization of the same partial differential equation, whose computer coding requires an implementation of the stabilized bi-conjugate gradient method. Our numerical results evince that the nonlinear approach results in a more efficient approximation to the solutions of the biofilm model considered, and demands less computer memory. Moreover, the positivity of initial profiles is preserved in the practice by the nonlinear scheme proposed. Copyright © 2013 Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Brito, P.E. de; Nazareno, H.N.
2012-01-01
The object of the present work is to analyze the effect of nonlinearity on wave packet propagation in a square lattice subject to a magnetic and an electric field in the Hall configuration, by using the Discrete Nonlinear Schrödinger Equation (DNLSE). In previous works we have shown that without the nonlinear term, the presence of the magnetic field induces the formation of vortices that remain stationary, while a wave packet is introduced in the system. As for the effect of an applied electric field, it was shown that the vortices propagate in a direction perpendicular to the electric field, similar behavior as presented in the classical treatment, we provide a quantum mechanics explanation for that. We have performed the calculations considering first the action of the magnetic field as well as the nonlinearity. The results indicate that for low values of the nonlinear parameter U the vortices remain stationary while preserving the form. For greater values of the parameter the picture gets distorted, the more so, the greater the nonlinearity. As for the inclusion of the electric field, we note that for small U, the wave packet propagates perpendicular to the applied field, until for greater values of U the wave gets partially localized in a definite region of the lattice. That is, for strong nonlinearity the wave packet gets partially trapped, while the tail of it can propagate through the lattice. Note that this tail propagation is responsible for the over-diffusion for long times of the wave packet under the action of an electric field. We have produced short films that show clearly the time evolution of the wave packet, which can add to the understanding of the dynamics.
Energy Technology Data Exchange (ETDEWEB)
Breton, J P [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1962-06-15
The present-day theories of separation by gaseous diffusion (Present and de BETHUNE, KYNCH, BOSANQUET) are all based on the same model in which the pores are cylindrical capillaries. In the theory presented here, we substitute for this model that of a disordered and isotropic bed of identical spheres, which describes more accurately most of the porous media. We take as our starting point DERIAGUINE and BAKANOV'S permeability theory, which expresses the flow of a simple gas in such a bed when the latter is of high porosity. We first generalise this theory in the case of medium and low porosities; then, we go on to a mixture of two gases, from which we deduce our separation theory. Finally we compare our results with those of Present and de BETHUNE. (author) [French] Les theories actuelles de la separation par diffusion gazeuse (PRESENT et de BETHUNE, KYNCH, BOSANQUET) reposent toutes sur le modele des pores capillaires cylindriques. Dans la theorie presentee ici, nous substituons a ce modele celui d'un empilement desordonne et isotropes de spheres identiques, qui decrit plus correctement la plupart des milieux poreux. Nous partons de la theorie de la permeabilite de DERIAGUINE et BAKANOV, qui exprime l'ecoulement d'un gaz simple dans un tel empilement dans le cas ou la porosite en est elevee. Nous generalisons d'abord cette theorie du cas des porosites moyennes ou faibles, puis, passant a un melange de deux gaz, nous en deduisons une theorie de la separation. Pour terminer, nous comparons nos resultats a ceux de PRESENT et de BETHUNE. (auteur)
A finite volume method for density driven flows in porous media
Directory of Open Access Journals (Sweden)
Hilhorst Danielle
2013-01-01
Full Text Available In this paper, we apply a semi-implicit finite volume method for the numerical simulation of density driven flows in porous media; this amounts to solving a nonlinear convection-diffusion parabolic equation for the concentration coupled with an elliptic equation for the pressure. We compute the solutions for two specific problems: a problem involving a rotating interface between salt and fresh water and the classical but difficult Henry’s problem. All solutions are compared to results obtained by running FEflow, a commercial software package for the simulation of groundwater flow, mass and heat transfer in porous media.
Directory of Open Access Journals (Sweden)
Roman Cherniha
2018-04-01
Full Text Available This review is devoted to search for Lie and Q-conditional (nonclassical symmetries and exact solutions of a class of reaction-diffusion-convection equations with exponential nonlinearities. A complete Lie symmetry classification of the class is derived via two different algorithms in order to show that the result depends essentially on the type of equivalence transformations used for the classification. Moreover, a complete description of Q-conditional symmetries for PDEs from the class in question is also presented. It is shown that all the well-known results for reaction-diffusion equations with exponential nonlinearities follow as particular cases from the results derived for this class of reaction-diffusion-convection equations. The symmetries obtained for constructing exact solutions of the relevant equations are successfully applied. The exact solutions are compared with those found by means of different techniques. Finally, an application of the exact solutions for solving boundary-value problems arising in population dynamics is presented.
Energy Technology Data Exchange (ETDEWEB)
Stafford, Paige L. [Univ. of Tennessee, Knoxville, TN (United States). Dept. of Geological Sciences
1996-05-01
Simulations of a tritium tracer experiment in fractured shale saprolite, conducted at the Oak Ridge National Laboratory, were performed using 1D and 2D equivalent porous medium (EPM) and discrete-fracture/matrix-diffusion (DFMD) models. The models successfully reproduced the general shape of the breakthrough curves in down-gradient monitoring wells which are characterized by rapid first arrival, a slow-moving center of mass, and a persistent ``tail`` of low concentration. In plan view, the plume shows a large degree of transverse spreading with the width almost as great as the length. EPM models were sensitive to dispersivity coefficient values which had to be large (relative to the 3.7m distance between the injection and monitoring wells) to fit the tail and transverse spreading. For example, to fit the tail a longitudinal dispersivity coefficient, α_{L}, of 0.8 meters for the 2D simulations was used. To fit the transverse spreading, a transverse dispersivity coefficient, α_{T}, of 0.8 to 0.08 meters was used indicating an α_{L}/α_{T} ratio between 10 and 1. Transverse spreading trends were also simulated using a 2D DFMD model using a few larger aperture fractures superimposed onto an EPM. Of the fracture networks studied, only those with truncated fractures caused transverse spreading. Simulated tritium levels in all of the cases were larger than observed values by a factor of approximately 100. Although this is partly due to input of too much tritium mass by the models it appears that dilution in the wells, which were not purged prior to sampling, is also a significant factor. The 1D and 2D EPM models were fitted to monitoring data from the first five years of the experiment and then used to predict future tritium concentrations.
International Nuclear Information System (INIS)
Stafford, P.L.
1996-05-01
Simulations of a tritium tracer experiment in fractured shale saprolite, conducted at the Oak Ridge National Laboratory, were performed using 1D and 2D equivalent porous medium (EPM) and discrete-fracture/matrix-diffusion (DFMD) models. The models successfully reproduced the general shape of the breakthrough curves in down-gradient monitoring wells which are characterized by rapid first arrival, a slow-moving center of mass, and a persistent ''tail'' of low concentration. In plan view, the plume shows a large degree of transverse spreading with the width almost as great as the length. EPM models were sensitive to dispersivity coefficient values which had to be large (relative to the 3.7m distance between the injection and monitoring wells) to fit the tail and transverse spreading. For example, to fit the tail a longitudinal dispersivity coefficient, α L , of 0.8 meters for the 2D simulations was used. To fit the transverse spreading, a transverse dispersivity coefficient, α T , of 0.8 to 0.08 meters was used indicating an α L /α T ratio between 10 and 1. Transverse spreading trends were also simulated using a 2D DFMD model using a few larger aperture fractures superimposed onto an EPM. Of the fracture networks studied, only those with truncated fractures caused transverse spreading. Simulated tritium levels in all of the cases were larger than observed values by a factor of approximately 100. Although this is partly due to input of too much tritium mass by the models it appears that dilution in the wells, which were not purged prior to sampling, is also a significant factor. The 1D and 2D EPM models were fitted to monitoring data from the first five years of the experiment and then used to predict future tritium concentrations
Zhao, Hewei; Yang, Shengchang; Guo, Xudong; Peng, Congjiao; Gu, Xiaoxuan; Deng, Chuanyuan; Chen, Luzhen
2018-02-01
Mangrove species have developed uniquely efficient water-use strategies in order to survive in highly saline and anaerobic environments. Herein, we estimated the stand water use of two diffuse-porous mangrove species of the same age, Sonneratia apetala Buch. Ham and Sonneratia caseolaris (L.) Engl., growing in a similar intertidal environment. Specifically, to investigate the radial patterns of axial sap flow density (Js) and understand the anatomical traits associated with them, we measured axial sap flow density in situ together with micromorphological observations. A significant decrease of Js was observed for both species. This result was accompanied by the corresponding observations of wood structure and blockages in xylem sapwood, which appeared to influence and, hence, explained the acute radial reductions of axial sap flow in the stems of both species. However, higher radial resistance in sapwood of S. caseolaris caused a steeper decline of Js radially when compared with S. apetala, thus explaining the latter's more efficient use of water. Without first considering acute reductions in Js into the sapwood from the outer bark, a total of ~55% and 51% of water use would have been overestimated, corresponding to average discrepancies in stand water use of 5.6 mm day-1 for S. apetala trees and 2.5 mm day-1 for S. caseolaris trees. This suggests that measuring radial pattern of Js is a critical factor in determining whole-tree or stand water use. © The Author(s) 2018. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.
Directory of Open Access Journals (Sweden)
Z. Abbas
Full Text Available An analysis is carried out to study the generalized slip condition and MHD flow of a nanofluid due to a contracting cylinder in the presence of non-linear radiative heat transfer using Buongiorno’s model. The Navier-Stokes along with energy and nanoparticle concentration equations is transformed to highly nonlinear ordinary differential equations using similarity transformations. These similar differential equations are then solved numerically by employing a shooting technique with Runge–Kutta–Fehlberg method. Dual solutions exist for a particular range of the unsteadiness parameter. The physical influence of the several important fluid parameters on the flow velocity, temperature and nanoparticle volume fraction is discussed and shown through graphs and table in detail. The present study indicates that as increase of Brownian motion parameter and slip velocity is to decrease the nanoparticle volume fraction. Keywords: Nanofluid, Contracting cylinder, Nonlinear thermal radiation, Generalized slip condition, Numerical solution
Stochastic porous media equations
Barbu, Viorel; Röckner, Michael
2016-01-01
Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found. The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model". The book will be of interest to PhD students and researchers in mathematics, physics and biology.
Carmeliet, J.; Abeele, van den K.E.A.
2004-01-01
The non-linear quasi-static and dynamic elastic behaviour of Berea sandstone has been experimentally analysed showing hysteresis and a strong influence of moisture especially in the lower saturation range. It is shown that non-linear hysteretic response originates within the "bond system" of the
Boundary control of fluid flow through porous media
DEFF Research Database (Denmark)
Hasan, Agus; Foss, Bjarne; Sagatun, Svein Ivar
2010-01-01
The flow of fluids through porous media can be described by the Boussinesq’s equation with mixed boundary conditions; a Neumann’s boundary condition and a nonlinear boundary condition. The nonlinear boundary condition provides a means to control the fluid flow through porous media. In this paper,......, some stabilizing controllers are constructed for various cases using Lyapunov design.......The flow of fluids through porous media can be described by the Boussinesq’s equation with mixed boundary conditions; a Neumann’s boundary condition and a nonlinear boundary condition. The nonlinear boundary condition provides a means to control the fluid flow through porous media. In this paper...
Energy Technology Data Exchange (ETDEWEB)
Tsuo, Y.S.; Menna, P.; Pitts, J.R. [National Renewable Energy Lab., Golden, CO (United States)] [and others
1996-05-01
The authors have studied a novel extrinsic gettering method that uses the large surface areas produced by a porous-silicon etch as gettering sites. The annealing step of the gettering used a high-flux solar furnace. They found that a high density of photons during annealing enhanced the impurity diffusion to the gettering sites. The authors used metallurgical-grade Si (MG-Si) prepared by directional solidification casing as the starting material. They propose to use porous-silicon-gettered MG-Si as a low-cost epitaxial substrate for polycrystalline silicon thin-film growth.
Keyes, Joseph T; Simon, Bruce R; Vande Geest, Jonathan P
2013-04-01
Arterial wall mass transport properties dictate local distribution of biomolecules or locally delivered dugs. Knowing how these properties vary between coronary artery locations could provide insight into how therapy efficacy is altered between arterial locations. We introduced an indocarbocyanine drug surrogate to the lumens of left anterior descending and right coronary (LADC; RC) arteries from pigs with or without a pressure gradient. Interstitial fluorescent intensity was measured on live samples with multiphoton microscopy. We also measured binding to porcine coronary SMCs in monoculture. Diffusive transport constants peaked in the middle sections of the LADC and RC arteries by 2.09 and 2.04 times, respectively, compared to the proximal and distal segments. There was no statistical difference between the average diffusivity value between LADC and RC arteries. The convection coefficients had an upward trend down each artery, with the RC being higher than the LADC by 3.89 times. This study demonstrates that the convective and diffusive transport of lipophilic molecules changes between the LADC and the RC arteries as well as along their length. These results may have important implications in optimizing drug delivery for the treatment of coronary artery disease.
Barber, Jared; Tanase, Roxana; Yotov, Ivan
2016-06-01
Several Kalman filter algorithms are presented for data assimilation and parameter estimation for a nonlinear diffusion model of epithelial cell migration. These include the ensemble Kalman filter with Monte Carlo sampling and a stochastic collocation (SC) Kalman filter with structured sampling. Further, two types of noise are considered -uncorrelated noise resulting in one stochastic dimension for each element of the spatial grid and correlated noise parameterized by the Karhunen-Loeve (KL) expansion resulting in one stochastic dimension for each KL term. The efficiency and accuracy of the four methods are investigated for two cases with synthetic data with and without noise, as well as data from a laboratory experiment. While it is observed that all algorithms perform reasonably well in matching the target solution and estimating the diffusion coefficient and the growth rate, it is illustrated that the algorithms that employ SC and KL expansion are computationally more efficient, as they require fewer ensemble members for comparable accuracy. In the case of SC methods, this is due to improved approximation in stochastic space compared to Monte Carlo sampling. In the case of KL methods, the parameterization of the noise results in a stochastic space of smaller dimension. The most efficient method is the one combining SC and KL expansion. Copyright © 2016 Elsevier Inc. All rights reserved.
Studies of Tracer Dispersion and Fluid Flow in Porous Media
Energy Technology Data Exchange (ETDEWEB)
Rage, T.
1996-12-31
This doctoral thesis explores the connection between the topology of a porous medium and its macroscopic transport properties and is based on computerized simulation. In porous media, both diffusion and convection contribute to the dispersion of a tracer and their combined effect is emphasized. The governing equations are solved numerically, using finite differences and Monte Carlo technique. The influence of finite Reynolds number on the outcome of echo-experiments is discussed. Comparing experiments and simulations it is found that nonlinear inertial forces lead to a visible deformation of a returned tracer at surprisingly small Reynolds numbers. In a study of tracer dispersion and fluid flow in periodic arrays of discs it is demonstrated that the mechanisms of mechanical dispersion in periodic media and in natural (non-periodic) porous media are essentially different. Measurements of the percolation probability distribution of a sandstone sample is presented. Local porosity theory predicts that this simple geometric function of a porous medium is of dominant importance for its macroscopic transport properties. It is demonstrated that many aspects of transport through fractures can be studied by using simple but realistic models and readily available computer resources. An example may be the transport of hydrocarbon fluids from the source rock to a reservoir. 165 refs., 44 figs., 1 table
Directory of Open Access Journals (Sweden)
Sameh E. Ahmed
2017-12-01
Full Text Available The present paper deals with the effects of slip boundary conditions and chemical reaction on the heat and mass transfer by mixed convective boundary layer flow of a non-Newtonian fluid over a nonlinear stretching sheet. The Casson fluid model is used to characterize the non-Newtonian fluid behavior. First order chemical reactions are considered. Similar solutions are used to convert the partial differential equations governing the problem to ordinary differential equations. The velocity, temperature and concentration profiles are obtained, numerically, using the MATLAB function bvp4c and those are used to compute the entropy generation number. The effect of increasing values of the Casson parameter is found to suppress the velocity field and temperature distribution. But the concentration is enhanced with the increasing of Casson parameter. The viscous dissipation, temperature and concentration irreversibility are determined and discussed in details.
Asymptotic behavior of the nonlinear diffusion equation n/sub t/ = (n-1n/sub x/)/sub x/
International Nuclear Information System (INIS)
Berryman, J.G.; Holland, C.J.
1982-01-01
The asymptotic behavior of the equation n/sub t/ = (ln n)/sub x/x is studied on the finite interval 0 0 and initial data n(x,0)> or =n 0 . We prove that asymptotically ln[n(x,t)/n 0 ]→A exp(-π 2 t/n 0 )2/sup 1/2/ sin πx and also provide rigorous upper and lower bounds on the asymptotic amplitude A in terms of integrals of nonlinear functions of the initial data. The rigorous bounds are compared to values of A obtained from computer experiments. The lower bound L = (2/sup 3/2//π)exp[li(1+Q)-γ], where li is the logarithmic integral, γ is Euler's constant, and Q = (π/2)∫[n(x,0)/n 0 -1]sin πx dx, is found to be the best known estimate of A
Burger, Karin; Koehler, Thomas; Chabior, Michael; Allner, Sebastian; Marschner, Mathias; Fehringer, Andreas; Willner, Marian; Pfeiffer, Franz; Noël, Peter
2014-12-29
Phase-contrast x-ray computed tomography has a high potential to become clinically implemented because of its complementarity to conventional absorption-contrast.In this study, we investigate noise-reducing but resolution-preserving analytical reconstruction methods to improve differential phase-contrast imaging. We apply the non-linear Perona-Malik filter on phase-contrast data prior or post filtered backprojected reconstruction. Secondly, the Hilbert kernel is replaced by regularized iterative integration followed by ramp filtered backprojection as used for absorption-contrast imaging. Combining the Perona-Malik filter with this integration algorithm allows to successfully reveal relevant sample features, quantitatively confirmed by significantly increased structural similarity indices and contrast-to-noise ratios. With this concept, phase-contrast imaging can be performed at considerably lower dose.
Nonlinear Fokker-Planck Equations Fundamentals and Applications
Frank, Till Daniel
2005-01-01
Providing an introduction to the theory of nonlinear Fokker-Planck equations, this book discusses fundamental properties of transient and stationary solutions, emphasizing the stability analysis of stationary solutions by means of self-consistency equations, linear stability analysis, and Lyapunov's direct method. Also treated are Langevin equations and correlation functions. Nonlinear Fokker-Planck Equations addresses various phenomena such as phase transitions, multistability of systems, synchronization, anomalous diffusion, cut-off solutions, travelling-wave solutions and the emergence of power law solutions. A nonlinear Fokker-Planck perspective to quantum statistics, generalized thermodynamics, and linear nonequilibrium thermodynamics is given. Theoretical concepts are illustrated where possible by simple examples. The book also reviews several applications in the fields of condensed matter physics, the physics of porous media and liquid crystals, accelerator physics, neurophysics, social sciences, popul...
Diffusion Under Geometrical Constraint
Ogawa, Naohisa
2014-01-01
Here we discus the diffusion of particles in a curved tube. This kind of transport phenomenon is observed in biological cells and porous media. To solve such a problem, we discuss the three dimensional diffusion equation with a confining wall forming a thinner tube. We find that the curvature appears in a effective diffusion coefficient for such a quasi-one-dimensional system. As an application to higher dimensional case, we discuss the diffusion in a curved surface with ...
Porous media geometry and transports
Adler, Pierre
1992-01-01
The goal of ""Porous Media: Geometry and Transports"" is to provide the basis of a rational and modern approach to porous media. This book emphasizes several geometrical structures (spatially periodic, fractal, and random to reconstructed) and the three major single-phase transports (diffusion, convection, and Taylor dispersion).""Porous Media"" serves various purposes. For students it introduces basic information on structure and transports. Engineers will find this book useful as a readily accessible assemblage of al the major experimental results pertaining to single-phase tr
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
Abstract. Carbon in dense as well as porous solid form is used in a variety of applications. Activated porous carbons are made through pyrolysis and activation of carbonaceous natural as well as synthetic precursors. Pyrolysed woods replicate the structure of original wood but as such possess very low surface areas and ...
Sadeghifar, Hamidreza; Djilali, Ned; Bahrami, Majid
2015-01-01
This paper reports on measurements of thermal conductivity of a graphite bipolar plate (BPP) as a function of temperature and its thermal contact resistance (TCR) with treated and untreated gas diffusion layers (GDLs). The thermal conductivity of the BPP decreases with temperature and its thermal contact resistance with GDLs, which has been overlooked in the literature, is found to be dominant over a relatively wide range of compression. The effects of PTFE loading, micro porous layer (MPL), compression, and BPP out-of-flatness are also investigated experimentally. It is found that high PTFE loadings, MPL and even small BPP out-of-flatness increase the BPP-GDL thermal contact resistance dramatically. The paper also presents the effect of cyclic load on the total resistance of a GDL-BPP assembly, which sheds light on the behavior of these materials under operating conditions in polymer electrolyte membrane fuel cells.
Directory of Open Access Journals (Sweden)
I.L. Animasaun
2016-06-01
Full Text Available This article presents the effects of nonlinear thermal radiation and induced magnetic field on viscoelastic fluid flow toward a stagnation point. It is assumed that there exists a kind of chemical reaction between chemical species A and B. The diffusion coefficients of the two chemical species in the viscoelastic fluid flow are unequal. Since chemical species B is a catalyst at the horizontal surface, hence homogeneous and heterogeneous schemes are of the isothermal cubic autocatalytic reaction and first order reaction respectively. The transformed governing equations are solved numerically using Runge–Kutta integration scheme along with Newton’s method. Good agreement is obtained between present and published numerical results for a limiting case. The influence of some pertinent parameters on skin friction coefficient, local heat transfer rate, together with velocity, induced magnetic field, temperature, and concentration profiles is illustrated graphically and discussed. Based on all of these assumptions, results indicate that the effects of induced magnetic and viscoelastic parameters on velocity, transverse velocity and velocity of induced magnetic field are almost the same but opposite in nature. The strength of heterogeneous reaction parameter is very helpful to reduce the concentration of bulk fluid and increase the concentration of catalyst at the surface.
Influence of surface wettability on cathode electroluminescence of porous silicon
International Nuclear Information System (INIS)
Goryachev, D.N.; Sreseli, O.M.; Belyakov, L.V.
1997-01-01
Influence of porous silicon wettability on efficiency of its cathode electroluminescence in electrolytes was investigated. It was revealed that increase of porous silicon wettability by electrolyte improved contact with a sublayer and provided generation of sufficient quantity of charge carriers. Diffusion - ionic, not electronic mechanism of charge transfer to the centers of micro crystallite electroluminescence is observed in porous silicon - electrolyte systems
Ullah, Imran; Bhattacharyya, Krishnendu; Shafie, Sharidan; Khan, Ilyas
2016-01-01
Numerical results are presented for the effect of first order chemical reaction and thermal radiation on mixed convection flow of Casson fluid in the presence of magnetic field. The flow is generated due to unsteady nonlinearly stretching sheet placed inside a porous medium. Convective conditions on wall temperature and wall concentration are also employed in the investigation. The governing partial differential equations are converted to ordinary differential equations using suitable transformations and then solved numerically via Keller-box method. It is noticed that fluid velocity rises with increase in radiation parameter in the case of assisting flow and is opposite in the case of opposing fluid while radiation parameter has no effect on fluid velocity in the forced convection. It is also seen that fluid velocity and concentration enhances in the case of generative chemical reaction whereas both profiles reduces in the case of destructive chemical reaction. Further, increase in local unsteadiness parameter reduces fluid velocity, temperature and concentration. Over all the effects of physical parameters on fluid velocity, temperature and concentration distribution as well as on the wall shear stress, heat and mass transfer rates are discussed in detail.
Ledenyov, Dimitri O.; Ledenyov, Viktor O.
2014-01-01
The authors perform an original research on the fundamentals of winning virtuous strategies creation toward the leveraged buyout transactions implementation during the private equity investment in the conditions of the resonant absorption of discrete information in the diffusion - type financial system with the induced nonlinearities at the influences by the Schumpeterian creative disruption processes in the free market economy. We propose that the money is a financial computing process, whic...
Positronium chemistry in porous materials
International Nuclear Information System (INIS)
Kobayashi, Y.; Ito, K.; Oka, T.; Hirata, K.
2007-01-01
Porous materials have fascinated positron and positronium chemists for over decades. In the early 1970s it was already known that ortho-positronium (o-Ps) exhibits characteristic long lifetimes in silica gels, porous glass and zeolites. Since then, our understanding of Ps formation, diffusion and annihilation has been drastically deepened. Ps is now well recognized as a powerful porosimetric and chemical probe to study the average pore size, pore size distribution, pore connectivity and surface properties of various porous materials including thin films. In this paper, developments of Ps chemistry in porous materials undertaken in the past some 40 yr are surveyed and problems to be addressed in future are briefly discussed
International Nuclear Information System (INIS)
Garrett, G.A.; Shacter, J.
1978-01-01
A gaseous diffusion system is described comprising a plurality of diffusers connected in cascade to form a series of stages, each of the diffusers having a porous partition dividing it into a high pressure chamber and a low pressure chamber, and means for combining a portion of the enriched gas from a succeeding stage with a portion of the enriched gas from the low pressure chamber of each stage and feeding it into one extremity of the high pressure chamber thereof
Czech Academy of Sciences Publication Activity Database
Veselý, M.; Bultreys, T.; Peksa, M.; Lang, J.; Cnudde, V.; van Hoorebeke, L.; Kočiřík, Milan; Hejtmánek, Vladimír; Šolcová, Olga; Soukup, Karel; Gerke, K.; Stallmach, F.; Čapek, P.
2015-01-01
Roč. 110, č. 1 (2015), s. 81-111 ISSN 0169-3913 R&D Projects: GA ČR(CZ) GAP204/11/1206 Institutional support: RVO:61388955 ; RVO:67985858 Keywords : Isobaric counter-current diffusion * Knudsen flow * Pulsed field gradient NMR Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 1.653, year: 2015
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.
Tritium transport in lithium ceramics porous media
International Nuclear Information System (INIS)
Tam, S.W.; Ambrose, V.
1991-01-01
A random network model has been utilized to analyze the problem of tritium percolation through porous Li ceramic breeders. Local transport in each pore channel is described by a set of convection-diffusion-reaction equations. Long range transport is described by a matrix technique. The heterogeneous structure of the porous medium is accounted for via Monte Carlo methods. The model was then applied to an analysis of the relative contribution of diffusion and convective flow to tritium transport in porous lithium ceramics. 15 refs., 4 figs
DEFF Research Database (Denmark)
Johannesson, Björn
2010-01-01
There exist, mainly, two different continuum approaches to calculate transient multi species ionic diffusion. One of them is based on explicitly assuming a zero current in the diffusing mixture together with an introduction of a streaming electrical potential in the constitutive equations...... of the coupled set of equation in favor of the staggering approach. A one step truly implicit time stepping scheme is adopted together with an implementation of a modified Newton-Raphson iterational scheme for search of equilibrium at each considered time step calculation. Results from the zero current case...... difference of the two types of potentials, that is, the streaming electrical potential and the electrical field is carefully examined. A novel numerical method based on the finite element approach is established for the zero current method case. The proposed numerical method uses the direct calculation...
Thermal and optical properties of porous silicon
Directory of Open Access Journals (Sweden)
Silva A. Ferreira da
2001-01-01
Full Text Available Thermal diffusivity and optical absorption have been investigated for porous silicon, at room temperature, using photoacoustic spectroscopy. The experimental results obtained conform well with the existing studies recently published. The value obtained for thermal diffusivity is 0.045 ± 0.002 cm²/s.The absorption onsets show energy structures, differing from the ordinary semiconductor of bulk type.
A non-Linear transport model for determining shale rock characteristics
Ali, Iftikhar; Malik, Nadeem
2016-04-01
Unconventional hydrocarbon reservoirs consist of tight porous rocks which are characterised by nano-scale size porous networks with ultra-low permeability [1,2]. Transport of gas through them is not well understood at the present time, and realistic transport models are needed in order to determine rock properties and for estimating future gas pressure distribution in the reservoirs. Here, we consider a recently developed non-linear gas transport equation [3], ∂p-+ U ∂p- = D ∂2p-, t > 0, (1) ∂t ∂x ∂x2 complimented with suitable initial and boundary conditions, in order to determine shale rock properties such as the permeability K, the porosity φ and the tortuosity, τ. In our new model, the apparent convection velocity, U = U(p,px), and the apparent diffusivity D = D(p), are both highly non-linear functions of the pressure. The model incorporate various flow regimes (slip, surface diffusion, transition, continuum) based upon the Knudsen number Kn, and also includes Forchchiemers turbulence correction terms. In application, the model parameters and associated compressibility factors are fully pressure dependent, giving the model more realism than previous models. See [4]. Rock properties are determined by solving an inverse problem, with model parameters adjustment to minimise the error between the model simulation and available data. It is has been found that the proposed model performs better than previous models. Results and details of the model will be presented at the conference. Corresponding author: namalik@kfupm.edu.sa and nadeem_malik@cantab.net References [1] Cui, X., Bustin, A.M. and Bustin, R., "Measurements of gas permeability and diffusivity of tight reservoir rocks: different approaches and their applications", Geofluids 9, 208-223 (2009). [2] Chiba R., Fomin S., Chugunov V., Niibori Y. and Hashida T., "Numerical Simulation of Non Fickian Diffusion and Advection in a Fractured Porous Aquifer", AIP Conference Proceedings 898, 75 (2007
Energy Technology Data Exchange (ETDEWEB)
Schmocker, U
1980-07-01
Repositories in geological formations are planned for the final disposal of radioactive wastes produced by nuclear power. Generally, water entry leading to leaching of the waste matrix is considered as the critical process which can result in release of radionuclides from a waste repository. In risk analyses for waste repositories the migration of radionuclides through the geosphere is usually described mathematically by a one-dimensional transport model. On the other hand the hydrological calculational models used for determining the critical migration paths are invariably two- or three-dimensional. A one-dimensional transport calculation always gives conservative results for a specific migration path because the influence of the transverse dispersion/diffusion effect is neglected. This effect results in an additional decrease of the nuclide concentration along the migration path. On the other hand radionuclides can spread to adjacent geological formations which are not taken into account in a one-dimensional model. If the water velocities in these formations are higher than along the original (one-dimensional) migration path or if the distance to the biosphere (e.g. lake, river or well) is shorter, then the process of the transverse diffusion/dispersion can represent an additional risk. The present work deals with the influence of the transverse diffusion/dispersion effect on the migration of radionuclides through the geosphere. We restrict ourselves to migration in porous media which is the standard approach of most existing transport models. For modelling the transport of radionuclides in fissured systems there exist only a few preliminary calculational approaches to date. We are mainly interested in analytically soluble problems which take into account the transverse diffusion/dispersion effect. This procedure permits investigation of the most important effects in a simple and direct manner. 17 refs., 36 figs., 2 tabs.
Biesheuvel, P.M.; Fu, Y.; Bazant, M.Z.
2012-01-01
We present porous electrode theory for the general situation of electrolytes containing mixtures of mobile ions of arbitrary valencies and diffusion coefficients (mobilities). We focus on electrodes composed of primary particles that are porous themselves. The predominantly bimodal distribution of
Homogenization of complex flows in porous media and applications
International Nuclear Information System (INIS)
Hutridurga-Ramaiah, Harsha
2013-01-01
Our work is a contribution to the understanding of transport of solutes in a porous medium. It has applications in groundwater contaminant transport, CO 2 sequestration, underground storage of nuclear waste, oil reservoir simulations. We derive expressions for the effective Taylor dispersion taking into account convection, diffusion, heterogeneous geometry of the porous medium and reaction phenomena. Microscopic phenomena at the pore scale are up-scaled to obtain effective behaviour at the observation scale. Method of two-scale convergence with drift from the theory of homogenization is employed as an up-scaling technique. In the first part of our work, we consider reactions of mass exchange type, adsorption/desorption, at the fluid-solid interface of the porous medium. Starting with coupled convection-diffusion equations for bulk and surface concentrations of a single solute, coupled via adsorption isotherms, at a microscopic scale we derive effective equations at the macroscopic scale. We consider the microscopic system with highly oscillating coefficients in a strong convection regime i.e., large Peclet regime. The presence of strong convection in the microscopic model leads to the induction of a large drift in the concentration profiles. Both linear and nonlinear adsorption isotherms are considered and the results are compared. In the second part of our work we generalize our results on single component flow to multicomponent flow in a linear setting. In the latter case, the effective parameters are obtained using Factorization principle and two-scale convergence with drift. The behaviour of effective parameters with respect to Peclet number and Damkohler number are numerically studied. Freefem++ is used to perform numerical tests in two dimensions. (author)
Analysis of the kinetics of methanol oxidation in a porous Pt-Ru anode
Energy Technology Data Exchange (ETDEWEB)
Sun, Yan-Ping; Xing, Lei [Chemical Engineering Department, Taiyuan University of Technology, Shanxi 030024 (China); Scott, Keith [School of Chemical Engineering and Advanced Materials, Merz Court, University of Newcastle, Newcastle upon Tyne NE1 7RU (United Kingdom)
2010-01-01
A kinetic model of a porous Pt-Ru anode for methanol oxidation is presented. It was based on the dual-site mechanism for methanol oxidation and used to predict anode performance and the influence of species adsorption on the overall oxidation (macro-) kinetics. The performance of the porous Pt-Ru anode depended on the parameters of the intrinsic chemical kinetics of methanol oxidation and physical parameters such as electrode thickness, surface area, effective diffusion and charge transfer coefficients and concentration of methanol and temperature. The model was solved by using the finite difference method with a subroutine for solving a set of nonlinear algebraic equations in each step. Surface coverage ratio distributions of adsorbed species, effectiveness of the porous electrode and macro-polarisation curves were obtained. The simulated polarisation curves were compared to experimental polarisation data for methanol oxidation on Pt-Ru porous anodes at different temperatures and methanol concentrations. The intrinsic kinetic parameters were regressed from the corresponding experimental data. The predicted polarisation curves calculated by the model, were consistent with experimental polarisation data at lower current densities. The departure of experimental data from the predicted polarisation curves at high concentration and high apparent current densities was believed to be due to two-phase flow in the electrode. (author)
Energy Technology Data Exchange (ETDEWEB)
Garcia Velarde, M
1977-07-01
Thermo convective instabilities in horizontal fluid layers are discussed with emphasis on the Rayleigh-Bernard model problem. Steady solutions and time-dependent phenomena (relaxation oscillations and transition to turbulence) are studied within the nonlinear Boussinesq-Oberbeck approximation. Homogeneous steady solutions, limit cycles, and inhomogeneous (ordered) spatial structures are also studied in simple reaction-diffusion systems. Lastly, the non-periodic attractor that appears at large Rayleigh numbers in the truncated Boussinesq-Oberbeck model of Lorenz, is constructed, and a discussion of turbulent behavior is given. (Author) 105 refs.
International Nuclear Information System (INIS)
Garcia Velarde, M.
1977-01-01
Thermoconvective instabilities in horizontal fluid layers are discussed with emphasis on the Rayleigh-Benard model problem. Steady solutions and time-dependent phenomena (relaxation oscillations and transition to turbulence) are studied within the nonlinear Boussinesq-Oberbeck approximation. Homogeneous steady solutions, limit cycles, and inhomogeneous (ordered) spatial structures are also studied in simple reaction-diffusion systems. Lastly, the non-periodic attractor that appears at large Rayleigh numbers in the truncated Boussinesq-Oberbeck model of Lorenz, is constructed, and a discussion of turbulent behavior is given. (author) [es
International Nuclear Information System (INIS)
Garcia Velarde, M.
1977-01-01
Thermo convective instabilities in horizontal fluid layers are discussed with emphasis on the Rayleigh-Bernard model problem. Steady solutions and time-dependent phenomena (relaxation oscillations and transition to turbulence) are studied within the nonlinear Boussinesq-Oberbeck approximation. Homogeneous steady solutions, limit cycles, and inhomogeneous (ordered) spatial structures are also studied in simple reaction-diffusion systems. Lastly, the non-periodic attractor that appears at large Rayleigh numbers in the truncated Boussinesq-Oberbeck model of Lorenz, is constructed, and a discussion of turbulent behavior is given. (Author) 105 refs
AULISA, EUGENIO
2009-08-01
Motivated by the reservoir engineering concept of the well Productivity Index, we introduced and analyzed a functional, denoted as "diffusive capacity", for the solution of the initial-boundary value problem (IBVP) for a linear parabolic equation.21 This IBVP described laminar (linear) Darcy flow in porous media; the considered boundary conditions corresponded to different regimes of the well production. The diffusive capacities were then computed as steady state invariants of the solutions to the corresponding time-dependent boundary value problem. Here similar features for fast or turbulent nonlinear flows subjected to the Forchheimer equations are analyzed. It is shown that under some hydrodynamic and thermodynamic constraints, there exists a so-called pseudo steady state regime for the Forchheimer flows in porous media. In other words, under some assumptions there exists a steady state invariant over a certain class of solutions to the transient IBVP modeling the Forchheimer flow for slightly compressible fluid. This invariant is the diffusive capacity, which serves as the mathematical representation of the so-called well Productivity Index. The obtained results enable computation of the well Productivity Index by resolving a single steady state boundary value problem for a second-order quasilinear elliptic equation. Analytical and numerical studies highlight some new relations for the well Productivity Index in linear and nonlinear cases. The obtained analytical formulas can be potentially used for the numerical well block model as an analog of Piecemann. © 2009 World Scientific Publishing Company.
Ho, Clifford K
2006-01-01
This book presents a compilation of state-of-the art studies on gas and vapor transport processes in porous and fractured media. A broad set of models and processes are presented, including advection/diffusion, the Dusty Gas Model, enhanced vapor diffusion, phase change, coupled processes, solid/vapor sorption, and vapor-pressure lowering. Numerous applications are also presented that illustrate these processes and models in current problems facing the scientific community. This book fills a gap in the general area of transport in porous and fractured media; an area that has historically been dominated by studies of liquid-phase flow and transport. This book identifies gas and vapor transport processes that may be important or dominant in various applications, and it exploits recent advances in computational modeling and experimental methods to present studies that distinguish the relative importance of various mechanisms of transport in complex media.
Diffusion Based Photon Mapping
DEFF Research Database (Denmark)
Schjøth, Lars; Fogh Olsen, Ole; Sporring, Jon
2007-01-01
. To address this problem we introduce a novel photon mapping algorithm based on nonlinear anisotropic diffusion. Our algorithm adapts according to the structure of the photon map such that smoothing occurs along edges and structures and not across. In this way we preserve the important illumination features......, while eliminating noise. We call our method diffusion based photon mapping....
Diffusion Based Photon Mapping
DEFF Research Database (Denmark)
Schjøth, Lars; Olsen, Ole Fogh; Sporring, Jon
2006-01-01
. To address this problem we introduce a novel photon mapping algorithm based on nonlinear anisotropic diffusion. Our algorithm adapts according to the structure of the photon map such that smoothing occurs along edges and structures and not across. In this way we preserve the important illumination features......, while eliminating noise. We call our method diffusion based photon mapping....
Nonlinear acceleration of transport criticality problems
International Nuclear Information System (INIS)
Park, H.; Knoll, D.A.; Newman, C.K.
2011-01-01
We present a nonlinear acceleration algorithm for the transport criticality problem. The algorithm combines the well-known nonlinear diffusion acceleration (NDA) with a recently developed, Newton-based, nonlinear criticality acceleration (NCA) algorithm. The algorithm first employs the NDA to reduce the system to scalar flux, then the NCA is applied to the resulting drift-diffusion system. We apply a nonlinear elimination technique to eliminate the eigenvalue from the Jacobian matrix. Numerical results show that the algorithm reduces the CPU time a factor of 400 in a very diffusive system, and a factor of 5 in a non-diffusive system. (author)
International Nuclear Information System (INIS)
Lalis, A.; Rouviere, R.; Simon, G.
1976-01-01
A multipassage diffuser having 2p passages comprises a leak-tight cylindrical enclosure closed by a top cover and a bottom end-wall, parallel porous tubes which are rigidly assembled in sectors between tube plates and through which the gas mixture flows, the tube sectors being disposed at uniform intervals on the periphery of the enclosure. The top tube plates are rigidly fixed to an annular header having the shape of a half-torus and adapted to communicate with the tubes of the corresponding sector. Each passage is constituted by a plurality of juxtaposed sectors in which the mixture circulates in the same direction, the header being divided into p portions limited by radial partition-walls and each constituting two adjacent passages. The diffuser is provided beneath the bottom end-wall with p-1 leak-tight chambers each adapted to open into two different portions of the header, and with two collector-chambers each fitted with a nozzle for introducing the gas mixture and discharging the fraction of the undiffused mixture. By means of a central orifice formed in the bottom end-wall the enclosure communicates with a shaft for discharging the diffused fraction of the gas mixture
International Nuclear Information System (INIS)
Habib, S.
1994-01-01
We consider a simple quantum system subjected to a classical random force. Under certain conditions it is shown that the noise-averaged Wigner function of the system follows an integro-differential stochastic Liouville equation. In the simple case of polynomial noise-couplings this equation reduces to a generalized Fokker-Planck form. With nonlinear noise injection new ''quantum diffusion'' terms rise that have no counterpart in the classical case. Two special examples that are not of a Fokker-Planck form are discussed: the first with a localized noise source and the other with a spatially modulated noise source
Apparatus for diffusion separation
International Nuclear Information System (INIS)
Nierenberg, W.A.; Pontius, R.B.
1976-01-01
The method of testing the separation efficiency of porous permeable membranes is described which comprises causing a stream of a gaseous mixture to flow into contact with one face of a finely porous permeable membrane under such conditions that a major fraction of the mixture diffuses through the membrane, maintaining a rectangular cross section of the gaseous stream so flowing past said membrane, continuously recirculating the gas that diffuses through said membrane and continuously withdrawing the gas that does not diffuse through said membrane and maintaining the volume of said recirculating gas constant by continuously introducing into said continuously recirculating gas stream a mass of gas equivalent to that which is continuously withdrawn from said gas stream and comparing the concentrations of the light component in the entering gas, the withdrawn gas and the recirculated gas in order to determine the efficiency of said membrane
Fractional diffusion equations and anomalous diffusion
Evangelista, Luiz Roberto
2018-01-01
Anomalous diffusion has been detected in a wide variety of scenarios, from fractal media, systems with memory, transport processes in porous media, to fluctuations of financial markets, tumour growth, and complex fluids. Providing a contemporary treatment of this process, this book examines the recent literature on anomalous diffusion and covers a rich class of problems in which surface effects are important, offering detailed mathematical tools of usual and fractional calculus for a wide audience of scientists and graduate students in physics, mathematics, chemistry and engineering. Including the basic mathematical tools needed to understand the rules for operating with the fractional derivatives and fractional differential equations, this self-contained text presents the possibility of using fractional diffusion equations with anomalous diffusion phenomena to propose powerful mathematical models for a large variety of fundamental and practical problems in a fast-growing field of research.
Measuring methods of matrix diffusion
International Nuclear Information System (INIS)
Muurinen, A.; Valkiainen, M.
1988-03-01
In Finland the spent nuclear fuel is planned to be disposed of at large depths in crystalline bedrock. The radionuclides which are dissolved in the groundwater may be able to diffuse into the micropores of the porous rock matrix and thus be withdrawn from the flowing water in the fractures. This phenomenon is called matrix diffusion. A review over matrix diffusion is presented in the study. The main interest is directed to the diffusion of non-sorbing species. The review covers diffusion experiments and measurements of porosity, pore size, specific surface area and water permeability
From conservative to reactive transport under diffusion-controlled conditions
Babey, Tristan; de Dreuzy, Jean-Raynald; Ginn, Timothy R.
2016-05-01
We assess the possibility to use conservative transport information, such as that contained in transit time distributions, breakthrough curves and tracer tests, to predict nonlinear fluid-rock interactions in fracture/matrix or mobile/immobile conditions. Reference simulated data are given by conservative and reactive transport simulations in several diffusive porosity structures differing by their topological organization. Reactions includes nonlinear kinetically controlled dissolution and desorption. Effective Multi-Rate Mass Transfer models (MRMT) are calibrated solely on conservative transport information without pore topology information and provide concentration distributions on which effective reaction rates are estimated. Reference simulated reaction rates and effective reaction rates evaluated by MRMT are compared, as well as characteristic desorption and dissolution times. Although not exactly equal, these indicators remain very close whatever the porous structure, differing at most by 0.6% and 10% for desorption and dissolution. At early times, this close agreement arises from the fine characterization of the diffusive porosity close to the mobile zone that controls fast mobile-diffusive exchanges. At intermediate to late times, concentration gradients are strongly reduced by diffusion, and reactivity can be captured by a very limited number of rates. We conclude that effective models calibrated solely on conservative transport information like MRMT can accurately estimate monocomponent kinetically controlled nonlinear fluid-rock interactions. Their relevance might extend to more advanced biogeochemical reactions because of the good characterization of conservative concentration distributions, even by parsimonious models (e.g., MRMT with 3-5 rates). We propose a methodology to estimate reactive transport from conservative transport in mobile-immobile conditions.
Energy Technology Data Exchange (ETDEWEB)
Geiger, S.; Cortis, A.; Birkholzer, J.T.
2010-04-01
Solute transport in fractured porous media is typically 'non-Fickian'; that is, it is characterized by early breakthrough and long tailing and by nonlinear growth of the Green function-centered second moment. This behavior is due to the effects of (1) multirate diffusion occurring between the highly permeable fracture network and the low-permeability rock matrix, (2) a wide range of advection rates in the fractures and, possibly, the matrix as well, and (3) a range of path lengths. As a consequence, prediction of solute transport processes at the macroscale represents a formidable challenge. Classical dual-porosity (or mobile-immobile) approaches in conjunction with an advection-dispersion equation and macroscopic dispersivity commonly fail to predict breakthrough of fractured porous media accurately. It was recently demonstrated that the continuous time random walk (CTRW) method can be used as a generalized upscaling approach. Here we extend this work and use results from high-resolution finite element-finite volume-based simulations of solute transport in an outcrop analogue of a naturally fractured reservoir to calibrate the CTRW method by extracting a distribution of retention times. This procedure allows us to predict breakthrough at other model locations accurately and to gain significant insight into the nature of the fracture-matrix interaction in naturally fractured porous reservoirs with geologically realistic fracture geometries.
Limiting diffusion current at rotating disk electrode with dense particle layer.
Weroński, P; Nosek, M; Batys, P
2013-09-28
Exploiting the concept of diffusion permeability of multilayer gel membrane and porous multilayer we have derived a simple analytical equation for the limiting diffusion current at rotating disk electrode (RDE) covered by a thin layer with variable tortuosity and porosity, under the assumption of negligible convection in the porous film. The variation of limiting diffusion current with the porosity and tortuosity of the film can be described in terms of the equivalent thickness of stagnant solution layer, i.e., the average ratio of squared tortuosity to porosity. In case of monolayer of monodisperse spherical particles, the equivalent layer thickness is an algebraic function of the surface coverage. Thus, by means of cyclic voltammetry of RDE with a deposited particle monolayer we can determine the monolayer surface coverage. The effect of particle layer adsorbed on the surface of RDE increases non-linearly with surface coverage. We have tested our theoretical results experimentally by means of cyclic voltammetry measurements of limiting diffusion current at the glassy carbon RDE covered with a monolayer of 3 μm silica particles. The theoretical and experimental results are in a good agreement at the surface coverage higher than 0.7. This result suggests that convection in a monolayer of 3 μm monodisperse spherical particles is negligibly small, in the context of the coverage determination, in the range of very dense particle layers.
Diffusion in compacted betonite
International Nuclear Information System (INIS)
Muurinen, A.; Rantanen, J.
1985-01-01
The objective of this report is to collect the literature bearing on the diffusion in compacted betonite, which has been suggested as possible buffer material for the disposal of spent fuel. Diffusion in a porous, water-saturated material is usually described as diffusion in the pore-water where sorption on the solid matter can delay the migration in the instationary state. There are also models which take into consideration that the sorbed molecules can also move while being sorbed. Diffusion experiments in compacted bentonite have been reported by many authors. Gases, anions, cations and actinides have been used as diffusing molecules. The report collects the results and the information on the measurement methods. On the basis of the results can be concluded that different particles possibly follow different diffusion mechanisms. The parameters which affect the diffusion seem to be for example the size, the electric charge and the sorption properties of the diffusing molecule. The report also suggest the parameters to be used in the diffusion calculation of the safety analyses of spent fuel disposal. (author)
Directory of Open Access Journals (Sweden)
Mohammed Almakki
2017-07-01
Full Text Available The entropy generation in unsteady three-dimensional axisymmetric magnetohydrodynamics (MHD nanofluid flow over a non-linearly stretching sheet is investigated. The flow is subject to thermal radiation and a chemical reaction. The conservation equations are solved using the spectral quasi-linearization method. The novelty of the work is in the study of entropy generation in three-dimensional axisymmetric MHD nanofluid and the choice of the spectral quasi-linearization method as the solution method. The effects of Brownian motion and thermophoresis are also taken into account. The nanofluid particle volume fraction on the boundary is passively controlled. The results show that as the Hartmann number increases, both the Nusselt number and the Sherwood number decrease, whereas the skin friction increases. It is further shown that an increase in the thermal radiation parameter corresponds to a decrease in the Nusselt number. Moreover, entropy generation increases with respect to some physical parameters.
Numerical modelling of two phase flow with hysteresis in heterogeneous porous media
Energy Technology Data Exchange (ETDEWEB)
Abreu, E. [Instituto Nacional de Matematica Pura e Aplicada (IMPA), Rio de Janeiro, RJ (Brazil); Furtado, F.; Pereira, F. [University of Wyoming, Laramie, WY (United States). Dept. of Mathematicsatics; Souza, G. [Universidade do Estado do Rio de Janeiro (UERJ), RJ (Brazil)
2008-07-01
Numerical simulators are necessary for the understanding of multiphase flow in porous media in order to optimize hydrocarbon recovery. In this work, the immiscible flow of two incompressible phases, a problem very common in waterflooding of petroleum reservoirs, is considered and numerical simulation techniques are presented. The system of equations which describe this type of flow form a coupled, highly nonlinear system of time-dependent partial differential equations (PDEs). The equation for the saturation of the invading fluid is a convection-dominated, degenerate parabolic PDE whose solutions typically exhibit sharp fronts (i.e., internal layers with strong gradients) and is very difficult to approximate numerically. It is well known that accurate modeling of convective and diffusive processes is one of the most daunting tasks in the numerical approximation of PDEs. Particularly difficult is the case where convection dominates diffusion. Specifically, we consider the injection problem for a model of two-phase (water/oil) flow in a core sample of porous rock, taking into account hysteresis effects in the relative permeability of the oil phase. (author)
Amine Functionalized Porous Network
Eddaoudi, Mohamed; Guillerm, Vincent; Weselinski, Lukasz Jan; Alkordi, Mohamed H.; Mohideen, Mohamed Infas Haja; Belmabkhout, Youssef
2015-01-01
Amine groups can be introduced in porous materials by a direct (one pot) or post-synthetic modification (PSM) process on aldehyde groups, and the resulting porous materials have increased gas affinity.
Amine Functionalized Porous Network
Eddaoudi, Mohamed
2015-05-28
Amine groups can be introduced in porous materials by a direct (one pot) or post-synthetic modification (PSM) process on aldehyde groups, and the resulting porous materials have increased gas affinity.
Energy Technology Data Exchange (ETDEWEB)
Holden, Helge; Karlsen, Kenneth H.; Lie, Knut-Andreas
1999-10-01
We present and analyze a numerical method for the solution of a class of scalar, multi-dimensional, nonlinear degenerate convection-diffusion equations. The method is based on operator splitting to separate the convective and the diffusive terms in the governing equation. The nonlinear, convective part is solved using front tracking and dimensional splitting, while the nonlinear diffusion equation is solved by a suitable difference scheme. We verify L{sup 1} compactness of the corresponding set of approximate solutions and derive precise entropy estimates. In particular, these results allow us to pass to the limit in our approximations and recover an entropy solution of the problem in question. The theory presented covers a large class of equations. Important subclasses are hyperbolic conservation laws, porous medium type equations, two-phase reservoir flow equations, and strongly degenerate equations coming from the recent theory of sedimentation-consolidation processes. A thorough numerical investigation of the method analyzed in this paper (and similar methods) is presented in a companion paper. (author)
Positronium chemistry in porous adsorbents
International Nuclear Information System (INIS)
Foti, G.; Nagy, L.G.; Moravcsik, G.; Schay, G.
1981-01-01
Kinetic studies on the annihilation of orthopositronium in porous adsorbents have been performed using lifetime spectroscopy. The positron source applied was 22 Na with 0.2 MBq activity. The adsorbents investigated were silica gels of different particle size and pore structure. The appearance of the long-lived component in the lifetime spectra can be explained by the diffusion of the orthopositronium into the pores affected by the particle size and the pore size of the adsorbent, the coverage on it and the chemical nature of the adsorbate. The long-term aim of the work is to determine and to explain these effects. (author)
Amplitude equations for a sub-diffusive reaction-diffusion system
International Nuclear Information System (INIS)
Nec, Y; Nepomnyashchy, A A
2008-01-01
A sub-diffusive reaction-diffusion system with a positive definite memory operator and a nonlinear reaction term is analysed. Amplitude equations (Ginzburg-Landau type) are derived for short wave (Turing) and long wave (Hopf) bifurcation points
An Iterative Implicit Scheme for Nanoparticles Transport with Two-Phase Flow in Porous Media
El-Amin, Mohamed
2016-06-01
In this paper, we introduce a mathematical model to describe the nanoparticles transport carried by a two-phase flow in a porous medium including gravity, capillary forces and Brownian diffusion. Nonlinear iterative IMPES scheme is used to solve the flow equation, and saturation and pressure are calculated at the current iteration step and then the transport equation is solved implicitly. Therefore, once the nanoparticles concentration is computed, the two equations of volume of the nanoparticles available on the pore surfaces and the volume of the nanoparticles entrapped in pore throats are solved implicitly. The porosity and the permeability variations are updated at each time step after each iteration loop. Numerical example for regular heterogenous permeability is considered. We monitor the changing of the fluid and solid properties due to adding the nanoparticles. Variation of water saturation, water pressure, nanoparticles concentration and porosity are presented graphically.
International Nuclear Information System (INIS)
Boyd, R.W.
1992-01-01
Nonlinear optics is the study of the interaction of intense laser light with matter. This book is a textbook on nonlinear optics at the level of a beginning graduate student. The intent of the book is to provide an introduction to the field of nonlinear optics that stresses fundamental concepts and that enables the student to go on to perform independent research in this field. This book covers the areas of nonlinear optics, quantum optics, quantum electronics, laser physics, electrooptics, and modern optics
Energy Technology Data Exchange (ETDEWEB)
BARTON,THOMAS J.; BULL,LUCY M.; KLEMPERER,WALTER G.; LOY,DOUGLAS A.; MCENANEY,BRIAN; MISONO,MAKOTO; MONSON,PETER A.; PEZ,GUIDO; SCHERER,GEORGE W.; VARTULI,JAMES C.; YAGHI,OMAR M.
1999-11-09
Tailoring of porous materials involves not only chemical synthetic techniques for tailoring microscopic properties such as pore size, pore shape, pore connectivity, and pore surface reactivity, but also materials processing techniques for tailoring the meso- and the macroscopic properties of bulk materials in the form of fibers, thin films and monoliths. These issues are addressed in the context of five specific classes of porous materials: oxide molecular sieves, porous coordination solids, porous carbons, sol-gel derived oxides, and porous heteropolyanion salts. Reviews of these specific areas are preceded by a presentation of background material and review of current theoretical approaches to adsorption phenomena. A concluding section outlines current research needs and opportunities.
International Nuclear Information System (INIS)
Mundy, J.N.; Rothman, S.J.; Lam, N.Q.; Nowicki, L.J.; Hoff, H.A.
1978-01-01
The lack of understanding of self-diffusion in Group VI metals together with the wide scatter in the measured values of tungsten self-diffusion has prompted the present measurements to be made over a wide temperature range (1/2Tsub(m) to Tsub(m)). The diffusion coefficients have been measured in the temperature range 1430-2630 0 C. The present measurements show non-linear Arrhenius behavior but a reliable two-exponential fit of the data should await further measurements. (Auth.)
Diffusion Based Photon Mapping
DEFF Research Database (Denmark)
Schjøth, Lars; Sporring, Jon; Fogh Olsen, Ole
2008-01-01
. To address this problem, we introduce a photon mapping algorithm based on nonlinear anisotropic diffusion. Our algorithm adapts according to the structure of the photon map such that smoothing occurs along edges and structures and not across. In this way, we preserve important illumination features, while...
Tozawa, Tomokazu; Jones, James T. A.; Swamy, Shashikala I.; Jiang, Shan; Adams, Dave J.; Shakespeare, Stephen; Clowes, Rob; Bradshaw, Darren; Hasell, Tom; Chong, Samantha Y.; Tang, Chiu; Thompson, Stephen; Parker, Julia; Trewin, Abbie; Bacsa, John; Slawin, Alexandra M. Z.; Steiner, Alexander; Cooper, Andrew I.
2009-12-01
Porous materials are important in a wide range of applications including molecular separations and catalysis. We demonstrate that covalently bonded organic cages can assemble into crystalline microporous materials. The porosity is prefabricated and intrinsic to the molecular cage structure, as opposed to being formed by non-covalent self-assembly of non-porous sub-units. The three-dimensional connectivity between the cage windows is controlled by varying the chemical functionality such that either non-porous or permanently porous assemblies can be produced. Surface areas and gas uptakes for the latter exceed comparable molecular solids. One of the cages can be converted by recrystallization to produce either porous or non-porous polymorphs with apparent Brunauer-Emmett-Teller surface areas of 550 and 23m2g-1, respectively. These results suggest design principles for responsive porous organic solids and for the modular construction of extended materials from prefabricated molecular pores.
A design strategy for magnetorheological dampers using porous valves
International Nuclear Information System (INIS)
Hu, W; Robinson, R; Wereley, N M
2009-01-01
To design a porous-valve-based magnetorheological (MR) damper, essential design parameters are presented. The key elements affecting the damper performance are identified using flow analysis in porous media and an empirical magnetic field distribution in the porous valve. Based on a known MR fluid, the relationship between the controllable force of the damper and the porous valve characteristics, i.e. porosity and tortuosity, is developed. The effect of the porosity and tortuosity on the field-off damping force is exploited by using semi-empirical flow analysis. The critical flow rate for the onset of nonlinear viscous damping force is determined. Using the above design elements, an MR damper using by-pass porous valve is designed and tested. The experimental damper force and equivalent damping are compared with the predicted results to validate this design strategy.
A design strategy for magnetorheological dampers using porous valves
Energy Technology Data Exchange (ETDEWEB)
Hu, W; Robinson, R; Wereley, N M [Smart Structures Laboratory, Alfred Gessow Rotorcraft Center, Department of Aerospace Engineering, University of Maryland, College Park, MD 20742 (United States)], E-mail: wereley@umd.edu
2009-02-01
To design a porous-valve-based magnetorheological (MR) damper, essential design parameters are presented. The key elements affecting the damper performance are identified using flow analysis in porous media and an empirical magnetic field distribution in the porous valve. Based on a known MR fluid, the relationship between the controllable force of the damper and the porous valve characteristics, i.e. porosity and tortuosity, is developed. The effect of the porosity and tortuosity on the field-off damping force is exploited by using semi-empirical flow analysis. The critical flow rate for the onset of nonlinear viscous damping force is determined. Using the above design elements, an MR damper using by-pass porous valve is designed and tested. The experimental damper force and equivalent damping are compared with the predicted results to validate this design strategy.
Bloembergen, Nicolaas
1996-01-01
Nicolaas Bloembergen, recipient of the Nobel Prize for Physics (1981), wrote Nonlinear Optics in 1964, when the field of nonlinear optics was only three years old. The available literature has since grown by at least three orders of magnitude.The vitality of Nonlinear Optics is evident from the still-growing number of scientists and engineers engaged in the study of new nonlinear phenomena and in the development of new nonlinear devices in the field of opto-electronics. This monograph should be helpful in providing a historical introduction and a general background of basic ideas both for expe
Recent topics in non-linear partial differential equations 4
Mimura, M
1989-01-01
This fourth volume concerns the theory and applications of nonlinear PDEs in mathematical physics, reaction-diffusion theory, biomathematics, and in other applied sciences. Twelve papers present recent work in analysis, computational analysis of nonlinear PDEs and their applications.
Periodic and solitary wave solutions of cubic–quintic nonlinear ...
Indian Academy of Sciences (India)
Hence, most of the real nonlinear physical equations possess variable ... evolution of the system with time and second term represents the convective flux term. The ... Travelling wave solutions of nonlinear reaction-diffusion equations are.
Cosmic ray diffusion: report of the workshop in cosmic ray diffusion theory
International Nuclear Information System (INIS)
Birmingham, T.J.; Jones, F.C.
1975-02-01
A workshop in cosmic ray diffusion theory was held at Goddard Space Flight Center on May 16-17, 1974. Topics discussed and summarized are: (1) cosmic ray measurements as related to diffusion theory; (2) quasi-linear theory, nonlinear theory, and computer simulation of cosmic ray pitch-angle diffusion; and (3) magnetic field fluctuation measurements as related to diffusion theory. (auth)
Capacitance effects in porous media
International Nuclear Information System (INIS)
Jasti, J.K.; Vaidya, R.N.; Fogler, H.S.
1987-01-01
The velocity dependence of the parameters in the Coats-Smith model for tracer dispersion and tailing in porous media was investigated in this study. Numerical simulations show that eddies with recirculation flow are formed in the pockets due to flow separation. The tracer transport between the eddies in the dead zones and the main channel was found to be diffusion limited. The simulations reveal that in the Stokes' flow regime the mass transfer coefficient between the two regions is independent of interstitial velocity. Core flood experiments were performed using radioactive tracers to verify the hypothesis that the capcitance effects are not due to a change in flowing fraction. The experimental results confirm that racer tailing is a function of the ratio of the molecular diffusivity to the flow rate. In light of these findings, the authors investigated the validity of the Coats-Smith model to predict dispersion and tailing in porous medium. Their studies indicate that the Coats-Smith model may be used, however, certain restrictions apply to the procedure for estimation of parameters and are described in this paper
On the viscous dissipation modeling of thermal fluid flow in a porous medium
Salama, Amgad; El-Amin, Mohamed; Abbas, Ibrahim A A; Sun, Shuyu
2011-01-01
wall that is immersed in the porous medium and is kept at constant higher temperature. The boundary layer approximations were used to simplify the set of the governing, nonlinear partial differential equations, which were then non
Curry, D. M.; Cox, J. E.
1972-01-01
Coupled nonlinear partial differential equations describing heat and mass transfer in a porous matrix are solved in finite difference form with the aid of a new iterative technique (the strongly implicit procedure). Example numerical results demonstrate the characteristics of heat and mass transport in a porous matrix such as a charring ablator. It is emphasized that multidimensional flow must be considered when predicting the thermal response of a porous material subjected to nonuniform boundary conditions.
On some applications of diffusion processes for image processing
International Nuclear Information System (INIS)
Morfu, S.
2009-01-01
We propose a new algorithm inspired by the properties of diffusion processes for image filtering. We show that purely nonlinear diffusion processes ruled by Fisher equation allows contrast enhancement and noise filtering, but involves a blurry image. By contrast, anisotropic diffusion, described by Perona and Malik algorithm, allows noise filtering and preserves the edges. We show that combining the properties of anisotropic diffusion with those of nonlinear diffusion provides a better processing tool which enables noise filtering, contrast enhancement and edge preserving.
Caserta, A.; Kanivetsky, R.; Salusti, E.
2017-11-01
We here analyze a new model of transients of pore pressure p and solute density ρ in geologic porous media. This model is rooted in the nonlinear wave theory, its focus is on advection and effect of large pressure jumps on strain. It takes into account nonlinear and also time-dependent versions of the Hooke law about stress, rate and strain. The model solutions strictly relate p and ρ evolving under the effect of a strong external stress. As a result, the presence of quick and sharp transients in low permeability rocks is unveiled, i.e., the nonlinear "Burgers solitons". We, therefore, show that the actual transport process in porous rocks for large signals is not only the linear diffusion, but also a solitons presence could control the process. A test of a presence of solitons is applied to Pierre shale, Bearpaw shale, Boom clay and Oznam-Mugu silt and clay. An application about the presence of solitons for nuclear waste disposal and salt water intrusions is also discussed. Finally, in a kind of "theoretical experiment" we show that solitons could also be present in higher permeability rocks (Jordan and St. Peter sandstones), thus supporting the idea of a possible occurrence of osmosis also in sandstones.
Coupling nonlinear Stokes and Darcy flow using mortar finite elements
Ervin, Vincent J.; Jenkins, Eleanor W.; Sun, Shuyu
2011-01-01
We study a system composed of a nonlinear Stokes flow in one subdomain coupled with a nonlinear porous medium flow in another subdomain. Special attention is paid to the mathematical consequence of the shear-dependent fluid viscosity for the Stokes
Confocal imaging of protein distributions in porous silicon optical structures
International Nuclear Information System (INIS)
De Stefano, Luca; D'Auria, Sabato
2007-01-01
The performances of porous silicon optical biosensors depend strongly on the arrangement of the biological probes into their sponge-like structures: it is well known that in this case the sensing species do not fill the pores but instead cover their internal surface. In this paper, the direct imaging of labelled proteins into different porous silicon structures by using a confocal laser microscope is reported. The distribution of the biological matter in the nanostructured material follows a Gaussian behaviour which is typical of the diffusion process in the porous media but with substantial differences between a porous silicon monolayer and a multilayer such as a Bragg mirror. Even if semi-quantitative, the results can be very useful in the design of the porous silicon based biosensing devices
Hydrodynamic dispersion within porous biofilms
Davit, Y.
2013-01-23
Many microorganisms live within surface-associated consortia, termed biofilms, that can form intricate porous structures interspersed with a network of fluid channels. In such systems, transport phenomena, including flow and advection, regulate various aspects of cell behavior by controlling nutrient supply, evacuation of waste products, and permeation of antimicrobial agents. This study presents multiscale analysis of solute transport in these porous biofilms. We start our analysis with a channel-scale description of mass transport and use the method of volume averaging to derive a set of homogenized equations at the biofilm-scale in the case where the width of the channels is significantly smaller than the thickness of the biofilm. We show that solute transport may be described via two coupled partial differential equations or telegrapher\\'s equations for the averaged concentrations. These models are particularly relevant for chemicals, such as some antimicrobial agents, that penetrate cell clusters very slowly. In most cases, especially for nutrients, solute penetration is faster, and transport can be described via an advection-dispersion equation. In this simpler case, the effective diffusion is characterized by a second-order tensor whose components depend on (1) the topology of the channels\\' network; (2) the solute\\'s diffusion coefficients in the fluid and the cell clusters; (3) hydrodynamic dispersion effects; and (4) an additional dispersion term intrinsic to the two-phase configuration. Although solute transport in biofilms is commonly thought to be diffusion dominated, this analysis shows that hydrodynamic dispersion effects may significantly contribute to transport. © 2013 American Physical Society.
Parametric study of boiling heat transfer in porous media
International Nuclear Information System (INIS)
Shi, B.; Jones, B.G.; Pan, C.
1996-01-01
Detailed numerical modeling and parametric variation studies were conducted on boiling heat transfer processes in porous deposits with emphasis on applications associated with light water nuclear power reactor systems. The processes of boiling heat transfer in the porous corrosion deposits typically involve phase changes in finite volumetric regions in the porous media. The study examined such processes in two porous media configurations, without chimneys (homogeneous porous structures) and with chimneys (heterogeneous porous structures). A 1-D model and a 2-D model were developed to simulate two-phase flows with phase changes, without dry-out, inside the porous media for both structural configurations. For closure of the governing equations, an empirical correlation of the evaporation rate for phase changes inside the porous media was introduced. In addition, numerical algorithms were developed to solve the coupled nonlinear equations of mass, momentum, energy, capillary pressure, and evaporation rate. The distributions of temperature, thermodynamic saturation, liquid pressure, vapor pressure, liquid velocity, and vapor velocity were predicted. Furthermore, the effects of heat flux, system pressure, porosity, particle diameter, chimney population density, chimney radius, and crud thickness on the all superheat, critical heat flux, and minimum saturation were examined. The predictions were found to be in good agreement with the available experimental results
Yoshida, Zensho
2010-01-01
This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy, "nonlinear science" is explained as a challenge of deconstruction of the modern sciences. This book is not a technical guide to teach mathematical tools of nonlinear analysis, nor a zoology of so-called nonlinear phenomena. By critically analyzing the structure of linear theories, and cl
Nayfeh, Ali Hasan
1995-01-01
Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses sim
Effect of static porosity fluctuations on reactive transport in a porous medium
L'Heureux, Ivan
2018-02-01
Reaction-diffusive transport phenomena in porous media are ubiquitous in engineering applications, biological and geochemical systems. The porosity field is usually random in space, but most models consider the porosity field as a well-defined deterministic function of space and time and ignore the porosity fluctuations. They use a reaction-diffusion equation written in terms of an average porosity and average concentration fields. In this contribution, we treat explicitly the effect of spatial porosity fluctuations on the dynamics of a concentration field for the case of a one-dimensional reaction-transport system with nonlinear kinetics. Three basic assumptions are considered. (i) The porosity fluctuations are assumed to have Gaussian properties and an arbitrary variance; (ii) we assume that the noise correlation length is small compared to the relevant macroscopic length scale; (iii) and we assume that the kinetics of the reactive term in the equations for the fluctuations is a self-consistently determined constant. Elimination of the fluctuating part of the concentration field from the dynamics leads to a renormalized equation involving the average concentration field. It is shown that the noise leads to a renormalized (generally smaller) diffusion coefficient and renormalized kinetics. Within the framework of the approximations used, numerical simulations are in agreement with our theory. We show that the porosity fluctuations may have a significant effect on the transport of a reactive species, even in the case of a homogeneous average porosity.
Directory of Open Access Journals (Sweden)
Parama Ghoshal
2017-12-01
Full Text Available Reactive convection in a porous medium has received recent interest in the context of the geological storage of carbon dioxide in saline formations. We study theoretically and numerically the gravitational instability of a diffusive boundary layer in the presence of a first-order precipitation reaction. We compare the predictions from normal mode, linear stability analysis, and nonlinear numerical simulations, and discuss the relative deviations. The application of our findings to the storage of carbon dioxide in a siliciclastic aquifer shows that while the reactive-diffusive layer can become unstable within a timescale of 1 to 1.5 months after the injection of carbon dioxide, it can take almost 10 months for sufficiently vigorous convection to produce a considerable increase in the dissolution flux of carbon dioxide.
Coupled models in porous media: reactive transport and fractures
International Nuclear Information System (INIS)
Amir, L.
2008-12-01
This thesis deals with numerical simulation of coupled models for flow and transport in porous media. We present a new method for coupling chemical reactions and transport by using a Newton-Krylov method, and we also present a model of flow in fractured media, based on a domain decomposition method that takes into account the case of intersecting fractures. This study is composed of three parts: the first part contains an analysis, and implementation, of various numerical methods for discretizing advection-diffusion problems, in particular by using operator splitting methods. The second part is concerned with a fully coupled method for modeling transport and chemistry problems. The coupled transport-chemistry model is described, after discretization in time, by a system of nonlinear equations. The size of the system, namely the number of grid points times the number a chemical species, precludes a direct solution of the linear system. To alleviate this difficulty, we solve the system by a Newton-Krylov method, so as to avoid forming and factoring the Jacobian matrix. In the last part, we present a model of flow in 3D for intersecting fractures, by using a domain decomposition method. The fractures are treated as interfaces between sub-domains. We show existence and uniqueness of the solution, and we validate the model by numerical tests. (author)
Palmero, Faustino; Lemos, M; Sánchez-Rey, Bernardo; Casado-Pascual, Jesús
2018-01-01
This book presents an overview of the most recent advances in nonlinear science. It provides a unified view of nonlinear properties in many different systems and highlights many new developments. While volume 1 concentrates on mathematical theory and computational techniques and challenges, which are essential for the study of nonlinear science, this second volume deals with nonlinear excitations in several fields. These excitations can be localized and transport energy and matter in the form of breathers, solitons, kinks or quodons with very different characteristics, which are discussed in the book. They can also transport electric charge, in which case they are known as polarobreathers or solectrons. Nonlinear excitations can influence function and structure in biology, as for example, protein folding. In crystals and other condensed matter, they can modify transport properties, reaction kinetics and interact with defects. There are also engineering applications in electric lattices, Josephson junction a...
On the viscous dissipation modeling of thermal fluid flow in a porous medium
Salama, Amgad
2011-02-24
The problem of viscous dissipation and thermal dispersion in saturated porous medium is numerically investigated for the case of non-Darcy flow regime. The fluid is induced to flow upward by natural convection as a result of a semi-infinite vertical wall that is immersed in the porous medium and is kept at constant higher temperature. The boundary layer approximations were used to simplify the set of the governing, nonlinear partial differential equations, which were then non-dimensionalized and solved using the finite elements method. The results for the details of the governing parameters are presented and investigated. It is found that the irreversible process of transforming the kinetic energy of the moving fluid to heat energy via the viscosity of the moving fluid (i.e.; viscous dissipation) resulted in insignificant generation of heat for the range of parameters considered in this study. On the other hand, thermal dispersion has shown to disperse heat energy normal to the wall more effectively compared with the normal diffusion mechanism. © 2011 Springer-Verlag.
Hierarchical Porous Structures
Energy Technology Data Exchange (ETDEWEB)
Grote, Christopher John [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-06-07
Materials Design is often at the forefront of technological innovation. While there has always been a push to generate increasingly low density materials, such as aero or hydrogels, more recently the idea of bicontinuous structures has gone more into play. This review will cover some of the methods and applications for generating both porous, and hierarchically porous structures.
Solution of the porous media equation by Adomian's decomposition method
International Nuclear Information System (INIS)
Pamuk, Serdal
2005-01-01
The particular exact solutions of the porous media equation that usually occurs in nonlinear problems of heat and mass transfer, and in biological systems are obtained using Adomian's decomposition method. Also, numerical comparison of particular solutions in the decomposition method indicate that there is a very good agreement between the numerical solutions and particular exact solutions in terms of efficiency and accuracy
International Nuclear Information System (INIS)
1998-01-01
This conference day of the French society of thermal engineers was devoted to the analysis of heat transfers and fluid flows during boiling phenomena in porous media. This book of proceedings comprises 8 communications entitled: 'boiling in porous medium: effect of natural convection in the liquid zone'; 'numerical modeling of boiling in porous media using a 'dual-fluid' approach: asymmetrical characteristic of the phenomenon'; 'boiling during fluid flow in an induction heated porous column'; 'cooling of corium fragment beds during a severe accident. State of the art and the SILFIDE experimental project'; 'state of knowledge about the cooling of a particulates bed during a reactor accident'; 'mass transfer analysis inside a concrete slab during fire resistance tests'; 'heat transfers and boiling in porous media. Experimental analysis and modeling'; 'concrete in accidental situation - influence of boundary conditions (thermal, hydric) - case studies'. (J.S.)
Non-Boussinesq Dissolution-Driven Convection in Porous Media
Amooie, M. A.; Soltanian, M. R.; Moortgat, J.
2017-12-01
Geological carbon dioxide (CO2) sequestration in deep saline aquifers has been increasingly recognized as a feasible technology to stabilize the atmospheric carbon concentrations and subsequently mitigate the global warming. Solubility trapping is one of the most effective storage mechanisms, which is associated initially with diffusion-driven slow dissolution of gaseous CO2 into the aqueous phase, followed by density-driven convective mixing of CO2 throughout the aquifer. The convection includes both diffusion and fast advective transport of the dissolved CO2. We study the fluid dynamics of CO2 convection in the underlying single aqueous-phase region. Two modeling approaches are employed to define the system: (i) a constant-concentration condition for CO2 in aqueous phase at the top boundary, and (ii) a sufficiently low, constant injection-rate for CO2 from top boundary. The latter allows for thermodynamically consistent evolution of the CO2 composition and the aqueous phase density against the rate at which the dissolved CO2 convects. Here we accurately model the full nonlinear phase behavior of brine-CO2 mixture in a confined domain altered by dissolution and compressibility, while relaxing the common Boussinesq approximation. We discover new flow regimes and present quantitative scaling relations for global characters of spreading, mixing, and dissolution flux in two- and three-dimensional media for the both model types. We then revisit the universal Sherwood-Rayleigh scaling that is under debate for porous media convective flows. Our findings confirm the sublinear scaling for the constant-concentration case, while reconciling the classical linear scaling for the constant-injection model problem. The results provide a detailed perspective into how the available modeling strategies affect the prediction ability for the total amount of CO2 dissolved in the long term within saline aquifers of different permeabilities.
Saturation at Low X and Nonlinear Evolution
International Nuclear Information System (INIS)
Stasto, A.M.
2002-01-01
In this talk the results of the analytical and numerical analysis of the nonlinear Balitsky-Kovchegov equation are presented. The characteristic BFKL diffusion into infrared regime is suppressed by the generation of the saturation scale Q s . We identify the scaling and linear regimes for the solution. We also study the impact of subleading corrections onto the nonlinear evolution. (author)
Diffusion Influenced Adsorption Kinetics.
Miura, Toshiaki; Seki, Kazuhiko
2015-08-27
When the kinetics of adsorption is influenced by the diffusive flow of solutes, the solute concentration at the surface is influenced by the surface coverage of solutes, which is given by the Langmuir-Hinshelwood adsorption equation. The diffusion equation with the boundary condition given by the Langmuir-Hinshelwood adsorption equation leads to the nonlinear integro-differential equation for the surface coverage. In this paper, we solved the nonlinear integro-differential equation using the Grünwald-Letnikov formula developed to solve fractional kinetics. Guided by the numerical results, analytical expressions for the upper and lower bounds of the exact numerical results were obtained. The upper and lower bounds were close to the exact numerical results in the diffusion- and reaction-controlled limits, respectively. We examined the validity of the two simple analytical expressions obtained in the diffusion-controlled limit. The results were generalized to include the effect of dispersive diffusion. We also investigated the effect of molecular rearrangement of anisotropic molecules on surface coverage.
International Nuclear Information System (INIS)
Silva, T.L. da.
1987-01-01
Is this thesis, a numerical method for the solution of the linear diffusion equation for a plasma containing two types of ions, with the possibility of charge exchange, has been developed. It has been shown that the decay time of the electron and ion densities is much smaller than that in a plasma containing only a single type of ion. A non-linear diffusion equation, which includes the effects of an external electric field varying linearly in time, to describe a slightly ionized plasma has also been developed. It has been verified that the decay of the electron density in the presence of such an electric field is very slow. (author)
International Nuclear Information System (INIS)
Ene, H.I.; Poliwevski, D.
1987-01-01
Thermal flows in porous media are important in a wide range of areas: oil recovery, geothermal development, chemical and nuclear industry, civil engineering, energy storage and energy conversion. This book uses a systematic, rigorous and unified treatment to provide a general understanding of the phenomena involved. General equations for single- or multiphase flows (including an arbitrary number of components inside each phase), diffusion and chemical reactions are presented. The boundary conditions which may be imposed, the non-dimensional para meters, the structures of the solutions, the stability of the finite amplitude solutions and many other related topics ae also studied. Although the treatment is basically mathematical, specific physical problems are also dealt with. There are two major fields of applications: natural convection and underground combustion. Both are discussed in detail. Various examples with exact or numerical solutions, for the case of bounded or unbounded domains, are presented, accompanied by extensive comment
Boyd, Robert W
2013-01-01
Nonlinear Optics is an advanced textbook for courses dealing with nonlinear optics, quantum electronics, laser physics, contemporary and quantum optics, and electrooptics. Its pedagogical emphasis is on fundamentals rather than particular, transitory applications. As a result, this textbook will have lasting appeal to a wide audience of electrical engineering, physics, and optics students, as well as those in related fields such as materials science and chemistry.Key Features* The origin of optical nonlinearities, including dependence on the polarization of light* A detailed treatment of the q
Salamon, David; Da Silva Teixeira, Sandra; Dutczak, S.M.; Stamatialis, Dimitrios
2014-01-01
Nowadays, diffusion through scaffold and tissue usually limits transport, and forms potentially hypoxic regions. Several methods are used for preparation of 3D hydroxyapatite scaffolds, however, production of a scaffold including porous hollow fibers for nutrition delivery is difficult and
Contaminant flow and transport simulation in cracked porous media using locally conservative schemes
Song, Pu; Sun, Shuyu
2012-01-01
The purpose of this paper is to analyze some features of contaminant flow passing through cracked porous medium, such as the influence of fracture network on the advection and diffusion of contaminant species, the impact of adsorption on the overall
Schoofs, Stan; Trompert, Ron A.; Hansen, Ulrich
1999-01-01
Horizontally layered structures can develop in porous or partially molten environments, such as hydrothermal systems, magmatic intrusions and the early Earth's mantle. The porosity f of these natural environments is typically small. Since dissolved chemical elements unlike heat cannot diffuse
National Research Council Canada - National Science Library
Drazin, P. G
1992-01-01
This book is an introduction to the theories of bifurcation and chaos. It treats the solution of nonlinear equations, especially difference and ordinary differential equations, as a parameter varies...
Gasinski, Leszek
2005-01-01
Hausdorff Measures and Capacity. Lebesgue-Bochner and Sobolev Spaces. Nonlinear Operators and Young Measures. Smooth and Nonsmooth Analysis and Variational Principles. Critical Point Theory. Eigenvalue Problems and Maximum Principles. Fixed Point Theory.
Nonlinear differential equations
Energy Technology Data Exchange (ETDEWEB)
Dresner, L.
1988-01-01
This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.
Nonlinear differential equations
International Nuclear Information System (INIS)
Dresner, L.
1988-01-01
This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics
Fabricating porous silicon carbide
Shor, Joseph S. (Inventor); Kurtz, Anthony D. (Inventor)
1994-01-01
The formation of porous SiC occurs under electrochemical anodization. A sample of SiC is contacted electrically with nickel and placed into an electrochemical cell which cell includes a counter electrode and a reference electrode. The sample is encapsulated so that only a bare semiconductor surface is exposed. The electrochemical cell is filled with an HF electrolyte which dissolves the SiC electrochemically. A potential is applied to the semiconductor and UV light illuminates the surface of the semiconductor. By controlling the light intensity, the potential and the doping level, a porous layer is formed in the semiconductor and thus one produces porous SiC.
Stability of Gradient Field Corrections for Quantitative Diffusion MRI
Rogers, Baxter P.; Blaber, Justin; Welch, E. Brian; Ding, Zhaohua; Anderson, Adam W.; Landman, Bennett A.
2017-01-01
In magnetic resonance diffusion imaging, gradient nonlinearity causes significant bias in the estimation of quantitative diffusion parameters such as diffusivity, anisotropy, and diffusion direction in areas away from the magnet isocenter. This bias can be substantially reduced if the scanner- and coil-specific gradient field nonlinearities are known. Using a set of field map calibration scans on a large (29 cm diameter) phantom combined with a solid harmonic approximation of the gradient fie...
Modelling of a diffusion-sorption experiment on sandstone
International Nuclear Information System (INIS)
Smith, P.A.
1989-11-01
The results of a diffusion-sorption experiment on a sample of Darley Dale sandstone, using simulated groundwater spiked with a mixture of 125 I, 85 Sr and 137 Cs, are modelled by a one-dimensional porous medium approach in which sorption is described by Freundlich isotherms. The governing equations are solved analytically for the special case of a linear isotherm, and numerically using the computer code RANCHDIFF for non-linear isotherms. A set of time-dependent, ordinary differential equations is obtained using the Lagrange interpolation technique and integrated by Gear's variable order predictor-corrector method. It is shown that the sorption behaviour of 85 Sr can be modelled successfully by a linear isotherm, using a sorption parameter consistent with batch-sorption tests. The behaviour of 137 Cs may be modelled by a non-linear isotherm, but the amount of 137 Cs sorbed is less than that anticipated from batch-sorption tests. 125 I is assumed to be non-sorbing and is used to determine the porosity of the sandstone. (author) 10 figs., 4 tabs., 6 refs
DEFF Research Database (Denmark)
Mosekilde, Erik
Through a significant number of detailed and realistic examples this book illustrates how the insights gained over the past couple of decades in the fields of nonlinear dynamics and chaos theory can be applied in practice. Aomng the topics considered are microbiological reaction systems, ecological...... food-web systems, nephron pressure and flow regulation, pulsatile secretion of hormones, thermostatically controlled radiator systems, post-stall maneuvering of aircrafts, transfer electron devices for microwave generation, economic long waves, human decision making behavior, and pattern formation...... in chemical reaction-diffusion systems....
Diffusing diffusivity: a new derivation and comparison with simulations
Indian Academy of Sciences (India)
Rohit Jain
active media, where the relation of Eq.(1) is not valid at all times.4–6 ... tional diffusion of dumbbells in 2D porous media of stationary hard ..... reflecting boundary condition at D = 0, i.e., πeq(D) = 1. D0 .... Superdiffusion and viscoelastic vortex flows in a two- .... gator for Free, Linear, and Harmonic Potentials in the. Over- and ...
Scaling theory of drying in porous media
International Nuclear Information System (INIS)
Tsimpanogiannis, I.N.; Yortsos, Y.C.; Poulou, S.; Kanellopoulos, N.; Stubos, A.K.
1999-01-01
Concepts of immiscible displacements in porous media driven by mass transfer are utilized to model drying of porous media. Visualization experiments of drying in two-dimensional glass micromodels are conducted to identify pore-scale mechanisms. Then, a pore network approach is used to analyze the advancing drying front. It is shown that in a porous medium, capillarity induces a flow that effectively limits the extent of the front, which would otherwise be of the percolation type, to a finite width. In conjuction with the predictions of a macroscale stable front, obtained from a linear stability analysis, the process is shown to be equivalent to invasion percolation in a stabilizing gradient. A power-law scaling relation of the front width with a diffusion-based capillary number is also obtained. This capillary number reflects the fact that drying is controlled by diffusion in contrast to external drainage. The scaling exponent predicted is compatible with the experimental results of Shaw [Phys Rev. Lett. 59, 1671 (1987)]. A framework for a continuum description of the upstream drying regimes is also developed. copyright 1999 The American Physical Society
International Nuclear Information System (INIS)
Lenain, Roland
2015-01-01
This thesis is devoted to the implementation of a domain decomposition method applied to the neutron transport equation. The objective of this work is to access high-fidelity deterministic solutions to properly handle heterogeneities located in nuclear reactor cores, for problems' size ranging from color-sets of assemblies to large reactor cores configurations in 2D and 3D. The innovative algorithm developed during the thesis intends to optimize the use of parallelism and memory. The approach also aims to minimize the influence of the parallel implementation on the performances. These goals match the needs of APOLLO3 project, developed at CEA and supported by EDF and AREVA, which must be a portable code (no optimization on a specific architecture) in order to achieve best estimate modeling with resources ranging from personal computer to compute cluster available for engineers analyses. The proposed algorithm is a Parallel Multigroup-Block Jacobi one. Each sub-domain is considered as a multi-group fixed-source problem with volume-sources (fission) and surface-sources (interface flux between the sub-domains). The multi-group problem is solved in each sub-domain and a single communication of the interface flux is required at each power iteration. The spectral radius of the resolution algorithm is made similar to the one of a classical resolution algorithm with a nonlinear diffusion acceleration method: the well-known Coarse Mesh Finite Difference. In this way an ideal scalability is achievable when the calculation is parallelized. The memory organization, taking advantage of shared memory parallelism, optimizes the resources by avoiding redundant copies of the data shared between the sub-domains. Distributed memory architectures are made available by a hybrid parallel method that combines both paradigms of shared memory parallelism and distributed memory parallelism. For large problems, these architectures provide a greater number of processors and the amount of
Opposing flow in square porous annulus: Influence of Dufour effect
International Nuclear Information System (INIS)
Athani, Abdulgaphur; Al-Rashed, Abdullah A. A. A.; Khaleed, H. M. T.
2016-01-01
Heat and mass transfer in porous medium is very important area of research which is also termed as double diffusive convection or thermo-solutal convection. The buoyancy ratio which is the ratio of thermal to concentration buoyancy can have negative values thus leading to opposing flow. This article is aimed to study the influence of Dufour effect on the opposing flow in a square porous annulus. The partial differential equations that govern the heat and mass transfer behavior inside porous medium are solved using finite element method. A three node triangular element is used to divide the porous domain into smaller elements. Results are presented with respect to geometric and physical parameters such as duct diameter ratio, Rayleigh number, radiation parameter etc. It is found that the heat transfer increase with increase in Rayleigh number and radiation parameter. It is observed that Dufour coefficient has more influence on velocity profile.
Opposing flow in square porous annulus: Influence of Dufour effect
Energy Technology Data Exchange (ETDEWEB)
Athani, Abdulgaphur, E-mail: abbu.bec@gmail.com [Dept. of Mechanical Engineering, Anjuman Institute of Technology & Management, Bhatkal (India); Al-Rashed, Abdullah A. A. A., E-mail: aa.alrashed@paaet.edu.kw [Dept. of Automotive and Marine Engineering Technology, College of Technological Studies, The Public Authority for Applied Education and Training (Kuwait); Khaleed, H. M. T., E-mail: khalid-tan@yahoo.com [Dept of Mechanical Engineering, Faculty of Engineering, Islamic University, Madinah Munawwarra (Saudi Arabia)
2016-06-21
Heat and mass transfer in porous medium is very important area of research which is also termed as double diffusive convection or thermo-solutal convection. The buoyancy ratio which is the ratio of thermal to concentration buoyancy can have negative values thus leading to opposing flow. This article is aimed to study the influence of Dufour effect on the opposing flow in a square porous annulus. The partial differential equations that govern the heat and mass transfer behavior inside porous medium are solved using finite element method. A three node triangular element is used to divide the porous domain into smaller elements. Results are presented with respect to geometric and physical parameters such as duct diameter ratio, Rayleigh number, radiation parameter etc. It is found that the heat transfer increase with increase in Rayleigh number and radiation parameter. It is observed that Dufour coefficient has more influence on velocity profile.
Curry, D. M.
1974-01-01
Numerical results of the heat and mass transfer in a porous matrix are presented. The coupled, nonlinear partial differential equations describing this physical phenomenon are solved in finite difference form for two dimensions, using a new iterative technique (the strongly implicit procedure). The influence of the external environment conditions (heating and pressure) is shown to produce two-dimensional flow in the porous matrix. Typical fluid and solid temperature distributions in the porous matrix and internal pressure distributions are presented.
Hindered bacterial mobility in porous media flow enhances dispersion
Dehkharghani, Amin; Waisbord, Nicolas; Dunkel, Jörn; Guasto, Jeffrey
2017-11-01
Swimming bacteria live in porous environments characterized by dynamic fluid flows, where they play a crucial role in processes ranging from the bioremediation to the spread of infections. We study bacterial transport in a quasi-two-dimensional porous microfluidic device, which is complemented by Langevin simulations. The cell trajectories reveal filamentous patterns of high cell concentration, which result from the accumulation of bacteria in the high-shear regions of the flow and their subsequent advection. Moreover, the effective diffusion coefficient of the motile bacteria is severely hindered in the transverse direction to the flow due to decorrelation of the cells' persistent random walk by shear-induced rotation. The hindered lateral diffusion has the surprising consequence of strongly enhancing the longitudinal bacterial transport through a dispersion effect. These results demonstrate the significant role of the flow and geometry in bacterial transport through porous media with potential implications for understanding ecosystem dynamics and engineering bioreactors. NSF CBET-1511340, NSF CAREER-1554095.
Global sensitivity analysis of multiscale properties of porous materials
Um, Kimoon; Zhang, Xuan; Katsoulakis, Markos; Plechac, Petr; Tartakovsky, Daniel M.
2018-02-01
Ubiquitous uncertainty about pore geometry inevitably undermines the veracity of pore- and multi-scale simulations of transport phenomena in porous media. It raises two fundamental issues: sensitivity of effective material properties to pore-scale parameters and statistical parameterization of Darcy-scale models that accounts for pore-scale uncertainty. Homogenization-based maps of pore-scale parameters onto their Darcy-scale counterparts facilitate both sensitivity analysis (SA) and uncertainty quantification. We treat uncertain geometric characteristics of a hierarchical porous medium as random variables to conduct global SA and to derive probabilistic descriptors of effective diffusion coefficients and effective sorption rate. Our analysis is formulated in terms of solute transport diffusing through a fluid-filled pore space, while sorbing to the solid matrix. Yet it is sufficiently general to be applied to other multiscale porous media phenomena that are amenable to homogenization.
In situ measurement of diffusivity
International Nuclear Information System (INIS)
Berne, F.; Pocachard, J.
2004-01-01
The mechanism of molecular diffusion controls the migration of contaminants in very low-permeability porous media, like underground facilities for the storage of hazardous waste. Determining of relevant diffusion coefficients is therefore of prime importance. A few techniques exist for in situ measurement of the quantity, but they suffer from many handicaps (duration, complexity and cost of the experiments). We propose here two innovative methods that have some potential to improve the situation. So far, we have found them feasible on the basis of design calculations and laboratory experiments. This work is presently protected by a patent. (author)
In situ measurement of diffusivity
International Nuclear Information System (INIS)
Berne, Ph.; Pocachard, J.
2005-01-01
The mechanism of molecular diffusion controls the migration of contaminants in very low-permeability porous media, like underground facilities for the storage of hazardous waste. Determining the relevant diffusion coefficients is, therefore, of prime importance. A few techniques exist for the in situ measurement of that quantity, but they suffer from many handicaps (duration, complexity and cost of the experiments). We propose here two innovative methods that have some potential to improve this situation. So far, we have found them feasible on the basis of design calculations and laboratory experiments. This work is presently protected by a patent. (author)
Strategy for Predicting Effective Transport Properties of Complex Porous Structures
Czech Academy of Sciences Publication Activity Database
Salejová, G.; Grof, Z.; Šolcová, Olga; Schneider, Petr; Kosek, J.
2011-01-01
Roč. 35, č. 2 (2011), s. 200-211 ISSN 0098-1354 Institutional research plan: CEZ:AV0Z40720504 Keywords : porous media * pore space reconstruction * effective diffusivity Subject RIV: CI - Industrial Chemistry, Chemical Engineering Impact factor: 2.320, year: 2011
Ruszczynski, Andrzej
2011-01-01
Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates the theory and the methods of nonlinear optimization in a unified, clear, and mathematically rigorous fashion, with detailed and easy-to-follow proofs illustrated by numerous examples and figures. The book covers convex analysis, the theory of optimality conditions, duality theory, and numerical methods for solving unconstrained and constrained optimization problems. It addresses not only classical material but also modern top...
Modelling multiphase flow inside the porous media of a polymer electrolyte membrane fuel cell
DEFF Research Database (Denmark)
Berning, Torsten; Kær, Søren Knudsen
2011-01-01
Transport processes inside polymer electrolyte membrane fuel cells (PEMFC’s) are highly complex and involve convective and diffusive multiphase, multispecies flow through porous media along with heat and mass transfer and electrochemical reactions in conjunction with water transport through...... an electrolyte membrane. We will present a computational model of a PEMFC with focus on capillary transport of water through the porous layers and phase change and discuss the impact of the liquid phase boundary condition between the porous gas diffusion layer and the flow channels, where water droplets can...
Modelling of the filling up of a porous plate
International Nuclear Information System (INIS)
Sampaio, R.; Gama, R.M.S. da.
1985-01-01
A generalization of Darcy's law is constructed using Mixture Theory to describe the transient flow of an incompressible fluid through a rigid solid porous matrix. The model is used to study the process of filling-up of an one dimensional unsaturated porous medium that is mathematically described by a system of nonlinear hyperbolic equations that is non-homogeneous due to the drag force between the fluid and the solid matrix. The system is analysed throughly and solved numerically using the Glimm-Chorin method with a splitting to treat the non-homogeneous term. The results are discussed and shown to describe well the filling-up process. (Author) [pt
Directory of Open Access Journals (Sweden)
Yong Tae Kim
2018-03-01
Full Text Available We have developed a sequential stereolithographic co-printing process using two different resins for fabricating porous barriers in microfluidic devices. We 3D-printed microfluidic channels with a resin made of poly(ethylene glycol diacrylate (MW = 258 (PEG-DA-258, a UV photoinitiator, and a UV sensitizer. The porous barriers were created within the microchannels in a different resin made of either PEG-DA (MW = 575 (PEG-DA-575 or 40% (w/w in water PEG-DA (MW = 700 (40% PEG-DA-700. We showed selective hydrogen ion diffusion across a 3D-printed PEG-DA-575 porous barrier in a cross-channel diffusion chip by observing color changes in phenol red, a pH indicator. We also demonstrated the diffusion of fluorescein across a 3D-printed 40% PEG-DA-700 porous barrier in a symmetric-channel diffusion chip by measuring fluorescence intensity changes across the porous barrier. Creating microfluidic chips with integrated porous barriers using a semi-automated 3D printing process shortens the design and processing time, avoids assembly and bonding complications, and reduces manufacturing costs compared to micromolding processes. We believe that our digital manufacturing method for fabricating selective porous barriers provides an inexpensive, simple, convenient and reproducible route to molecule delivery in the fields of molecular filtration and cell-based microdevices.
Energy Technology Data Exchange (ETDEWEB)
Marsden, S.S.
1986-07-01
In 1978 a literature search on selective blocking of fluid flow in porous media was done by Professor S.S. Marsden and two of his graduate students, Tom Elson and Kern Huppy. This was presented as SUPRI Report No. TR-3 entitled ''Literature Preview of the Selected Blockage of Fluids in Thermal Recovery Projects.'' Since then a lot of research on foam in porous media has been done on the SUPRI project and a great deal of new information has appeared in the literature. Therefore we believed that a new, up-to-date search should be done on foam alone, one which would be helpful to our students and perhaps of interest to others. This is a chronological survey showing the development of foam flow, blockage and use in porous media, starting with laboratory studies and eventually getting into field tests and demonstrations. It is arbitrarily divided into five-year time periods. 81 refs.
Porous material neutron detector
Diawara, Yacouba [Oak Ridge, TN; Kocsis, Menyhert [Venon, FR
2012-04-10
A neutron detector employs a porous material layer including pores between nanoparticles. The composition of the nanoparticles is selected to cause emission of electrons upon detection of a neutron. The nanoparticles have a maximum dimension that is in the range from 0.1 micron to 1 millimeter, and can be sintered with pores thereamongst. A passing radiation generates electrons at one or more nanoparticles, some of which are scattered into a pore and directed toward a direction opposite to the applied electrical field. These electrons travel through the pore and collide with additional nanoparticles, which generate more electrons. The electrons are amplified in a cascade reaction that occurs along the pores behind the initial detection point. An electron amplification device may be placed behind the porous material layer to further amplify the electrons exiting the porous material layer.
Qu, Yongquan; Zhou, Hailong; Duan, Xiangfeng
2011-01-01
In this minreview, we summarize recent progress in the synthesis, properties and applications of a new type of one-dimensional nanostructures — single crystalline porous silicon nanowires. The growth of porous silicon nanowires starting from both p- and n-type Si wafers with a variety of dopant concentrations can be achieved through either one-step or two-step reactions. The mechanistic studies indicate the dopant concentration of Si wafers, oxidizer concentration, etching time and temperature can affect the morphology of the as-etched silicon nanowires. The porous silicon nanowires are both optically and electronically active and have been explored for potential applications in diverse areas including photocatalysis, lithium ion battery, gas sensor and drug delivery. PMID:21869999
Structural and elastic properties of porous silicon
Energy Technology Data Exchange (ETDEWEB)
Matthai, C C [Department of Physics and Astronomy, University of Wales College of Cardiff, Cardiff CF2 3YB (United Kingdom); Gavartin, J L [Department of Physics and Astronomy, University of Wales College of Cardiff, Cardiff CF2 3YB (United Kingdom); Cafolla, A A [Department of Physics, Dublin City University, Dublin (Ireland)
1995-01-15
We have implemented a modified diffusion-limited aggregation model to simulate the porous silicon structure obtained by electrochemical dissolution. The resulting fractal structures were fully equilibrated using the molecular dynamics method. An analysis of the relaxed structure shows it to be quite stable with the presence of one-, two- and three-coordinated atoms as well as the four-coordinated atoms found in bulk silicon. It is suggested that the different substructures or nanocrystals might be responsible for the observed photoluminescence. ((orig.))
Porous metal for orthopedics implants
Matassi, Fabrizio; Botti, Alessandra; Sirleo, Luigi; Carulli, Christian; Innocenti, Massimo
2013-01-01
Porous metal has been introduced to obtain biological fixation and improve longevity of orthopedic implants. The new generation of porous metal has intriguing characteristics that allows bone healing and high osteointegration of the metallic implants. This article gives an overview about biomaterials properties of the contemporary class of highly porous metals and about the clinical use in orthopaedic surgery.
Electrokinetics in porous media
Luong, D.T.
2014-01-01
This thesis presents the PhD research on electrokinetics in porous media. Electrokinetic phenomena are induced by the relative motion between a fluid and a solid surface and are directly related to the existence of an electric double layer between the fluid and the solid grain surface.
International Nuclear Information System (INIS)
Michaud, Georges; Montmerle, Thierry
1977-01-01
This paper is dealing with the origin of the elements in the universe. The scheme of nucleosynthesis is kept to explain the stellar generation of helium, carbon, etc... from the initial hydrogen; but a nonlinear theory is then elaborated to account for the anomalous abundances which were observed. The chemical elements would diffuse throughout the outer layers of a star under the action of the opposite forces of gravitation and radiation. This theory, with completing the nucleosynthesis, would contribute to give a consistent scheme of the elemental origin and abundances [fr
AULISA, EUGENIO; IBRAGIMOV, AKIF; VALKO, PETER; WALTON, JAY
2009-01-01
This IBVP described laminar (linear) Darcy flow in porous media; the considered boundary conditions corresponded to different regimes of the well production. The diffusive capacities were then computed as steady state invariants of the solutions
Nonlinear Elliptic Differential Equations with Multivalued Nonlinearities
Indian Academy of Sciences (India)
In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all R R . Assuming the existence of an upper and of a lower ...
Mass Transfer and Porous Media (MTPM)
Energy Technology Data Exchange (ETDEWEB)
Rotenberg, B.; Marry, V.; Malikova, N.; Vuilleumier, R.; Giffaut, E.; Turq, P.; Robinet, J.C.; Diaz, N.; Sardini, P.; Goutelard, F.; Menut, D.; Parneix, J.C.; Sammartino, S.; Pret, D.; Coelho, D.; Jougnot, D.; Revil, A.; Boulin, P.F.; Angulo-Jaramillo, R.; Daian, J.F.; Talandier, J.; Berne, P.; Cochepin, B.; Trotignon, L.; Bildstein, O.; Steefel, C.; Lagneau, V.; Van der Lee, J.; Birchall, D.J.; Harrington, J.F.; Noy, D.J.; Sellin, P.; Bildstein, O.; Piault, E.; Trotignon, L.; Montarnal, P.; Deville, E.; Genty, A.; Le Potier, C.; Imbert, C.; Semete, P.; Desgree, P.; Fevrier, B.; Courtois, A.; Touze, G.; Sboui, A.; Roberts, J.E.; Jaffre, J.; Glaus, M.A.; Rosse, R.; Van Loon, L.R.; Matray, J.M.; Parneix, J.C.; Tinseau, E.; Pret, D.; Mayor, J.C.; Ohkubo, T.; Kikuchi, H.; Yamaguchi, M.; Alonso, U.; Missana, T.; Garcia-Gutierrez, M.; Patelli, A.; Siitari-Kauppi, M.; Leskinen, A.; Rigato, V.; Samper, J.; Dewonck, S.; Zheng, L.; Yang, Q.; Naves, A.; Dai, Z.; Samper, J.; Wolfsberg, A.; Levitt, D.; Cormenzana, J.L.; Missana, T.; Mingarro, M.; Schampera, B.; Dultz, S.; Riebe, B.; Samper, J.; Yang, Q.; Genty, A.; Perraud, D.; Poller, A.; Mayer, G.; Croise, J.; Marschall, P.; Krooss, B.; Matray, J.M.; Tanaka, T.; Vogel, P.; Lavanchy, J.M.; Enssle, C.P.; Cruchaudet, M.; Dewonck, S.; Descostes, M.; Blin, V.; Radwan, J.; Poinssot, C.; Mibus, J.; Sachs, S.; Devol-Brown, I.; Motellier, S.; Tinseau, E.; Thoby, D.; Marsal, F.; DeWindt, L.; Tinseau, E.; Pellegrini, D.; Bauer, A.; Fiehn, B.; Marquardt, Ch.; Romer, J.; Gortzen, A.; Kienzler, B
2007-07-01
This session gathers 48 articles (posters) dealing with: interlayer / micro-pore exchange of water and ions in clays: a molecular dynamics study; the multi-scale characterisation of mineral and textural spatial heterogeneities in Callovo-Oxfordian argilite and its consequence on solute species diffusion modelling; the diffusion of ions in unsaturated clay rocks: Theory and application to the Callovo- Oxfordian argillite; the porous media characterization with respect to gas transfer in Callovo Oxfordian argillite; the predictions on a 2-D cementation experiment in porous medium: intercomparison on the Comedie project; the large-scale gas injection test (LASGIT) at the Aespoe hard rock laboratory in Sweden; simulating the geochemical coupling between vitrified waste, canister and near-field on the alliances platform; toward radionuclide transport calculations on whole radioactive waste disposal with CAST3M platform; the experimental study of the water permeability of a partially saturated argillite; a mixed hexahedral finite elements for Darcy flow calculation in clay porous media; the diffusive properties of stainless steel filter discs before and after use in diffusion experiments with compacted clays; the structural organization of porosity in the Opalinus clay at the Mont Terri Rock Laboratory under saturated and unsaturated conditions; the evaluation of pore structure in compacted saturated Bentonite using NMR relaxometry; diffusion coefficients measurement in consolidated clays: a combination of micro-scale profiling and solid pore structure analyses; the numerical interpretation of in-situ DIR diffusion experiments on the Callovo- Oxfordian clay at the Meuse/Haute-Marne URL the identification of relative conductivity models for water flow and solute transport in unsaturated compacted Bentonite; diffusion experiments in Callovo- Oxfordian clay from the Meuse/Haute-Marne URL, France: experimental setup and data analyses; the transport in organo
International Nuclear Information System (INIS)
Carlen, E.A.
1984-01-01
In Nelson's stochastic mechanics, quantum phenomena are described in terms of diffusions instead of wave functions. These diffusions are formally given by stochastic differential equations with extremely singular coefficients. Using PDE methods, we prove the existence of solutions. This reult provides a rigorous basis for stochastic mechanics. (orig.)
Lesellier, E
2012-03-09
The chromatographic efficiency, in terms of plate number per second, was dramatically improved by the introduction of sub-two microns particles with ultra-high pressure liquid chromatography (UHPLC). On the other hand, the recent development of superficially porous particles, called core-shell or fused-core particles, appears to allow the achievement of the same efficiency performances at higher speed without high pressure drops. CO₂-based mobile phases exhibiting much lower viscosities than aqueous based mobile phases allow better theoretical efficiencies, even with 3-5 μm particles, but with relative low pressure drops. They also allow much higher flow rates or much longer columns while using conventional instruments capable to operate below 400 bar. Moreover, the use of superficially porous particles in SFC could enhance the chromatographic performances even more. The kinetic behavior of ODS phases bonded on these particles was studied, with varied flow rates, outlet (and obviously inlet) pressures, temperatures, by using a homologous series (alkylbenzenes) with 10% modifier (methanol or acetonitrile) in the carbon dioxide mobile phase. Results were also compared with classical fully porous particles, having different sizes, from 2.5 to 5 μm. Superior efficiency (N) and reduced h were obtained with these new ODS-bonded particles in regards to classical ones, showing their great interest for use in SFC. However, surprising behavior were noticed, i.e. the increase of the theoretical plate number vs. the increase of the chain length of the compounds. This behavior, opposite to the one classically reported vs. the retention factor, was not depending on the outlet pressure, but on the flow rate and the temperature changes. The lower radial trans-column diffusion on this particle types could explain these results. This diffusion reduction with these ODS-bonded superficially porous particles seems to decrease with the increase of the residence time of compounds
Numerical simulation of non-linear phenomena in geotechnical engineering
DEFF Research Database (Denmark)
Sørensen, Emil Smed
Geotechnical problems are often characterized by the non-linear behavior of soils and rock which are strongly linked to the inherent properties of the porous structure of the material as well as the presence and possible flow of any surrounding fluids. Dynamic problems involving such soil-fluid i...
Scaling of chaos in strongly nonlinear lattices.
Mulansky, Mario
2014-06-01
Although it is now understood that chaos in complex classical systems is the foundation of thermodynamic behavior, the detailed relations between the microscopic properties of the chaotic dynamics and the macroscopic thermodynamic observations still remain mostly in the dark. In this work, we numerically analyze the probability of chaos in strongly nonlinear Hamiltonian systems and find different scaling properties depending on the nonlinear structure of the model. We argue that these different scaling laws of chaos have definite consequences for the macroscopic diffusive behavior, as chaos is the microscopic mechanism of diffusion. This is compared with previous results on chaotic diffusion [M. Mulansky and A. Pikovsky, New J. Phys. 15, 053015 (2013)], and a relation between microscopic chaos and macroscopic diffusion is established.
Energy Technology Data Exchange (ETDEWEB)
Eltayeb, I A; Elbashir, T B A, E-mail: ieltayeb@squ.edu.om, E-mail: elbashir@squ.edu.om [Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, Muscat 123 (Oman)
2017-08-15
The linear and nonlinear stabilities of second sound waves in a rotating porous Darcy–Brinkman layer in local thermal non-equilibrium are studied when the heat flux in the solid obeys the Cattaneo law. The simultaneous action of the Brinkman effect (effective viscosity) and rotation is shown to destabilise the layer, as compared to either of them acting alone, for both stationary and overstable modes. The effective viscosity tends to favour overstable modes while rotation tends to favour stationary convection. Rapid rotation invokes a negative viscosity effect that suppresses the stabilising effect of porosity so that the stability characteristics resemble those of the classical rotating Benard layer. A formal weakly nonlinear analysis yields evolution equations of the Landau–Stuart type governing the slow time development of the amplitudes of the unstable waves. The equilibrium points of the evolution equations are analysed and the overall development of the amplitudes is examined. Both overstable and stationary modes can exhibit supercritical stability; supercritical instability, subcritical instability and stability are not possible. The dependence of the supercritical stability on the relative values of the six dimensionless parameters representing thermal non-equilibrium, rotation, porosity, relaxation time, thermal diffusivities and Brinkman effect is illustrated as regions in regime diagrams in the parameter space. The dependence of the heat transfer and the mean heat flux on the parameters of the problem is also discussed. (paper)
Tecklenburg, Jan; Neuweiler, Insa; Dentz, Marco; Carrera, Jesus; Geiger, Sebastian
2013-04-01
Flow processes in geotechnical applications do often take place in highly heterogeneous porous media, such as fractured rock. Since, in this type of media, classical modelling approaches are problematic, flow and transport is often modelled using multi-continua approaches. From such approaches, multirate mass transfer models (mrmt) can be derived to describe the flow and transport in the "fast" or mobile zone of the medium. The porous media is then modeled with one mobile zone and multiple immobile zones, where the immobile zones are connected to the mobile zone by single rate mass transfer. We proceed from a mrmt model for immiscible displacement of two fluids, where the Buckley-Leverett equation is expanded by a sink-source-term which is nonlocal in time. This sink-source-term models exchange with an immobile zone with mass transfer driven by capillary diffusion. This nonlinear diffusive mass transfer can be approximated for particular imbibition or drainage cases by a linear process. We present a numerical scheme for this model together with simulation results for a single fracture test case. We solve the mrmt model with the finite volume method and explicit time integration. The sink-source-term is transformed to multiple single rate mass transfer processes, as shown by Carrera et. al. (1998), to make it local in time. With numerical simulations we studied immiscible displacement in a single fracture test case. To do this we calculated the flow parameters using information about the geometry and the integral solution for two phase flow by McWorther and Sunnada (1990). Comparision to the results of the full two dimensional two phase flow model by Flemisch et. al. (2011) show good similarities of the saturation breakthrough curves. Carrera, J., Sanchez-Vila, X., Benet, I., Medina, A., Galarza, G., and Guimera, J.: On matrix diffusion: formulations, solution methods and qualitative effects, Hydrogeology Journal, 6, 178-190, 1998. Flemisch, B., Darcis, M
Nonlinear lattice waves in heterogeneous media
International Nuclear Information System (INIS)
Laptyeva, T V; Ivanchenko, M V; Flach, S
2014-01-01
We discuss recent advances in the understanding of the dynamics of nonlinear lattice waves in heterogeneous media, which enforce complete wave localization in the linear wave equation limit, especially Anderson localization for random potentials, and Aubry–André localization for quasiperiodic potentials. Additional nonlinear terms in the wave equations can either preserve the phase-coherent localization of waves, or destroy it through nonintegrability and deterministic chaos. Spreading wave packets are observed to show universal features in their dynamics which are related to properties of nonlinear diffusion equations. (topical review)
Models of diffuse solar radiation
Energy Technology Data Exchange (ETDEWEB)
Boland, John; Ridley, Barbara [Centre for Industrial and Applied Mathematics, University of South Australia, Mawson Lakes Boulevard, Mawson Lakes, SA 5095 (Australia); Brown, Bruce [Department of Statistics and Applied Probability, National University of Singapore, Singapore 117546 (Singapore)
2008-04-15
For some locations both global and diffuse solar radiation are measured. However, for many locations, only global is measured, or inferred from satellite data. For modelling solar energy applications, the amount of radiation on a tilted surface is needed. Since only the direct component on a tilted surface can be calculated from trigonometry, we need to have diffuse on the horizontal available. There are regression relationships for estimating the diffuse on a tilted surface from diffuse on the horizontal. Models for estimating the diffuse radiation on the horizontal from horizontal global that have been developed in Europe or North America have proved to be inadequate for Australia [Spencer JW. A comparison of methods for estimating hourly diffuse solar radiation from global solar radiation. Sol Energy 1982; 29(1): 19-32]. Boland et al. [Modelling the diffuse fraction of global solar radiation on a horizontal surface. Environmetrics 2001; 12: 103-16] developed a validated model for Australian conditions. We detail our recent advances in developing the theoretical framework for the approach reported therein, particularly the use of the logistic function instead of piecewise linear or simple nonlinear functions. Additionally, we have also constructed a method, using quadratic programming, for identifying values that are likely to be erroneous. This allows us to eliminate outliers in diffuse radiation values, the data most prone to errors in measurement. (author)
Graded/Gradient Porous Biomaterials
Directory of Open Access Journals (Sweden)
Xigeng Miao
2009-12-01
Full Text Available Biomaterials include bioceramics, biometals, biopolymers and biocomposites and they play important roles in the replacement and regeneration of human tissues. However, dense bioceramics and dense biometals pose the problem of stress shielding due to their high Young’s moduli compared to those of bones. On the other hand, porous biomaterials exhibit the potential of bone ingrowth, which will depend on porous parameters such as pore size, pore interconnectivity, and porosity. Unfortunately, a highly porous biomaterial results in poor mechanical properties. To optimise the mechanical and the biological properties, porous biomaterials with graded/gradient porosity, pores size, and/or composition have been developed. Graded/gradient porous biomaterials have many advantages over graded/gradient dense biomaterials and uniform or homogenous porous biomaterials. The internal pore surfaces of graded/gradient porous biomaterials can be modified with organic, inorganic, or biological coatings and the internal pores themselves can also be filled with biocompatible and biodegradable materials or living cells. However, graded/gradient porous biomaterials are generally more difficult to fabricate than uniform or homogenous porous biomaterials. With the development of cost-effective processing techniques, graded/gradient porous biomaterials can find wide applications in bone defect filling, implant fixation, bone replacement, drug delivery, and tissue engineering.
Model of two-temperature convective transfer in porous media
Gruais, Isabelle; Poliševski, Dan
2017-12-01
In this paper, we study the asymptotic behaviour of the solution of a convective heat transfer boundary problem in an ɛ -periodic domain which consists of two interwoven phases, solid and fluid, separated by an interface. The fluid flow and its dependence with respect to the temperature are governed by the Boussinesq approximation of the Stokes equations. The tensors of thermal diffusion of both phases are ɛ -periodic, as well as the heat transfer coefficient which is used to describe the first-order jump condition on the interface. We find by homogenization that the two-scale limits of the solutions verify the most common system used to describe local thermal non-equilibrium phenomena in porous media (see Nield and Bejan in Convection in porous media, Springer, New York, 1999; Rees and Pop in Transport phenomena in porous media III, Elsevier, Oxford, 2005). Since now, this system was justified only by volume averaging arguments.
Acoustics of multiscale sorptive porous materials
Venegas, R.; Boutin, C.; Umnova, O.
2017-08-01
This paper investigates sound propagation in multiscale rigid-frame porous materials that support mass transfer processes, such as sorption and different types of diffusion, in addition to the usual visco-thermo-inertial interactions. The two-scale asymptotic method of homogenization for periodic media is successively used to derive the macroscopic equations describing sound propagation through the material. This allowed us to conclude that the macroscopic mass balance is significantly modified by sorption, inter-scale (micro- to/from nanopore scales) mass diffusion, and inter-scale (pore to/from micro- and nanopore scales) pressure diffusion. This modification is accounted for by the dynamic compressibility of the effective saturating fluid that presents atypical properties that lead to slower speed of sound and higher sound attenuation, particularly at low frequencies. In contrast, it is shown that the physical processes occurring at the micro-nano-scale do not affect the macroscopic fluid flow through the material. The developed theory is exemplified by introducing an analytical model for multiscale sorptive granular materials, which is experimentally validated by comparing its predictions with acoustic measurements on granular activated carbons. Furthermore, we provide empirical evidence supporting an alternative method for measuring sorption and mass diffusion properties of multiscale sorptive materials using sound waves.
Nield, Donald A
2013-01-01
Convection in Porous Media, 4th Edition, provides a user-friendly introduction to the subject, covering a wide range of topics, such as fibrous insulation, geological strata, and catalytic reactors. The presentation is self-contained, requiring only routine mathematics and the basic elements of fluid mechanics and heat transfer. The book will be of use not only to researchers and practicing engineers as a review and reference, but also to graduate students and others entering the field. The new edition features approximately 1,750 new references and covers current research in nanofluids, cellular porous materials, strong heterogeneity, pulsating flow, and more. Recognized as the standard reference in the field Includes a comprehensive, 250-page reference list Cited over 2300 times to date in its various editions Serves as an introduction for those entering the field and as a comprehensive reference for experienced researchers Features new sections on nanofluids, carbon dioxide sequestration, and applications...
Porous electrode preparation method
Arons, R.M.; Dusek, J.T.
1983-10-18
A porous sintered plaque is provided with a bimodal porosity that is especially well suited for use as an electrode within a molten carbonate fuel cell. The coarse porosity is sufficient for admitting gases into contact with the reaction surfaces while the fine porosity is wetted with and retains molten electrolyte on the reaction sites. The electrode structure is prepared by providing a very fine powder of such as nickel oxide and blending the powder with a suitable decomposable binder to form a solid mass. The mass is comminuted into agglomerate size particles substantially larger than the fine oxide particles and formed into a cohesive compact for subsequent sintering. Sintering is carried out at sufficient conditions to bind the agglomerates together into a porous structure having both coarse and fine porosity. Where lithiated nickel oxide cathodes are prepared, the sintering conditions can be moderate enough to retain substantial quantities of lithium within the electrode for adequate conductivity. 2 figs.
Spectral theory and nonlinear functional analysis
Lopez-Gomez, Julian
2001-01-01
This Research Note addresses several pivotal problems in spectral theory and nonlinear functional analysis in connection with the analysis of the structure of the set of zeroes of a general class of nonlinear operators. It features the construction of an optimal algebraic/analytic invariant for calculating the Leray-Schauder degree, new methods for solving nonlinear equations in Banach spaces, and general properties of components of solutions sets presented with minimal use of topological tools. The author also gives several applications of the abstract theory to reaction diffusion equations and systems.The results presented cover a thirty-year period and include recent, unpublished findings of the author and his coworkers. Appealing to a broad audience, Spectral Theory and Nonlinear Functional Analysis contains many important contributions to linear algebra, linear and nonlinear functional analysis, and topology and opens the door for further advances.
Energy Technology Data Exchange (ETDEWEB)
Garralaga Rojas, Enrique; Hensen, Jan; Brendel, Rolf [Institut fuer Solarenergieforschung Hameln (ISFH), Emmerthal (Germany); Carstensen, Juergen; Foell, Helmut [Chair for General Materials Science, Faculty of Engineering, Christian-Albrechts-University of Kiel (Germany)
2011-06-15
We present the reproducible fabrication of porous germanium (PGe) single- and multilayers. Mesoporous layers form on heavily doped 4'' p-type Ge wafers by electrochemical etching in highly concentrated HF-based electrolytes with concentrations in a range of 30-50 wt.%. Direct PGe formation is accompanied by a constant dissolution of the already-formed porous layer at the electrolyte/PGe interface, hence yielding a thinner substrate after etching. This effect inhibits multilayer formation as the starting layer is etched while forming the second layer. We avoid dissolution of the porous layer by alternating the etching bias from anodic to cathodic. PGe formation occurs during anodic etching whereas the cathodic step passivates pore walls with H-atoms and avoids electropolishing. The passivation lasts a limited time depending on the etching current density and electrolyte concentration, necessitating a repetition of the cathodic step at suitable intervals. With optimized alternating bias mesoporous multilayer production is possible. We control the porosity of each single layer by varying the etching current density and the electrolyte (copyright 2011 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Fu, Y. B.; Ogden, R. W.
2001-05-01
This collection of papers by leading researchers in the field of finite, nonlinear elasticity concerns itself with the behavior of objects that deform when external forces or temperature gradients are applied. This process is extremely important in many industrial settings, such as aerospace and rubber industries. This book covers the various aspects of the subject comprehensively with careful explanations of the basic theories and individual chapters each covering a different research direction. The authors discuss the use of symbolic manipulation software as well as computer algorithm issues. The emphasis is placed firmly on covering modern, recent developments, rather than the very theoretical approach often found. The book will be an excellent reference for both beginners and specialists in engineering, applied mathematics and physics.
Rajasekar, Shanmuganathan
2016-01-01
This introductory text presents the basic aspects and most important features of various types of resonances and anti-resonances in dynamical systems. In particular, for each resonance, it covers the theoretical concepts, illustrates them with case studies, and reviews the available information on mechanisms, characterization, numerical simulations, experimental realizations, possible quantum analogues, applications and significant advances made over the years. Resonances are one of the most fundamental phenomena exhibited by nonlinear systems and refer to specific realizations of maximum response of a system due to the ability of that system to store and transfer energy received from an external forcing source. Resonances are of particular importance in physical, engineering and biological systems - they can prove to be advantageous in many applications, while leading to instability and even disasters in others. The book is self-contained, providing the details of mathematical derivations and techniques invo...
Gas Permeation Characteristics across Nano-Porous Inorganic Membranes
Directory of Open Access Journals (Sweden)
M.R Othman, H. Mukhtar
2012-10-01
Full Text Available An overview of parameters affecting gas permeation in inorganic membranes is presented. These factors include membrane physical characteristics, operational parameters and gas molecular characteristics. The membrane physical characteristics include membrane materials and surface area, porosity, pore size and pore size distribution and membrane morphology. The operational parameters include feed flow rate and concentration, stage cut, temperature and pressure. The gas molecular characteristics include gas molecular weight, diameter, critical temperature, critical pressure, Lennard-Jones parameters and diffusion volumes. The current techniques of material characterization may require complementary method in describing microscopic heterogeneity of the porous ceramic media. The method to be incorporated in the future will be to apply a stochastic model and/or fractal dimension. Keywords: Inorganic membrane, surface adsorption, Knudsen diffusion, Micro-porous membrane, permeation, gas separation.
International Nuclear Information System (INIS)
Bakunov, V.S.; Balkevich, V.L.; Vlasov, A.S.; Guzman, I.Ya.; Lukin, E.S.; Poluboyarinov, D.N.; Poliskij, R.Ya.
1977-01-01
A review is made of manufacturing procedures and properties of oxide ceramics intended for high-temperature thermal insulation and thermal protection applications. Presented are structural characteristics of porous oxide refractories and their properties. Strength and thermal conductivity was shown to depend upon porosity. Described is a procedure for manufacturing porous ceramic materials from aluminium oxide, zirconium dioxide, magnesium oxide, beryllium oxide. The thermal resistance of porous ceramics from BeO is considerably greater than that of other high-refractoriness oxides. Listed are areas of application for porous materials based on oxides
Selective formation of porous silicon
Fathauer, Robert W. (Inventor); Jones, Eric W. (Inventor)
1993-01-01
A pattern of porous silicon is produced in the surface of a silicon substrate by forming a pattern of crystal defects in said surface, preferably by applying an ion milling beam through openings in a photoresist layer to the surface, and then exposing said surface to a stain etchant, such as HF:HNO3:H2O. The defected crystal will preferentially etch to form a pattern of porous silicon. When the amorphous content of the porous silicon exceeds 70 percent, the porous silicon pattern emits visible light at room temperature.
Asymptotics of the filtration problem for suspension in porous media
Directory of Open Access Journals (Sweden)
Kuzmina Ludmila Ivanovna
2015-01-01
Full Text Available The mechanical-geometric model of the suspension filtering in the porous media is considered. Suspended solid particles of the same size move with suspension flow through the porous media - a solid body with pores - channels of constant cross section. It is assumed that the particles pass freely through the pores of large diameter and are stuck at the inlet of pores that are smaller than the particle size. It is considered that one particle can clog only one small pore and vice versa. The particles stuck in the pores remain motionless and form a deposit. The concentrations of suspended and retained particles satisfy a quasilinear hyperbolic system of partial differential equations of the first order, obtained as a result of macro-averaging of micro-stochastic diffusion equations. Initially the porous media contains no particles and both concentrations are equal to zero; the suspension supplied to the porous media inlet has a constant concentration of suspended particles. The flow of particles moves in the porous media with a constant speed, before the wave front the concentrations of suspended and retained particles are zero. Assuming that the filtration coefficient is small we construct an asymptotic solution of the filtration problem over the concentration front. The terms of the asymptotic expansions satisfy linear partial differential equations of the first order and are determined successively in an explicit form. It is shown that in the simplest case the asymptotics found matches the known asymptotic expansion of the solution near the concentration front.
Porous Core-Shell Nanostructures for Catalytic Applications
Ewers, Trevor David
Porous core-shell nanostructures have recently received much attention for their enhanced thermal stability. They show great potential in the field of catalysis, as reactant gases can diffuse in and out of the porous shell while the core particle is protected from sintering, a process in which particles coalesce to form larger particles. Sintering is a large problem in industry and is the primary cause of irreversible deactivation. Despite the obvious advantages of high thermal stability, porous core-shell nanoparticles can be developed to have additional interactive properties from the combination of the core and shell together, rather than just the core particle alone. This dissertation focuses on developing new porous core-shell systems in which both the core and shell take part in catalysis. Two types of systems are explored; (1) yolk-shell nanostructures with reducible oxide shells formed using the Kirkendall effect and (2) ceramic-based porous oxide shells formed using sol-gel chemistry. Of the Kirkendall-based systems, Au FexOy and Cu CoO were synthesized and studied for catalytic applications. Additionally, ZnO was explored as a potential shelling material. Sol-gel work focused on optimizing synthetic methods to allow for coating of small gold particles, which remains a challenge today. Mixed metal oxides were explored as a shelling material to make dual catalysts in which the product of a reaction on the core particle becomes a reactant within the shell.
DEFF Research Database (Denmark)
Zhang, Chen; Chen, Qingyan; Heiselberg, Per Kvols
2015-01-01
geometrical model and the other is a porous media model. The numerical models are validated by the full-scale experimental studies in a climate chamber. The results indicate that porous media model performed better on predicting air flow characteristic below diffuse ceiling and air velocity near the floor...
Observation of time-varying photoconductivity and persistent photoconductivity in porous silicon
DEFF Research Database (Denmark)
Frello, T.; Veje, E.; Leistiko, Otto
1996-01-01
We have observed time-varying photoconductivity and persistent photoconductivity in porous silicon, both with time-evolution scales of the order of several minutes or hours. The time evolutions depend on the wavelength and the intensity of the illuminating light. The data indicate the presence...... of at least two competing mechanisms, one is tentatively related to photoinduced creation of charge carriers in the silicon substrate followed by diffusion into the porous silicon layer, and the other is tentatively related to desorption of hydrogen from the porous silicon. ©1996 American Institute of Physics....
Simon, Lin; Gidley, D W; Wetzel, J T; Monnig, K A; Ryan, E T; Simon, Jang; Douglas, Yu; Liang, M S; En, W G; Jones, E C; Sturm, J C; Chan, M J; Tiwari, S C; Hirose, M
2002-01-01
Positron Annihilation Lifetime Spectroscopy (PALS) is a useful tool to pre-screen metal barrier integrity for Si-based porous low-k dielectrics. Pore size of low-k, thickness of metal barrier Ta, positronium (Ps) leakage from PALS, trench sidewall morphology, electrical test from one level metal (1LM) pattern wafer and Cu diffusion analysis were all correlated. Macro-porous low-k (pore size >=200 AA) and large scale meso-porous low-k (>50~200 AA) encounter both Ps leakage and Cu diffusion into low-k dielectric in the 0.25 mu mL/0.3 mu mS structures when using SEMATECH in-house PVD Ta 250 AA as barrier layer. For small scale meso-porous (>20~50 AA) and micro- porous (<=20 AA) low-k, no Ps leakage and no Cu diffusion into low-k were observed even with PVD Ta 50 AA, which is proved also owing to sidewall densification to seal all sidewall pores due to plasma etch and ash. For future technology, smaller pore size of porous Si-based low-k (=<50 AA) will be preferential for dense low-k like trench sidewall to...
Energy Technology Data Exchange (ETDEWEB)
Wang, H.; Seki, M.; Furusaki, S. [The University of Tokyo, Tokyo (Japan)
1996-02-01
Lactic acid production using co-immobilized L.defbrveckii with porous particles has been studied. The effect of co-immobilization with porous particles was verified by measuring the variations of both overall production rate of lactic acid and effective diffusion coefficient in the co-immobilized gel. The effective diffusion coefficient decreased with increasing cell concentration in the co-immobilized gel. However, in the high cell density regimes, the effective diffusion coefficient in co-immobilized gel was higher than that without co-immobilized porous particles. The optimal volume fraction of porous particles in the co-immobilizing gel beads leas estimated experimentally at about 10%(v/v). An approximately 30% increase of the overall production rate was obtained compared to the control culture. Mathematical analysis showed that by co-immobilizing cells with porous particles, the steady-state concentration profiles of proton and undissociated lactic acid changed favorably inside the gel beads. The result indicates that co-immobilization with porous particles is a useful method to improve fermentation efficiency in processes using immobilized cells. 19 refs., 8 figs.
Percolation-enhanced nonlinear scattering from semicontinuous metal films
Breit, M.; von Plessen, G.; Feldmann, J.; Podolskiy, V. A.; Sarychev, A. K.; Shalaev, V. M.; Gresillon, S.; Rivoal, J. C.; Gadenne, P.
2001-03-01
Strongly enhanced second-harmonic generation (SHG), which is characterized by nearly isotropic distribution, is observed for gold-glass films near the percolation threshold. The diffuse-like SHG scattering, which can be thought of as nonlinear critical opalescence, is in sharp contrast with highly collimated linear reflection and transmission from these nanostructured semicontinuous metal films. Our observations, which can be explained by giant fluctuations of local nonlinear sources for SHG, verify recent predictions of percolation-enhanced nonlinear scattering.
International Nuclear Information System (INIS)
Sheng, Chan Kok; Mahmood Mat Yunus, W.; Yunus, Wan Md. Zin Wan; Abidin Talib, Zainal; Kassim, Anuar
2008-01-01
In this work, the porous silicon layer was prepared by the electrochemical anodization etching process on n-type and p-type silicon wafers. The formation of the porous layer has been identified by photoluminescence and SEM measurements. The optical absorption, energy gap, carrier transport and thermal properties of n-type and p-type porous silicon layers were investigated by analyzing the experimental data from photoacoustic measurements. The values of thermal diffusivity, energy gap and carrier transport properties have been found to be porosity-dependent. The energy band gap of n-type and p-type porous silicon layers was higher than the energy band gap obtained for silicon substrate (1.11 eV). In the range of porosity (50-76%) of the studies, our results found that the optical band-gap energy of p-type porous silicon (1.80-2.00 eV) was higher than that of the n-type porous silicon layer (1.70-1.86 eV). The thermal diffusivity value of the n-type porous layer was found to be higher than that of the p-type and both were observed to increase linearly with increasing layer porosity
Conceptual design of krypton recovery plant by porous membrane method
International Nuclear Information System (INIS)
Yoshida, Hiroshi; Fujine, Sachio; Shimizu, Toku; Saito, Keiichiro; Ouchi, Misao
1979-10-01
A conceptual design of a krypton recovery plant by porous membrane method was made to study feasibility of treating fuel reprocessing off-gas. Specifications of the plant could be clarified, such as off-gas pretreatment system, first cascade system of gaseous diffusion Hertz cascade composed of two-compartment diffusers, storage system, shield and housing and operating conditions. Capital costs and operating costs of the plant were estimated for different operating conditions and cost parameters. Technical and economic feasibility of the method compares favorably with those of the cryogenic distillation or the solvent absorption method. (author)
Boundary fluxes for nonlocal diffusion
Cortazar, Carmen; Elgueta, Manuel; Rossi, Julio D.; Wolanski, Noemi
We study a nonlocal diffusion operator in a bounded smooth domain prescribing the flux through the boundary. This problem may be seen as a generalization of the usual Neumann problem for the heat equation. First, we prove existence, uniqueness and a comparison principle. Next, we study the behavior of solutions for some prescribed boundary data including blowing up ones. Finally, we look at a nonlinear flux boundary condition.
The generalized Airy diffusion equation
Directory of Open Access Journals (Sweden)
Frank M. Cholewinski
2003-08-01
Full Text Available Solutions of a generalized Airy diffusion equation and an associated nonlinear partial differential equation are obtained. Trigonometric type functions are derived for a third order generalized radial Euler type operator. An associated complex variable theory and generalized Cauchy-Euler equations are obtained. Further, it is shown that the Airy expansions can be mapped onto the Bessel Calculus of Bochner, Cholewinski and Haimo.
Study of ODE limit problems for reaction-diffusion equations
Directory of Open Access Journals (Sweden)
Jacson Simsen
2018-01-01
Full Text Available In this work we study ODE limit problems for reaction-diffusion equations for large diffusion and we study the sensitivity of nonlinear ODEs with respect to initial conditions and exponent parameters. Moreover, we prove continuity of the flow and weak upper semicontinuity of a family of global attractors for reaction-diffusion equations with spatially variable exponents when the exponents go to 2 in \\(L^{\\infty}(\\Omega\\ and the diffusion coefficients go to infinity.
[Nonlinear magnetohydrodynamics
International Nuclear Information System (INIS)
1994-01-01
Resistive MHD equilibrium, even for small resistivity, differs greatly from ideal equilibrium, as do the dynamical consequences of its instabilities. The requirement, imposed by Faraday's law, that time independent magnetic fields imply curl-free electric fields, greatly restricts the electric fields allowed inside a finite-resistivity plasma. If there is no flow and the implications of the Ohm's law are taken into account (and they need not be, for ideal equilibria), the electric field must equal the resistivity times the current density. The vanishing of the divergence of the current density then provides a partial differential equation which, together with boundary conditions, uniquely determines the scalar potential, the electric field, and the current density, for any given resistivity profile. The situation parallels closely that of driven shear flows in hydrodynamics, in that while dissipative steady states are somewhat more complex than ideal ones, there are vastly fewer of them to consider. Seen in this light, the vast majority of ideal MHD equilibria are just irrelevant, incapable of being set up in the first place. The steady state whose stability thresholds and nonlinear behavior needs to be investigated ceases to be an arbitrary ad hoc exercise dependent upon the whim of the investigator, but is determined by boundary conditions and choice of resistivity profile
A tracer diffusion model derived from microstructure
International Nuclear Information System (INIS)
Lehikoinen, Jarmo; Muurinen, Arto; Olin, Markus
2012-01-01
Document available in extended abstract form only. Full text of publication follows: Numerous attempts have been made to explain the tracer diffusion of various solutes in compacted clays. These attempts have commonly suffered from an inability to describe the diffusion of uncharged and charged solutes with a single unified model. Here, an internally consistent approach to describing the diffusion of solutes in a heterogeneous porous medium, such as compacted bentonite, in terms of its microstructure is presented. The microstructure is taken to be represented by a succession of unit cells, which consist of two consecutive regions (Do, 1996). In the first region, the diffusion is viewed to occur in two parallel paths: one through microcrystalline units (micropores) and the other through meso-pores between the microcrystalline units. Solutes exiting these two paths are then joined together to continue diffusing through the second, disordered, region, connecting the two adjacent microcrystalline units. Adsorption (incl. co-ion exclusion) is thought to occur in the micropores, whereas meso-pores and the disordered region accommodate free species alone. Co-ions are also assumed to experience transfer resistance into and out of the micropores, which is characterized in the model by a transmission coefficient. Although the model is not new per se, its application to compacted clays has never been attempted before. It is shown that in the limit of strong adsorption, the effective diffusivity is limited from above only by the microstructural parameters of the model porous medium. As intuitive and logical as this result may appear, it has not been proven before. In the limit of vanishing disordered region, the effective diffusivity is no longer explicitly constrained by any of the model parameters. The tortuosity of the diffusion path, i.e. the quotient of the actual diffusion path length in the porous-medium coordinates and the characteristic length of the laboratory frame
Optical performance of hybrid porous silicon-porous alumina multilayers
Cencha, L. G.; Antonio Hernández, C.; Forzani, L.; Urteaga, R.; Koropecki, R. R.
2018-05-01
In this work, we study the optical response of structures involving porous silicon and porous alumina in a multi-layered hybrid structure. We performed a rational design of the optimal sequence necessary to produce a high transmission and selective filter, with potential applications in chemical and biosensors. The combination of these porous materials can be used to exploit its distinguishing features, i.e., high transparency of alumina and high refractive index of porous silicon. We assembled hybrid microcavities with a central porous alumina layer between two porous silicon Bragg reflectors. In this way, we constructed a Fabry-Perot resonator with high reflectivity and low absorption that improves the quality of the filter compared to a microcavity built only with porous silicon or porous alumina. We explored a simpler design in which one of the Bragg reflectors is replaced by the aluminium that remains bound to the alumina after its fabrication. We theoretically explored the potential of the proposal and its limitations when considering the roughness of the layers. We found that the quality of a microcavity made entirely with porous silicon shows a limit in the visible range due to light absorption. This limitation is overcome in the hybrid scheme, with the roughness of the layers determining the ultimate quality. Q-factors of 220 are experimentally obtained for microcavities supported on aluminium, while Q-factors around 600 are reached for microcavities with double Bragg reflectors, centred at 560 nm. This represents a four-fold increase with respect to the optimal porous silicon microcavity at this wavelength.
Comolli, Alessandro; Hakoun, Vivien; Dentz, Marco
2017-04-01
Achieving the understanding of the process of solute transport in heterogeneous porous media is of crucial importance for several environmental and social purposes, ranging from aquifers contamination and remediation, to risk assessment in nuclear waste repositories. The complexity of this aim is mainly ascribable to the heterogeneity of natural media, which can be observed at all the scales of interest, from pore scale to catchment scale. In fact, the intrinsic heterogeneity of porous media is responsible for the arising of the well-known non-Fickian footprints of transport, including heavy-tailed breakthrough curves, non-Gaussian spatial density profiles and the non-linear growth of the mean squared displacement. Several studies investigated the processes through which heterogeneity impacts the transport properties, which include local modifications to the advective-dispersive motion of solutes, mass exchanges between some mobile and immobile phases (e.g. sorption/desorption reactions or diffusion into solid matrix) and spatial correlation of the flow field. In the last decades, the continuous time random walk (CTRW) model has often been used to describe solute transport in heterogenous conditions and to quantify the impact of point heterogeneity, spatial correlation and mass transfer on the average transport properties [1]. Open issues regarding this approach are the possibility to relate measurable properties of the medium to the parameters of the model, as well as its capability to provide predictive information. In a recent work [2] the authors have shed new light on understanding the relationship between Lagrangian and Eulerian dynamics as well as on their evolution from arbitrary initial conditions. On the basis of these results, we derive a CTRW model for the description of Darcy-scale transport in d-dimensional media characterized by spatially random permeability fields. The CTRW approach models particle velocities as a spatial Markov process, which is
Newton-sor iterative method for solving the two-dimensional porous ...
African Journals Online (AJOL)
In this paper, we consider the application of the Newton-SOR iterative method in obtaining the approximate solution of the two-dimensional porous medium equation (2D PME). The nonlinear finite difference approximation equation to the 2D PME is derived by using the implicit finite difference scheme. The developed ...
Law of nonlinear flow in saturated clays and radial consolidation
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
It was derived that micro-scale amount level of average pore radius of clay changed from 0.01 to 0.1 micron by an equivalent concept of flow in porous media. There is good agreement between the derived results and test ones. Results of experiments show that flow in micro-scale pore of saturated clays follows law of nonlinear flow. Theoretical analyses demonstrate that an interaction of solid-liquid interfaces varies inversely with permeability or porous radius. The interaction is an important reason why nonlinear flow in saturated clays occurs. An exact mathematical model was presented for nonlinear flow in micro-scale pore of saturated clays. Dimension and physical meanings of parameters of it are definite. A new law of nonlinear flow in saturated clays was established. It can describe characteristics of flow curve of the whole process of the nonlinear flow from low hydraulic gradient to high one. Darcy law is a special case of the new law. A mathematical model was presented for consolidation of nonlinear flow in radius direction in saturated clays with constant rate based on the new law of nonlinear flow. Equations of average mass conservation and moving boundary, and formula of excess pore pressure distribution and average degree of consolidation for nonlinear flow in saturated clay were derived by using an idea of viscous boundary layer, a method of steady state in stead of transient state and a method of integral of an equation. Laws of excess pore pressure distribution and changes of average degree of consolidation with time were obtained. Results show that velocity of moving boundary decreases because of the nonlinear flow in saturated clay. The results can provide geology engineering and geotechnical engineering of saturated clay with new scientific bases. Calculations of average degree of consolidation of the Darcy flow are a special case of that of the nonlinear flow.
Experimental and theoretical investigations on diffusion process for rare earth ores
Energy Technology Data Exchange (ETDEWEB)
He, Ye; Li, Wenzhi Z. [Changchun Univ. (China)
2013-06-01
The diffusion reaction kinetics of weathered crust elution-deposited rare earth with mixed ammonium salts was studied. The influence of concentration of reagents and particle size of ore on diffusion rate was investigated. The results showed that the diffusion process and diffusion rate could be improved by increasing reagents concentration and decreasing diffusion flowing rate and particle size. The diffusion process could be explained with the shrinking core Model, which could be controlled by the diffusion rate of reacting reagents in porous solid layer.
Overall viscoplastic behavior of non-irradiated porous nuclear ceramics
International Nuclear Information System (INIS)
Monerie, Yann; Gatt, Jean-Marie
2006-01-01
This paper deals with the overall behavior of nonlinear viscous and porous nuclear ceramics. Bi-viscous isotropic porous materials are considered: the matrix is subjected to two power-law viscosities with different exponents related to two stationary temperature-activated creeping mechanisms (scattering-creep and dislocation-creep), and this matrix contains a low porosity volume fraction. The overall behavior of these types of composite materials is obtained with the help of quadratic strain-rate potentials combined with experimental-based coupling function depending on stress and temperature. For each creeping mechanism, the hollow sphere model of [Michel, J.-C., Suquet, P., 1992. The constitutive law of nonlinear viscous and porous materials. Journal of the Mechanics and Physics of Solids 40, 783-812] is used. Mechanical parameters of the resulting model are identified and validated in the particular case of non-irradiated uranium dioxide nuclear ceramics. This model predicts, under pure thermo-mechanical loading, a variation of the material volume and a variation of the porosity volume fraction (the so-called densification or swelling). (authors)
Effective Diffusivities of Gases in a Reconstructed Porous Body
Czech Academy of Sciences Publication Activity Database
Čapek, P.; Hejtmánek, Vladimír; Brabec, Libor; Zikánová, Arlette; Kočiřík, Milan
2008-01-01
Roč. 86, č. 7A (2008), s. 713-722 ISSN 0263-8762 R&D Projects: GA ČR GA203/05/0347 Institutional research plan: CEZ:AV0Z40720504; CEZ:AV0Z40400503 Keywords : stochastic reconstruction * random pore network * random Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 0.989, year: 2008
A new methodology for determination of macroscopic transport parameters in drying porous media
Attari Moghaddam, A.; Kharaghani, A.; Tsotsas, E.; Prat, M.
2015-12-01
Two main approaches have been used to model the drying process: The first approach considers the partially saturated porous medium as a continuum and partial differential equations are used to describe the mass, momentum and energy balances of the fluid phases. The continuum-scale models (CM) obtained by this approach involve constitutive laws which require effective material properties, such as the diffusivity, permeability, and thermal conductivity which are often determined by experiments. The second approach considers the material at the pore scale, where the void space is represented by a network of pores (PN). Micro- or nanofluidics models used in each pore give rise to a large system of ordinary differential equations with degrees of freedom at each node of the pore network. In this work, the moisture transport coefficient (D), the pseudo desorption isotherm inside the network and at the evaporative surface are estimated from the post-processing of the three-dimensional pore network drying simulations for fifteen realizations of the pore space geometry from a given probability distribution. A slice sampling method is used in order to extract these parameters from PN simulations. The moisture transport coefficient obtained in this way is shown in Fig. 1a. The minimum of average D values demonstrates the transition between liquid dominated moisture transport region and vapor dominated moisture transport region; a similar behavior has been observed in previous experimental findings. A function is fitted to the average D values and then is fed into the non-linear moisture diffusion equation. The saturation profiles obtained from PN and CM simulations are shown in Fig. 1b. Figure 1: (a) extracted moisture transport coefficient during drying for fifteen realizations of the pore network, (b) average moisture profiles during drying obtained from PN and CM simulations.
Westra, H.J.R.
2012-01-01
In this Thesis, nonlinear dynamics and nonlinear interactions are studied from a micromechanical point of view. Single and doubly clamped beams are used as model systems where nonlinearity plays an important role. The nonlinearity also gives rise to rich dynamic behavior with phenomena like
Muntean, A.; Böhm, M.
2009-01-01
Reaction–diffusion processes, where slow diffusion balances fast reaction, usually exhibit internal loci where the reactions are concentrated. Some modeling and simulation aspects of using kinetic free-boundary conditions to drive fast carbonation reaction fronts into unsaturated porous cement-based
Mechanics of adsorption-deformation coupling in porous media
Zhang, Yida
2018-05-01
This work extends Coussy's macroscale theory for porous materials interacting with adsorptive fluid mixtures. The solid-fluid interface is treated as an independent phase that obeys its own mass, momentum and energy balance laws. As a result, a surface strain energy term appears in the free energy balance equation of the solid phase, which further introduces the so-called adsorption stress in the constitutive equations of the porous skeleton. This establishes a fundamental link between the adsorption characteristics of the solid-fluid interface and the mechanical response of the porous media. The thermodynamic framework is quite general in that it recovers the coupled conduction laws, Gibbs isotherm and the Shuttleworth's equation for surface stress, and imposes no constraints on the magnitude of deformation and the functional form of the adsorption isotherms. A rich variety of coupling between adsorption and deformation is recovered as a result of combining different poroelastic models (isotropic vs. anisotropic, linear vs. nonlinear) and adsorption models (unary vs. mixture adsorption, uncoupled vs. stretch-dependent adsorption). These predictions are discussed against the backdrop of recent experimental data on coal swelling subjected to CO2 and CO2sbnd CH4 injections, showing the capability and versatility of the theory in capturing adsorption-induced deformation of porous materials.
Electrical behavior of free-standing porous silicon layers
International Nuclear Information System (INIS)
Bazrafkan, I.; Dariani, R.S.
2009-01-01
The electrical behavior of porous silicon (PS) layers has been investigated on one side of p-type silicon with various anodization currents and electrolytes. The two contact I-V characteristic is assigned by the metal/porous silicon rectifying interface, whereas, by using the van der Pauw technique, a nonlinear dependence of the current vs voltage was found. By using Dimethylformamide (DMF) in electrolyte, regular structures and columns were formed and porosity increased. Our results showed that by using DMF, surface resistivity of PS samples increased and became double for free-standing porous silicon (FPS). The reason could be due to increasing surface area and adsorbing some more gas molecules. Activation energy of PS samples was also increased from 0.31 to 0.34 eV and became 0.35 eV for FPS. The changes induced by storage are attributed to the oxidation process of the internal surface of free-standing porous silicon layers.
Percolation theory for flow in porous media
Hunt, Allen; Ghanbarian, Behzad
2014-01-01
This monograph presents, for the first time, a unified and comprehensive introduction to some of the basic transport properties of porous media, such as electrical and hydraulic conductivity, air permeability and diffusion. The approach is based on critical path analysis and the scaling of transport properties, which are individually described as functions of saturation. At the same time, the book supplies a tutorial on percolation theory for hydrologists, providing them with the tools for solving actual problems. In turn, a separate chapter serves to introduce physicists to some of the language and complications of groundwater hydrology necessary for successful modeling. The end-of-chapter problems often indicate open questions, which young researchers entering the field can readily start working on. This significantly revised and expanded third edition includes in particular two new chapters: one on advanced fractal-based models, and one devoted to the discussion of various open issues such as the role of d...
Thermal conductivity of highly porous mullite material
International Nuclear Information System (INIS)
Barea, Rafael; Osendi, Maria Isabel; Ferreira, Jose M.F.; Miranzo, Pilar
2005-01-01
The thermal diffusivity of highly porous mullite materials (35-60 vol.% porosity) has been measured up to 1000 deg C by the laser flash method. These materials were fabricated by a direct consolidation method based on the swelling properties of starch granules in concentrated aqueous suspensions and showed mainly spherical shaped pores of about 30 μm in diameter. From the point of view of heat conduction, they behave as a bi-phase material of voids dispersed in the continuous mullite matrix. The temperature dependence of thermal conductivity for the different porosities was modeled by a simple equation that considers the contribution to heat conduction of the mullite matrix and the gas inside the pores, as well as the radiation. The thermal conductivity of the matrix was taken from the measurements done in a dense mullite while the conductivity in the voids was assumed to be that of the testing atmosphere
Diffusion of Finite-Size Particles in Confined Geometries
Bruna, Maria
2013-05-10
The diffusion of finite-size hard-core interacting particles in two- or three-dimensional confined domains is considered in the limit that the confinement dimensions become comparable to the particle\\'s dimensions. The result is a nonlinear diffusion equation for the one-particle probability density function, with an overall collective diffusion that depends on both the excluded-volume and the narrow confinement. By including both these effects, the equation is able to interpolate between severe confinement (for example, single-file diffusion) and unconfined diffusion. Numerical solutions of both the effective nonlinear diffusion equation and the stochastic particle system are presented and compared. As an application, the case of diffusion under a ratchet potential is considered, and the change in transport properties due to excluded-volume and confinement effects is examined. © 2013 Society for Mathematical Biology.
Diffusion of Finite-Size Particles in Confined Geometries
Bruna, Maria; Chapman, S. Jonathan
2013-01-01
The diffusion of finite-size hard-core interacting particles in two- or three-dimensional confined domains is considered in the limit that the confinement dimensions become comparable to the particle's dimensions. The result is a nonlinear diffusion equation for the one-particle probability density function, with an overall collective diffusion that depends on both the excluded-volume and the narrow confinement. By including both these effects, the equation is able to interpolate between severe confinement (for example, single-file diffusion) and unconfined diffusion. Numerical solutions of both the effective nonlinear diffusion equation and the stochastic particle system are presented and compared. As an application, the case of diffusion under a ratchet potential is considered, and the change in transport properties due to excluded-volume and confinement effects is examined. © 2013 Society for Mathematical Biology.
Analytical solutions to matrix diffusion problems
Energy Technology Data Exchange (ETDEWEB)
Kekäläinen, Pekka, E-mail: pekka.kekalainen@helsinki.fi [Laboratory of Radiochemistry, Department of Chemistry, P.O. Box 55, FIN-00014 University of Helsinki (Finland)
2014-10-06
We report an analytical method to solve in a few cases of practical interest the equations which have traditionally been proposed for the matrix diffusion problem. In matrix diffusion, elements dissolved in ground water can penetrate the porous rock surronuding the advective flow paths. In the context of radioactive waste repositories this phenomenon provides a mechanism by which the area of rock surface in contact with advecting elements is greatly enhanced, and can thus be an important delay mechanism. The cases solved are relevant for laboratory as well for in situ experiments. Solutions are given as integral representations well suited for easy numerical solution.
On Diffusive Climatological Models.
Griffel, D. H.; Drazin, P. G.
1981-11-01
A simple, zonally and annually averaged, energy-balance climatological model with diffusive heat transport and nonlinear albedo feedback is solved numerically. Some parameters of the model are varied, one by one, to find the resultant effects on the steady solution representing the climate. In particular, the outward radiation flux, the insulation distribution and the albedo parameterization are varied. We have found an accurate yet simple analytic expression for the mean annual insolation as a function of latitude and the obliquity of the Earth's rotation axis; this has enabled us to consider the effects of the oscillation of the obliquity. We have used a continuous albedo function which fits the observed values; it considerably reduces the sensitivity of the model. Climatic cycles, calculated by solving the time-dependent equation when parameters change slowly and periodically, are compared qualitatively with paleoclimatic records.
Khan, Sami Ullah; Ali, Nasir; Abbas, Zaheer
2015-01-01
An analysis is carried out to study the heat transfer in unsteady two-dimensional boundary layer flow of a magnetohydrodynamics (MHD) second grade fluid over a porous oscillating stretching surface embedded in porous medium. The flow is induced due to infinite elastic sheet which is stretched periodically. With the help of dimensionless variables, the governing flow equations are reduced to a system of non-linear partial differential equations. This system has been solved numerically using the finite difference scheme, in which a coordinate transformation is used to transform the semi-infinite physical space to a bounded computational domain. The influence of the involved parameters on the flow, the temperature distribution, the skin-friction coefficient and the local Nusselt number is shown and discussed in detail. The study reveals that an oscillatory sheet embedded in a fluid-saturated porous medium generates oscillatory motion in the fluid. The amplitude and phase of oscillations depends on the rheology of the fluid as well as on the other parameters coming through imposed boundary conditions, inclusion of body force term and permeability of the porous medium. It is found that amplitude of flow velocity increases with increasing viscoelastic and mass suction/injection parameters. However, it decreases with increasing the strength of the applied magnetic field. Moreover, the temperature of fluid is a decreasing function of viscoelastic parameter, mass suction/injection parameter and Prandtl number.
Correlation of rates of tritium migration through porous concrete
Energy Technology Data Exchange (ETDEWEB)
Fukada, S.; Katayama, K.; Takeishi, T. [Kyushu University, Fukuoka (Japan); Edao, Y.; Kawamura, Y.; Hayashi, T.; Yamanishi, T. [JAEA-TPL, Muramatsu, Tokai-mura (Japan)
2015-03-15
In a nuclear facility when tritium leaks from a glovebox to room accidentally, an atmosphere detritiation system (ADS) starts operating, and HTO released is recovered by ADS. ADS starts when tritium activity in air becomes higher than its controlled level. Before ADS operates, the laboratory walls are the final enclosure facing tritium and are usually made of porous concrete coated with a hydrophobic paint. In the present study, previous data on the diffusivity and adsorption coefficient of concrete and paints are reviewed. Tritium penetrates and migrates into concrete by following 3 ways. First, gaseous HT or T{sub 2} easily penetrates into porous concrete. Its diffusivity is almost equal to that of H{sub 2}. When a gaseous molecule diffuses through pores with a smaller diameter than a mean free path, its migration rate is described by the Knudsen diffusion formula. The second mechanism is H{sub 2}O vapor diffusion in pores. Concrete holds a lot of structural water. Therefore, H{sub 2}O or HTO vapor can diffuse inside concrete pores along with adsorption-desorption and isotopic exchange with structural water, which is the third mechanism. Literature shows that the diffusivity of HTO through the epoxy-resin paint is determined as D(HTO)=1.0*10{sup -16} m{sup 2}/s. We have used this data to set a model and we have applied it to estimate residual tritium in laboratory walls. We have considered 2 accidental cases and a normal case: first, ADS starts operating 1 hour after 100 Ci HTO is released in the room, secondly, ADS starts 24 hours after 100 Ci HTO release and thirdly, when the walls are exposed to HTO for 10 years of normal operation. It appears that the immediate start up of ADS is indispensable for safety.
The effect of porosity on energetic porous silicon solid propellant micro-propulsion
International Nuclear Information System (INIS)
Churaman, Wayne A; Morris, Christopher J; Ramachandran, Raghav; Bergbreiter, Sarah
2015-01-01
Energetic porous silicon is investigated as an actuator for micro-propulsion based on thrust and impulse measurements for a variety of porous silicon porosity conditions. Porosity of 2 mm diameter, porous silicon microthruster devices was varied by changing the concentration of hydrofluoric acid and ethanol in an etch solution, by changing porous silicon etch depth, and by changing the resistivity of silicon wafers used for the etch process. The porosity varied from 30% to 75% for these experiments. The highest mean thrust and impulse values measured with a calibrated Kistler 9215 force sensor were 674 mN and 271 μN s, respectively, with a 73% porosity, 2 mm diameter porous silicon device etched in a 3 : 1 etch solution on a 3.6 Ω cm wafer to a target etch depth of 30 μm. As a result of changing porosity, a 23× increase in thrust performance and a 36× increase in impulse performance was demonstrated. Impulse values were also validated using a pendulum experiment in which the porous silicon microthruster was unconstrained, but several non-linearities in the pendulum experimental setup resulted in less consistent data than when measured by the force sensor for microthrusters at this size scale. These thrust and impulse results complement previous work in determining the effect of porosity on other porous silicon reaction metrics such as flame speed. (paper)
Nield, Donald A
1992-01-01
This book provides a user-friendly introduction to the topic of convection in porous media The authors as- sume that the reader is familiar with the basic elements of fluid mechanics and heat transfer, but otherwise the book is self-contained The book will be useful both as a review (for reference) and as a tutorial work, suitable as a textbook in a graduate course or seminar The book brings into perspective the voluminous research that has been performed during the last two decades The field has recently exploded because of worldwide concern with issues such as energy self-sufficiency and pollution of the environment Areas of application include the insulation of buildings and equipment, energy storage and recovery, geothermal reservoirs, nuclear waste disposal, chemical reactor engineering, and the storage of heat-generating materials such as grain and coal Geophysical applications range from the flow of groundwater around hot intrusions to the stability of snow against avalanches
Optimized manufacturable porous materials
DEFF Research Database (Denmark)
Andreassen, Erik; Andreasen, Casper Schousboe; Jensen, Jakob Søndergaard
Topology optimization has been used to design two-dimensional material structures with specific elastic properties, but optimized designs of three-dimensional material structures are more scarsely seen. Partly because it requires more computational power, and partly because it is a major challenge...... to include manufacturing constraints in the optimization. This work focuses on incorporating the manufacturability into the optimization procedure, allowing the resulting material structure to be manufactured directly using rapid manufacturing techniques, such as selective laser melting/sintering (SLM....../S). The available manufacturing methods are best suited for porous materials (one constituent and void), but the optimization procedure can easily include more constituents. The elasticity tensor is found from one unit cell using the homogenization method together with a standard finite element (FE) discretization...
DEFF Research Database (Denmark)
Yuan, Hao; Shapiro, Alexander
There is a considerable and ongoing effort aimed at understanding the transport and the deposition of suspended particles in porous media, especially non-Fickian transport and non-exponential deposition of particles. In this work, the influential parameters in filtration models are studied...... to understand their effects on the non-Fickian transport and the non-exponential deposition. The filtration models are validated by the comparisons between the modelling results and the experimental data.The elliptic equation with distributed filtration coefficients may be applied to model non-Fickian transport...... and hyperexponential deposition. The filtration model accounting for the migration of surface associated particles may be applied for non-monotonic deposition....
Biogenic Cracks in Porous Rock
Hemmerle, A.; Hartung, J.; Hallatschek, O.; Goehring, L.; Herminghaus, S.
2014-12-01
Microorganisms growing on and inside porous rock may fracture it by various processes. Some of the mechanisms of biofouling and bioweathering are today identified and partially understood but most emphasis is on chemical weathering, while mechanical contributions have been neglected. However, as demonstrated by the perseverance of a seed germinating and cracking up a concrete block, the turgor pressure of living organisms can be very significant. Here, we present results of a systematic study of the effects of the mechanical forces of growing microbial populations on the weathering of porous media. We designed a model porous medium made of glass beads held together by polydimethylsiloxane (PDMS), a curable polymer. The rheological properties of the porous medium, whose shape and size are tunable, can be controlled by the ratio of crosslinker to base used in the PDMS (see Fig. 1). Glass and PDMS being inert to most chemicals, we are able to focus on the mechanical processes of biodeterioration, excluding any chemical weathering. Inspired by recent measurements of the high pressure (~0.5 Mpa) exerted by a growing population of yeasts trapped in a microfluidic device, we show that yeast cells can be cultured homogeneously within porous medium until saturation of the porous space. We investigate then the effects of such an inner pressure on the mechanical properties of the sample. Using the same model system, we study also the complex interplay between biofilms and porous media. We focus in particular on the effects of pore size on the penetration of the biofilm within the porous sample, and on the resulting deformations of the matrix, opening new perspectives into the understanding of life in complex geometry. Figure 1. Left : cell culture growing in a model porous medium. The white spheres represent the grains, bonds are displayed in grey, and microbes in green. Right: microscopy picture of glass beads linked by PDMS bridges, scale bar: 100 μm.
Luminescence of porous silicon doped by erbium
International Nuclear Information System (INIS)
Bondarenko, V.P.; Vorozov, N.N.; Dolgij, L.N.; Dorofeev, A.M.; Kazyuchits, N.M.; Leshok, A.A.; Troyanova, G.N.
1996-01-01
The possibility of the 1.54 μm intensive luminescence in the silicon dense porous layers, doped by erbium, with various structures is shown. Low-porous materials of both porous type on the p-type silicon and porous silicon with wood-like structure on the n + type silicon may be used for formation of light-emitting structures
Directory of Open Access Journals (Sweden)
S.M. Arifuzzaman
2018-04-01
Full Text Available This paper concerns with the modelling of an unsteady natural convective and higher order chemically reactive magnetohydrodynamics (MHD fluid flow with the effect of heat and radiation absorption. The flow is generated through a vertical oscillating porous plate. Boundary layer approximations is carried out to establish a flow model which represents the time dependent momentum, energy and diffusion balance equations. Before being solved numerically, the governing partial differential equations (PDEs were transformed into a set of nonlinear ordinary differential equation (ODEs by using non-similar technique. A very efficient numerical approach solves the obtained nonlinear coupled ODEs so called Explicit Finite Difference Method (EFDM. An algorithm is implemented in Compaq Visual Fortran 6.6a as a solving tool. In addition, the stability and convergence analysis (SCA is examined and shown explicitly. The advantages of SCA is its optimizes the accuracy of system parameters such as Prandtl number (Pr and Schmidt number (Sc.The velocity, temperature and concentration fields in the boundary layer region are studied in detail and the outcomes are shown in graphically with the influence of various pertinent parameters such as Grashof number (Gr, modified Grashof number (Gr, magnetic parameter (M, Darcy number (Da,Prandtl number (Pr, Schmidt number (Sc, radiation (R, heat sink (Q,radiation absorption (Q1, Eckert number (Ec, Dufour number (Du,Soret number (Sr, Schmidt number (Sc, reaction index (P and chemical reaction (Kr. Furthermore, the effect of skin friction coefficient (Cf, Nusselt number (Nu and Sherwood number (Sh are also examined graphically. Keywords: MHD, Oscillating porous plate, Radiation absorption, High order chemical reaction, EFDM
On full-tensor permeabilities of porous media from numerical solutions of the Navier-Stokes equation
Wang, Y.; Sun, S.; Yu, B.
2013-01-01
A numerical method is proposed to compute full-tensor permeability of porous media without artificial simplification. Navier-Stokes (N-S) equation and Darcy's law are combined to design these numerical experiments. This method can successfully detect the permeability values in principle directions of the porous media and the anisotropic degrees. It is found that the same configuration of porous media may possess isotropic features at lower Reynolds numbers while manifesting anisotropic features at higher Reynolds numbers due to the nonlinearity from convection. Anisotropy becomes pronounced especially when convection is dominant. 2013 Yi Wang et al.
On full-tensor permeabilities of porous media from numerical solutions of the Navier-Stokes equation
Wang, Y.
2013-01-01
A numerical method is proposed to compute full-tensor permeability of porous media without artificial simplification. Navier-Stokes (N-S) equation and Darcy\\'s law are combined to design these numerical experiments. This method can successfully detect the permeability values in principle directions of the porous media and the anisotropic degrees. It is found that the same configuration of porous media may possess isotropic features at lower Reynolds numbers while manifesting anisotropic features at higher Reynolds numbers due to the nonlinearity from convection. Anisotropy becomes pronounced especially when convection is dominant. 2013 Yi Wang et al.
Nonlinear analysis on power reactor dynamics
International Nuclear Information System (INIS)
Konno, H.; Hayashi, K.
1997-01-01
We have shown that the origin of intermittent oscillation observed in a BWR can be ascribed to the couplings among the spatial modes starting from a non-linear center manifold equation with a delay-time and a spatial diffusion. We can reduce the problem to the stochastic coupled van der Pol oscillators with non-linear coupling term. This non-linear coupling term plays an important role to break the symmetry of the system and the non-linear damping of the system. The phenomenological generalization of van der Pol oscillator coupled by the linear diffusion term is not appropriate for describing the nuclear power reactors. However, one must start from the coupled partial differential equations by taking into account the two energy group neutrons, the thermo-hydraulic equations including two-phase flow. In this case, the diffusion constant must be a complex number as is demonstrated in a previous paper. The results will be reported in the near future. (J.P.N.)
International Nuclear Information System (INIS)
Anderson, R.C.
1976-01-01
A method is described for joining beryllium to beryllium by diffusion bonding. At least one surface portion of at least two beryllium pieces is coated with nickel. A coated surface portion is positioned in a contiguous relationship with another surface portion and subjected to an environment having an atmosphere at a pressure lower than ambient pressure. A force is applied on the beryllium pieces for causing the contiguous surface portions to abut against each other. The contiguous surface portions are heated to a maximum temperature less than the melting temperature of the beryllium, and the applied force is decreased while increasing the temperature after attaining a temperature substantially above room temperature. A portion of the applied force is maintained at a temperature corresponding to about maximum temperature for a duration sufficient to effect the diffusion bond between the contiguous surface portions
A multigrid Newton-Krylov method for flux-limited radiation diffusion
International Nuclear Information System (INIS)
Rider, W.J.; Knoll, D.A.; Olson, G.L.
1998-01-01
The authors focus on the integration of radiation diffusion including flux-limited diffusion coefficients. The nonlinear integration is accomplished with a Newton-Krylov method preconditioned with a multigrid Picard linearization of the governing equations. They investigate the efficiency of the linear and nonlinear iterative techniques
Pore size distribution effect on rarefied gas transport in porous media
Hori, Takuma; Yoshimoto, Yuta; Takagi, Shu; Kinefuchi, Ikuya
2017-11-01
Gas transport phenomena in porous media are known to strongly influence the performance of devices such as gas separation membranes and fuel cells. Knudsen diffusion is a dominant flow regime in these devices since they have nanoscale pores. Many experiments have shown that these porous media have complex structures and pore size distributions; thus, the diffusion coefficient in these media cannot be easily assessed. Previous studies have reported that the characteristic pore diameter of porous media can be defined in light of the pore size distribution; however, tortuosity factor, which is necessary for the evaluation of diffusion coefficient, is still unknown without gas transport measurements or simulations. Thus, the relation between pore size distributions and tortuosity factors is required to obtain the gas transport properties. We perform numerical simulations to prove the relation between them. Porous media are numerically constructed while satisfying given pore size distributions. Then, the mean-square displacement simulation is performed to obtain the tortuosity factors of the constructed porous media.. This paper is based on results obtained from a project commissioned by the New Energy and Industrial Development Organization (NEDO).
Unveiling the Formation Pathway of Single Crystalline Porous Silicon Nanowires
Zhong, Xing; Qu, Yongquan; Lin, Yung-Chen; Liao, Lei; Duan, Xiangfeng
2011-01-01
Porous silicon nanowire is emerging as an interesting material system due to its unique combination of structural, chemical, electronic, and optical properties. To fully understand their formation mechanism is of great importance for controlling the fundamental physical properties and enabling potential applications. Here we present a systematic study to elucidate the mechanism responsible for the formation of porous silicon nanowires in a two-step silver-assisted electroless chemical etching method. It is shown that silicon nanowire arrays with various porosities can be prepared by varying multiple experimental parameters such as the resistivity of the starting silicon wafer, the concentration of oxidant (H2O2) and the amount of silver catalyst. Our study shows a consistent trend that the porosity increases with the increasing wafer conductivity (dopant concentration) and oxidant (H2O2) concentration. We further demonstrate that silver ions, formed by the oxidation of silver, can diffuse upwards and re-nucleate on the sidewalls of nanowires to initiate new etching pathways to produce porous structure. The elucidation of this fundamental formation mechanism opens a rational pathway to the production of wafer-scale single crystalline porous silicon nanowires with tunable surface areas ranging from 370 m2·g−1 to 30 m2·g−1, and can enable exciting opportunities in catalysis, energy harvesting, conversion, storage, as well as biomedical imaging and therapy. PMID:21244020
Hydrodynamic dispersion within porous biofilms
Davit, Y.; Byrne, H.; Osborne, J.; Pitt-Francis, J.; Gavaghan, D.; Quintard, M.
2013-01-01
Many microorganisms live within surface-associated consortia, termed biofilms, that can form intricate porous structures interspersed with a network of fluid channels. In such systems, transport phenomena, including flow and advection, regulate
Vibrational modes of porous silicon
International Nuclear Information System (INIS)
Sabra, M.; Naddaf, M.
2012-01-01
On the basis of theoretical and experimental investigations, the origin of room temperature photoluminescence (PL) from porous silicon is found to related to chemical complexes constituted the surface, in particular, SiHx, SiOx and SiOH groups. Ab initio atomic and molecular electronic structure calculations on select siloxane compounds were used for imitation of infrared (IR) spectra of porous silicon. These are compared to the IR spectra of porous silicon recorded by using Fourier Transform Infrared Spectroscopy (FTIR). In contrast to linear siloxane, the suggested circular siloxane terminated with linear siloxane structure is found to well-imitate the experimental spectra. These results are augmented with EDX (energy dispersive x-ray spectroscopy) measurements, which showed that the increase of SiOx content in porous silicon due to rapid oxidation process results in considerable decrease in PL peak intensity and a blue shift in the peak position. (author)
Transport phenomena in porous media
Ingham, Derek B
1998-01-01
Research into thermal convection in porous media has substantially increased during recent years due to its numerous practical applications. These problems have attracted the attention of industrialists, engineers and scientists from many very diversified disciplines, such as applied mathematics, chemical, civil, environmental, mechanical and nuclear engineering, geothermal physics and food science. Thus, there is a wealth of information now available on convective processes in porous media and it is therefore appropriate and timely to undertake a new critical evaluation of this contemporary information. Transport Phenomena in Porous Media contains 17 chapters and represents the collective work of 27 of the world's leading experts, from 12 countries, in heat transfer in porous media. The recent intensive research in this area has substantially raised the expectations for numerous new practical applications and this makes the book a most timely addition to the existing literature. It includes recent major deve...
Porous substrates filled with nanomaterials
Worsley, Marcus A.; Baumann, Theodore F.; Satcher, Jr., Joe H.; Stadermann, Michael
2018-04-03
A composition comprising: at least one porous carbon monolith, such as a carbon aerogel, comprising internal pores, and at least one nanomaterial, such as carbon nanotubes, disposed uniformly throughout the internal pores. The nanomaterial can be disposed in the middle of the monolith. In addition, a method for making a monolithic solid with both high surface area and good bulk electrical conductivity is provided. A porous substrate having a thickness of 100 microns or more and comprising macropores throughout its thickness is prepared. At least one catalyst is deposited inside the porous substrate. Subsequently, chemical vapor deposition is used to uniformly deposit a nanomaterial in the macropores throughout the thickness of the porous substrate. Applications include electrical energy storage, such as batteries and capacitors, and hydrogen storage.
Design of Capillary Flows with Spatially Graded Porous Films
Joung, Young Soo; Figliuzzi, Bruno Michel; Buie, Cullen
2013-11-01
We have developed a new capillary tube model, consisting of multi-layered capillary tubes oriented in the direction of flow, to predict capillary speeds on spatially graded porous films. Capillary flows through thin porous media have been widely utilized for small size liquid transport systems. However, for most media it is challenging to realize arbitrary shapes and spatially functionalized micro-structures with variable flow properties. Therefore, conventional media can only be used for capillary flows obeying Washburn's equation and the modifications thereof. Given this background, we recently developed a method called breakdown anodization (BDA) to produce highly wetting porous films. The resulting surfaces show nearly zero contact angles and fast water spreading speed. Furthermore, capillary pressure and spreading diffusivity can be expressed as functions of capillary height when customized electric fields are used in BDA. From the capillary tube model, we derived a general capillary flow equation of motion in terms of capillary pressure and spreading diffusivity. The theoretical model shows good agreement with experimental capillary flows. The study will provide novel design methodologies for paper-based microfluidic devices.
Chemical vapor deposition of yttria stabilized zirconia in porous substrates
International Nuclear Information System (INIS)
Carolan, M.F.; Michaels, J.N.
1987-01-01
Electrochemical vapor deposition (EVD) of yttria stabilized zirconia (YSZ) is the preferred route to the production of thin films of YSZ on porous substrates. This process has been used in the construction of both fuel cells and steam electrolyzers. A critical aspect of the EVD process is an initial chemical vapor deposition phase in which the pores of a porous substrate are plugged by YSZ. In this process, water vapor and a mixture of gaseous zirconium chloride and yttrium chloride diffuse into the porous substrate from opposite sides and react to form YSZ and HCl ga. During the second stage of the process a continuous dense film of electrolyte is formed by a tarnishing-type process. Experimentally it is observed that the pores plug within a few pore diameters of the metal chloride face of the substrate. A kinetic rate expression that is first order in metal chloride but zero order in water is best able to explain this phenomenon. With this rate expression, the pores always plug near the metal chloride face. The model predicts less pore narrowing to occur as the ratio of the reaction rate to the diffusion rate of the metal chloride is increased. A kinetic rate expression that is first order in both water and metal chloride predicts that the pores plug much deeper in the substrate
Symmetry properties of fractional diffusion equations
Energy Technology Data Exchange (ETDEWEB)
Gazizov, R K; Kasatkin, A A; Lukashchuk, S Yu [Ufa State Aviation Technical University, Karl Marx strausse 12, Ufa (Russian Federation)], E-mail: gazizov@mail.rb.ru, E-mail: alexei_kasatkin@mail.ru, E-mail: lsu@mail.rb.ru
2009-10-15
In this paper, nonlinear anomalous diffusion equations with time fractional derivatives (Riemann-Liouville and Caputo) of the order of 0-2 are considered. Lie point symmetries of these equations are investigated and compared. Examples of using the obtained symmetries for constructing exact solutions of the equations under consideration are presented.
Inertial Effects on Flow and Transport in Heterogeneous Porous Media.
Nissan, Alon; Berkowitz, Brian
2018-02-02
We investigate the effects of high fluid velocities on flow and tracer transport in heterogeneous porous media. We simulate fluid flow and advective transport through two-dimensional pore-scale matrices with varying structural complexity. As the Reynolds number increases, the flow regime transitions from linear to nonlinear; this behavior is controlled by the medium structure, where higher complexity amplifies inertial effects. The result is, nonintuitively, increased homogenization of the flow field, which leads in the context of conservative chemical transport to less anomalous behavior. We quantify the transport patterns via a continuous time random walk, using the spatial distribution of the kinetic energy within the fluid as a characteristic measure.
Control of optical transport parameters of 'porous medium – supercritical fluid' systems
Energy Technology Data Exchange (ETDEWEB)
Zimnyakov, D A; Ushakova, O V; Yuvchenko, S A [Yuri Gagarin State Technical University of Saratov, Saratov (Russian Federation); Bagratashvili, V N [M. V. Lomonosov Moscow State University, Moscow (Russian Federation)
2015-11-30
The possibility of controlling optical transport parameters (in particular, transport scattering coefficient) of porous systems based on polymer fibres, saturated with carbon dioxide in different phase states (gaseous, liquid and supercritical) has been experimentally studied. An increase in the pressure of the saturating medium leads to a rise of its refractive index and, correspondingly, the diffuse-transmission coefficient of the system due to the decrease in the transport scattering coefficient. It is shown that, in the case of subcritical saturating carbon dioxide, the small-angle diffuse transmission of probed porous layers at pressures close to the saturated vapour pressure is determined by the effect of capillary condensation in pores. The immersion effect in 'porous medium – supercritical fluid' systems, where the fluid pressure is used as a control parameter, is considered. The results of reconstructing the values of transport scattering coefficient of probed layers for different refractive indices of a saturating fluid are presented. (radiation scattering)
Pressure-induced ferroelectric to antiferroelectric phase transformation in porous PZT95/5 ceramics
International Nuclear Information System (INIS)
Zeng, T.; Dong, X.L.; Chen, X.F.; Yao, C.H.; He, H.L.
2007-01-01
The hydrostatic pressure-induced ferroelectric to antiferroelectric (FE-AFE) phase transformation of PZT95/5 ceramics was investigated as a function of porosity, pore shape and pore size. FE-AFE phase transformations were more diffuse and occurred at lower hydrostatic pressures with increasing porosity. The porous PZT95/5 ceramics with spherical pores exhibited higher transformation pressures than those with irregular pores. Moreover, FE-AFE phase transformations of porous PZT95/5 ceramics with polydisperse irregular pores were more diffuse than those of porous PZT95/5 ceramics with monodisperse irregular pores. The relation between pore structure and hydrostatic pressure-induced FE-AFE transformation was established according to stress concentration theory. (copyright 2007 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
On Poisson Nonlinear Transformations
Directory of Open Access Journals (Sweden)
Nasir Ganikhodjaev
2014-01-01
Full Text Available We construct the family of Poisson nonlinear transformations defined on the countable sample space of nonnegative integers and investigate their trajectory behavior. We have proved that these nonlinear transformations are regular.
Existence and Uniqueness of Solutions to the Stochastic Porous Media Equations of Saturated Flows
International Nuclear Information System (INIS)
Ciotir, Ioana
2010-01-01
This paper proves the existence and uniqueness of nonnegative solutions for the stochastic porous media equations with multiplicative noise, infinite jump and discontinuous diffusivity function relevant in description of saturation processes in underground water infiltration in a bounded domain of R 3 .
Inverse solutions for a second-grade fluid for porous medium ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
to the free spiraling of electrons and ions about the magnetic lines of force before ... An understanding of the dynamics of fluids in porous media has practical ... viscous term in order to account for the vorticity diffusion caused by the boundary resis- ... The governing equations that describe the flow of a Newtonian fluid is the ...
Nonlinear multigrid solvers exploiting AMGe coarse spaces with approximation properties
DEFF Research Database (Denmark)
Christensen, Max la Cour; Vassilevski, Panayot S.; Villa, Umberto
2017-01-01
discretizations on general unstructured grids for a large class of nonlinear partial differential equations, including saddle point problems. The approximation properties of the coarse spaces ensure that our FAS approach for general unstructured meshes leads to optimal mesh-independent convergence rates similar...... to those achieved by geometric FAS on a nested hierarchy of refined meshes. In the numerical results, Newton’s method and Picard iterations with state-of-the-art inner linear solvers are compared to our FAS algorithm for the solution of a nonlinear saddle point problem arising from porous media flow...
Hereditary Diffuse Gastric Cancer
... Hereditary Diffuse Gastric Cancer Request Permissions Hereditary Diffuse Gastric Cancer Approved by the Cancer.Net Editorial Board , 10/2017 What is hereditary diffuse gastric cancer? Hereditary diffuse gastric cancer (HDGC) is a rare ...
Energy Technology Data Exchange (ETDEWEB)
Swisdak, M.; Drake, J. F. [Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD 20742 (United States); Opher, M., E-mail: swisdak@umd.edu, E-mail: drake@umd.edu, E-mail: mopher@bu.edu [Department of Astronomy, Boston University, 725 Commonwealth Avenue, Boston, MA 02215 (United States)
2013-09-01
The picture of the heliopause (HP)-the boundary between the domains of the Sun and the local interstellar medium (LISM)-as a pristine interface with a large rotation in the magnetic field fails to describe recent Voyager 1 (V1) data. Magnetohydrodynamic (MHD) simulations of the global heliosphere reveal that the rotation angle of the magnetic field across the HP at V1 is small. Particle-in-cell simulations, based on cuts through the MHD model at V1's location, suggest that the sectored region of the heliosheath (HS) produces large-scale magnetic islands that reconnect with the interstellar magnetic field while mixing LISM and HS plasma. Cuts across the simulation reveal multiple, anti-correlated jumps in the number densities of LISM and HS particles, similar to those observed, at the magnetic separatrices. A model is presented, based on both the observations and simulations, of the HP as a porous, multi-layered structure threaded by magnetic fields. This model further suggests that contrary to the conclusions of recent papers, V1 has already crossed the HP.
Molecular dynamics in porous media studied by nuclear magnetic resonance techniques
International Nuclear Information System (INIS)
Mattea, C.
2006-01-01
Field cycling NMR relaxometry was used to study dynamics of fluids under confinement in different scenarios: fluids flowing through porous media, fluids partially filling porous media and polymer melts in nanoscopic pores. Diffusion in partially filled porous media was also studied with the aid of an NMR diffusometry technique. It is shown that hydrodynamic flow influences the spin-lattice relaxation rate of water confined in mesoscopic porous media under certain conditions. The effect is predicted by an analytical theory and Monte Carlo simulations, and confirmed experimentally by field-cycling NMR relaxometry. Field-cycling NMR relaxometry has been applied to polar and non polar adsorbates in partially filled silica porous glasses. The dependence of the spin-lattice relaxation rate on the filling degree shows that limits for slow and fast exchange between different phases can be distinguished and identified depending on the pore size and polarity of the solvents. Diffusion in the same unsaturated systems was studied with the aid of NMR diffusometry technique. The effective diffusion coefficient of solvents with different polarities displays opposite tendencies as a function of the liquid content. A two-phase fast exchange model including Knudsen and ordinary diffusion and different effective tortuosities is presented accounting for these phenomena. In the case of polymer melts confined in narrow artificial tubes of a porous solid matrix with variable diameter (9 to 57 nm), the characteristics of reptation were experimentally verified using proton field cycling NMR relaxometry technique. This observation is independent of the molecular mass and pore size. In bulk, the same polymer melts show either Rouse or renormalized Rouse dynamics, depending on the molecular mass. The polymers under confinement show features specific for reptation even with a pore diameter 15 times larger than the Flory radius while bulk melts of the same polymers do not. (orig.)
Large-time behavior of solutions to a reaction-diffusion system with distributed microstructure
Muntean, A.
2009-01-01
Abstract We study the large-time behavior of a class of reaction-diffusion systems with constant distributed microstructure arising when modeling diffusion and reaction in structured porous media. The main result of this Note is the following: As t ¿ 8 the macroscopic concentration vanishes, while