Chaotic dynamics of large-scale double-diffusive convection in a porous medium

Science.gov (United States)

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.

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

A diffusivity model for predicting VOC diffusion in porous building materials based on fractal theory

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.

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)

Nonlinear hydromagnetic Rayleigh-Taylor instability for strong viscous fluids in porous media

CERN Document Server

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...

Analysis of Cattaneo-Christov heat and mass fluxes in the squeezed flow embedded in porous medium with variable mass diffusivity

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

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.

CROSS DIFFUSION AND NONLINEAR DIFFUSION PREVENTING BLOW UP IN THE KELLER–SEGEL MODEL

KAUST Repository

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.

Diffusion Driven Combustion Waves in Porous Media

Science.gov (United States)

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

Nonlinear diffusion equations

CERN Document Server

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

A diffusivity model for predicting VOC diffusion in porous building materials based on fractal theory.

Science.gov (United States)

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.

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)

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

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 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

CROSS DIFFUSION AND NONLINEAR DIFFUSION PREVENTING BLOW UP IN THE KELLER–SEGEL MODEL

KAUST Repository

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

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.

Nonlinear Cross-Diffusion with Size Exclusion

KAUST Repository

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

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 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.)

Evans functions and bifurcations of nonlinear waves of some nonlinear reaction diffusion equations

Science.gov (United States)

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.

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.

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

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

Global-local nonlinear model reduction for flows in heterogeneous porous media

KAUST Repository

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

KAUST Repository

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.

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)

On Diffusion and Permeation

KAUST Repository

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

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.

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

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

Error estimates for the finite volume discretization for the porous medium equation

NARCIS (Netherlands)

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

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)

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

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.

Ionic Diffusion and Kinetic Homogeneous Chemical Reactions in the Pore Solution of Porous Materials with Moisture Transport

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...

Pattern formation due to non-linear vortex diffusion

Science.gov (United States)

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.

Impact of local diffusion on macroscopic dispersion in three-dimensional porous media

Science.gov (United States)

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.

Retention and effective diffusion of model metabolites on porous graphitic carbon.

Science.gov (United States)

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.

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

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....

Numerical analyses on the effect of capillary condensation on gas diffusivities in porous media

Science.gov (United States)

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.

A numerical study of one-dimensional replicating patterns in reaction-diffusion systems with non-linear diffusion coefficients

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

A mixed-order nonlinear diffusion compressed sensing MR image reconstruction.

Science.gov (United States)

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.

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)

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)

Large time behaviour of oscillatory nonlinear solute transport in porous media

NARCIS (Netherlands)

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,

Non-destructive testing method for determining the solvent diffusion coefficient in the porous materials products

Science.gov (United States)

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.

Green functions and Langevin equations for nonlinear diffusion equations: A comment on ‘Markov processes, Hurst exponents, and nonlinear diffusion equations’ by Bassler et al.

Science.gov (United States)

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.

Anomalous water absorption in porous materials

CERN Document Server

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...

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.

Nonlinear Cross-Diffusion with Size Exclusion

KAUST Repository

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.

Self-diffusion of charged colloidal tracer spheres in transparent porous glass media: Effect of ionic strength and pore size

Science.gov (United States)

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.

Analytical and numerical investigation of double diffusion in thermally anisotropy multilayer porous medium

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.)

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

Estimation of Knudsen diffusion coefficients from tracer experiments conducted with a binary gas system and a porous medium

Science.gov (United States)

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

Super Nonlinear Electrodeposition-Diffusion-Controlled Thin-Film Selector.

Science.gov (United States)

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.

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).

Speciation of copper diffused in a bi-porous molecular sieve

Science.gov (United States)

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).

Nonlinear interaction and wave breaking with a submerged porous structure

Science.gov (United States)

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.

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.

Practical estimate of gradient nonlinearity for implementation of apparent diffusion coefficient bias correction.

Science.gov (United States)

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.

A coupled deformation-diffusion theory for fluid-saturated porous solids

Science.gov (United States)

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.

On Diffusion and Permeation

KAUST Repository

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.

Nonlinear reaction-diffusion systems conditional symmetry, exact solutions and their applications in biology

CERN Document Server

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,...

Moving water well: comparing hydraulic efficiency in twigs and trunks of coniferous, ring-porous, and diffuse-porous saplings from temperate and tropical forests

Science.gov (United States)

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...

A Nonlinear Diffusion Equation-Based Model for Ultrasound Speckle Noise Removal

Science.gov (United States)

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.

Nonlinear radiative peristaltic flow of hydromagnetic fluid through porous medium

Science.gov (United States)

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.

Non-linear frequency response of non-isothermal adsorption controlled by micropore diffusion with variable diffusivity

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.

Analysis and correction of gradient nonlinearity bias in apparent diffusion coefficient measurements.

Science.gov (United States)

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.

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.

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.

Analytical solution to the diffusion, sorption and decay chain equation in a saturated porous medium between two reservoirs

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

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

Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations

Science.gov (United States)

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.

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)

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)

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.

Methodology for using prompt gamma activation analysis to measure the binary diffusion coefficient of a gas in a porous medium

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.

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.

Experimental investigation of the diffusion coefficients in porous media by application of X-ray computer tomography

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...

An analytical method for solving exact solutions of the nonlinear Bogoyavlenskii equation and the nonlinear diffusive predator–prey system

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.

A non-Linear transport model for determining shale rock characteristics

Science.gov (United States)

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

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 ...

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

Automated sample preparation station for studying self-diffusion in porous solids with NMR spectroscopy

Science.gov (United States)

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.

Rigorous Derivation of a Nonlinear Diffusion Equation as Fast-Reaction Limit of a Continuous Coagulation-Fragmentation Model with Diffusion

KAUST Repository

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.

Rigorous Derivation of a Nonlinear Diffusion Equation as Fast-Reaction Limit of a Continuous Coagulation-Fragmentation Model with Diffusion

KAUST Repository

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.

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.

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

An approximate method for nonlinear diffusion applied to enzyme inactivation during drying

NARCIS (Netherlands)

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

Bifurcation of positive solutions to scalar reaction-diffusion equations with nonlinear boundary condition

Science.gov (United States)

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.

Electrochemical Impedance Imaging via the Distribution of Diffusion Times

Science.gov (United States)

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.

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...

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

Nonlinear diffusion equations as asymptotic limits of Cahn-Hilliard systems on unbounded domains via Cauchy's criterion

Science.gov (United States)

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.

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)

Nonlinear reaction-diffusion equations with delay: some theorems, test problems, exact and numerical solutions

Science.gov (United States)

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.

Kinetic theory of nonlinear diffusion in a weakly disordered nonlinear Schrödinger chain in the regime of homogeneous chaos.

Science.gov (United States)

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.

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.

Chemotaxis-fluid coupled model for swimming bacteria with nonlinear diffusion: Global existence and asymptotic behavior

KAUST Repository

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.

Real-time nonlinear feedback control of pattern formation in (bio)chemical reaction-diffusion processes: a model study.

Science.gov (United States)

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.

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)

Immiscible three-dimensional fingering in porous media: A weakly nonlinear analysis

Science.gov (United States)

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.

Nonlinear Fokker-Planck Equations Fundamentals and Applications

CERN Document Server

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...

Operator Splitting Methods for Degenerate Convection-Diffusion Equations I: Convergence and Entropy Estimates

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)

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

Fast and Accurate Poisson Denoising With Trainable Nonlinear Diffusion.

Science.gov (United States)

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.

Solid phase characterization and gas transfers through unsaturated porous media: experimental study and modeling applied diffusion of hydrogen through cement-based materials

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)

Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

Science.gov (United States)

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.

Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

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.

Preparation of Zeolitic Imidazolate Framework-8 (ZIF-8) Membrane on Porous Polymeric Support via Contra-Diffusion Method

KAUST Repository

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

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

Active-Set Reduced-Space Methods with Nonlinear Elimination for Two-Phase Flow Problems in Porous Media

KAUST Repository

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.

Active-Set Reduced-Space Methods with Nonlinear Elimination for Two-Phase Flow Problems in Porous Media

KAUST Repository

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.

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.

Analytical Solutions of Ionic Diffusion and Heat Conduction in Multilayered Porous Media

Directory of Open Access Journals (Sweden)

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.

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

Using Directional Diffusion Coefficients for Nonlinear Diffusion Acceleration of the First Order SN Equations in Near-Void Regions

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

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)

Turing instability for a competitor-competitor-mutualist model with nonlinear cross-diffusion effects

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).

Computational solutions for non-isothermal, nonlinear magneto-convection in porous media with hall/ionslip currents and ohmic dissipation

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.

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

Science.gov (United States)

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.

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

Finite element and network electrical simulation of rotating magnetofluid flow in nonlinear porous media with inclined magnetic field and hall currents

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

Effect of the Wavy permeable Interface on Double Diffusive Natural Convection in a Partially Porous Cavity

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.

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

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

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)

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

MATHEMATICAL FRAMEWORK OF THE WELL PRODUCTIVITY INDEX FOR FAST FORCHHEIMER (NON-DARCY) FLOWS IN POROUS MEDIA

KAUST Repository

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.

Connecting the molecular scale to the continuum scale for diffusion processes in smectite-rich porous media.

Science.gov (United States)

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.

Diffusion of organic pollutants within a biofilm in porous media

Science.gov (United States)

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

Self-diffusion in periodic porous media: a comparison of numerical simulation and eigenvalue methods.

Science.gov (United States)

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.

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

Diffusion and reaction within porous packing media: a phenomenological model.

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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.

A nonlinear equation for ionic diffusion in a strong binary electrolyte

Science.gov (United States)

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

A Fully Discrete Galerkin Method for a Nonlinear Space-Fractional Diffusion Equation

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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.

A gravitational procedure to measure the diffusion coefficient of mater in porous materials : a case study on concrete

NARCIS (Netherlands)

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

Moderately nonlinear diffuse-charge dynamics under an ac voltage.

Science.gov (United States)

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

Science.gov (United States)

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.

A nonlinear Fokker-Planck equation approach for interacting systems: Anomalous diffusion and Tsallis statistics

Science.gov (United States)

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.

From conservative to reactive transport under diffusion-controlled conditions

Science.gov (United States)

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.

Applicability of a geometrical model coupled to computed tomography to characterize the transport properties of porous materials: comparison with through diffusion experiments

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

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

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.)

Diffuse charge and Faradaic reactions in porous electrodes

NARCIS (Netherlands)

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

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.

An artificial nonlinear diffusivity method for supersonic reacting flows with shocks

Science.gov (United States)

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.

Determination of the diffusivity, dispersion, skewness and kurtosis in heterogeneous porous flow. Part I: Analytical solutions with the extended method of moments.

Science.gov (United States)

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

The onset of double diffusive convection in a viscoelastic fluid-saturated porous layer with non-equilibrium model.

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.

Limiting diffusion current at rotating disk electrode with dense particle layer.

Science.gov (United States)

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.

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)

Influence of diffusion on extraction kinetics in porous bodies. The case of uranium oxides; Influence de la diffusion sur la cinetique d'extraction dans un corps poreux. Cas des oxydes de l'uranium

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

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

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)

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.

Fractional Diffusion Equations and Anomalous Diffusion

Science.gov (United States)

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.

Transient TAP approach to investigate adsorption and diffusion of small alkanes in porous sulfated zirconia

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.)

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.

2016 CIME Course on Nonlocal and Nonlinear Diffusions and Interactions : New Methods and Directions

CERN Document Server

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.

A fast random walk algorithm for computing diffusion-weighted NMR signals in multi-scale porous media: A feasibility study for a Menger sponge

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)

Nonlinearly preconditioned semismooth Newton methods for variational inequality solution of two-phase flow in porous media

KAUST Repository

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.

Nonlinearly preconditioned semismooth Newton methods for variational inequality solution of two-phase flow in porous media

KAUST Repository

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.

Porous media geometry and transports

CERN Document Server

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

Stochastic porous media equations

CERN Document Server

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.

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)

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.

Digital Manufacturing of Selective Porous Barriers in Microchannels Using Multi-Material Stereolithography

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.

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

Porous silicon gettering

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.

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.

Fractional and fractal dynamics approach to anomalous diffusion in porous media: application to landslide behavior

Science.gov (United States)

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

The nonlinear interaction of convection modes in a box of a saturated porous medium

Science.gov (United States)

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.

On the Theory of Solitons of Fluid Pressure and Solute Density in Geologic Porous Media, with Applications to Shale, Clay and Sandstone

Science.gov (United States)

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.

Pore-Network Modeling of Water and Vapor Transport in the Micro Porous Layer and Gas Diffusion Layer of a Polymer Electrolyte Fuel Cell

NARCIS (Netherlands)

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

Evaluation of co-immobilized lactobacillus delbrueckii with porous particles for lactic acid production

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.

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 ...

Nonlinear optical susceptibilities in the diffusion modified AlxGa1-xN/GaN single quantum well

Science.gov (United States)

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.

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.)

Lie and Q-Conditional Symmetries of Reaction-Diffusion-Convection Equations with Exponential Nonlinearities and Their Application for Finding Exact Solutions

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.

Nonlinear traveling waves in rotating Rayleigh-Bacute enard convection: Stability boundaries and phase diffusion

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

Surface sealing using self-assembled monolayers and its effect on metal diffusion in porous low-k dielectrics studied using monoenergetic positron beams

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.

Pore size distribution effect on rarefied gas transport in porous media

Science.gov (United States)

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).

On the viscous dissipation modeling of thermal fluid flow in a porous medium

KAUST Repository

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.

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)

Formation of universal and diffusion regions of non-linear spectra of relativistic electrons in spatially limited sources

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.)

Solutions to aggregation-diffusion equations with nonlinear mobility constructed via a deterministic particle approximation

OpenAIRE

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...

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

A HIGH ORDER SOLUTION OF THREE DIMENSIONAL TIME DEPENDENT NONLINEAR CONVECTIVE-DIFFUSIVE PROBLEM USING MODIFIED VARIATIONAL ITERATION METHOD

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.

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

Application of nonlinear nodal diffusion generalized perturbation theory to nuclear fuel reload optimization

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

Diffusion Under Geometrical Constraint

OpenAIRE

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 ...

Non-linear diffusion and pattern formation in vortex matter

Science.gov (United States)

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)

Identification of the population density of a species model with nonlocal diffusion and nonlinear reaction

Science.gov (United States)

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.

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

Image classification using multiscale information fusion based on saliency driven nonlinear diffusion filtering.

Science.gov (United States)

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.

Effect of capillary condensation on gas transport properties in porous media

Science.gov (United States)

Yoshimoto, Yuta; Hori, Takuma; Kinefuchi, Ikuya; Takagi, Shu

2017-10-01

We investigate the effect of capillary condensation on gas diffusivity in porous media composed of randomly packed spheres with moderate wettability. To simulate capillary phenomena at the pore scale while retaining complex pore networks of the porous media, we employ density functional theory (DFT) for coarse-grained lattice gas models. The lattice DFT simulations reveal that capillary condensations preferentially occur at confined pores surrounded by solid walls, leading to the occlusion of narrow pores. 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 the 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. Moreover, we find that the ratio of the porosity to the tortuosity factor, which is a crucial parameter that determines an effective diffusion coefficient, can be reasonably related to the porosity even for the partially wet porous media.

Radionuclide behavior in water saturated porous media: Diffusion and infiltration coupling of thermodynamically and kinetically controlled radionuclide water - mineral interactions

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)

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

Effects of chemical reaction in thermal and mass diffusion of micropolar fluid saturated in porous regime with radiation and ohmic heating

Directory of Open Access Journals (Sweden)

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.

Gaseous diffusion system

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

Throughflow and non-uniform heating effects on double diffusive oscillatory convection in a porous medium

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.

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.)

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

Numerical Calculations of the Effect of Moisture Content and Moisture Flow on Ionic Multi-Species Diffusion in the Pore Solution of Porous Materials

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....

Electrochemistry and capacitive charging of porous electrodes in asymmetric multicomponent electrolytes

NARCIS (Netherlands)

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

Gas transport in porous media

CERN Document Server

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.

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...

Global sensitivity analysis of multiscale properties of porous materials

Science.gov (United States)

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.

Fractional diffusion equations and anomalous diffusion

CERN Document Server

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.

Onset of Convection in the Presence of a Precipitation Reaction in a Porous Medium: A Comparison of Linear Stability and Numerical Approaches

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.

Determination of distribution function of refraction index and anion diffusion depth in porous alumina photonic crystals

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.

Coupling nonlinear Stokes and Darcy flow using mortar finite elements

KAUST Repository

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

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.

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.

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)

Simultaneous measurement of thermal conductivity, thermal diffusivity and prediction of effective thermal conductivity of porous consolidated igneous rocks at room temperature

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%

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

Direct method of solving finite difference nonlinear equations for multicomponent diffusion in a gas centrifuge

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)

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

Positron annihilation lifetime spectroscopy (PALS) application in metal barrier layer integrity for porous low- k materials

CERN Document Server

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...

Effects of ring-porous and diffuse-porous stem wood anatomy on the hydraulic parameters used in a water flow and storage model.

Science.gov (United States)

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.

Upscaling solute transport in naturally fractured porous media with the continuous time random walk method

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.

Robust and fast nonlinear optimization of diffusion MRI microstructure models.

Science.gov (United States)

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

Nonlinear Dynamics of a Diffusing Interface

Science.gov (United States)

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.

Hindered bacterial mobility in porous media flow enhances dispersion

Science.gov (United States)

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.

Experimental study and modeling of gas diffusion through partially water saturated porous media. Application to Vycor glasses, geo-polymers and CEM V cement pastes

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

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)

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.)

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.

Convergence to equilibrium of renormalised solutions to nonlinear chemical reaction–diffusion systems

Science.gov (United States)

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.

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

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

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

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.

Nonlinear dynamics of capacitive charging and desalination by porous electrodes

NARCIS (Netherlands)

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

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.

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.)

Transient, compressible heat and mass transfer in porous media using the strongly implicit iteration procedure.

Science.gov (United States)

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.

Characterization of thermal, optical and carrier transport properties of porous silicon using the photoacoustic technique

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

Numerical Analysis of the Reaction-diffusion Equation for Soluble Starch and Dextrin as Substrates of Immobilized Amyloglucosidase in a Porous Support by Using Least Square Method

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.

Mathematical modelling of nonlinear thermal radiation effects on EMHD peristaltic pumping of viscoelastic dusty fluid through a porous medium duct

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

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

Diffusion Influenced Adsorption Kinetics.

Science.gov (United States)

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.

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.

Design of Capillary Flows with Spatially Graded Porous Films

Science.gov (United States)

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.

Effective potentials in nonlinear polycrystals and quadrature formulae

Science.gov (United States)

Michel, Jean-Claude; Suquet, Pierre

2017-08-01

This study presents a family of estimates for effective potentials in nonlinear polycrystals. Noting that these potentials are given as averages, several quadrature formulae are investigated to express these integrals of nonlinear functions of local fields in terms of the moments of these fields. Two of these quadrature formulae reduce to known schemes, including a recent proposition (Ponte Castañeda 2015 Proc. R. Soc. A 471, 20150665 (doi:10.1098/rspa.2015.0665)) obtained by completely different means. Other formulae are also reviewed that make use of statistical information on the fields beyond their first and second moments. These quadrature formulae are applied to the estimation of effective potentials in polycrystals governed by two potentials, by means of a reduced-order model proposed by the authors (non-uniform transformation field analysis). It is shown how the quadrature formulae improve on the tangent second-order approximation in porous crystals at high stress triaxiality. It is found that, in order to retrieve a satisfactory accuracy for highly nonlinear porous crystals under high stress triaxiality, a quadrature formula of higher order is required.

Stability of Gradient Field Corrections for Quantitative Diffusion MRI

OpenAIRE

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...

Perturbed invariant subspaces and approximate generalized functional variable separation solution for nonlinear diffusion-convection equations with weak source

Science.gov (United States)

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.

Fem Simulation of Triple Diffusive Natural Convection Along Inclined Plate in Porous Medium: Prescribed Surface Heat, Solute and Nanoparticles Flux

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.

Micropore engineering of carbonized porous aromatic framework (PAF-1) for supercapacitors application.

Science.gov (United States)

Li, Yanqiang; Roy, Soumyajit; Ben, Teng; Xu, Shixian; Qiu, Shilun

2014-07-07

Micropore engineering of porous carbons on the effect of capacitance was explored using a carbonized porous aromatic framework (PAF-1). The porous carbons obtained through different carbonization methods show different pore structures enabling us to do this. The capacitance was measured both in aqueous electrolyte and different organic electrolytes. The porous carbons prepared by KOH activation show both high microporous volume, which is beneficial for charge storage, and mesoporous volume, which is devoted to fast ion diffusion in the pores; properties which are highly desirable. It shows a capacitance as high as 280 F g(-1) and 203 F g(-1) at a current density of 1 A g(-1) in 6.0 M KOH and 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (EMImTFSI), respectively. We also demonstrate the effect of diffusion and that of geometric packing of the electrolyte ions in the pores, where a commensurate match of the electrolyte ions with the pores of carbonized materials control and influence significantly the capacitance of these materials.

Correction of Gradient Nonlinearity Bias in Quantitative Diffusion Parameters of Renal Tissue with Intra Voxel Incoherent Motion.

Science.gov (United States)

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.

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....

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

Impact of porosity variation on diffusive transport: experimentation vs simulation

International Nuclear Information System (INIS)

Fatnassi, Ikram

2015-01-01

Reactions induced by the diffusion of reactants from different sources may alter rock confinement properties, and are therefore critical processes to assess short-term and long-term behaviour of rocks displaying a low permeability, such as argillites which are used as barriers in underground storage installation. In order to test transport-chemistry codes based on a continuous approach, the author of this research thesis reports the development and performance of simplest as possible experiments of sealing/dissolution diffusion, by using porous media of increasing complexity: compact sand, sintered glass, stoneware, chalk, until a material close to that envisaged within the frame of a storage like a Tournemire argillite. The principle of these experiments relies on the characterisation of the diffusive behaviour of an inert tracer within a porous medium submitted to dissolution reactions (attack of a carbonate matrix by an acid solution) and/or precipitation of mineral compounds (calcium oxalate, gypsum or barite) which results in an evolution of porosity and a modification of the diffusive transport of the studied tracer. At the end of the experiment, porous media and precipitates are characterised by SEM-EDS [fr

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

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 ...

Effect of static porosity fluctuations on reactive transport in a porous medium

Science.gov (United States)

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.

On the effective diffusivity of gases in PEM fuel cell electrodes

International Nuclear Information System (INIS)

Karan, K.; Pharoah, J.G.

2004-01-01

'Full text:' Gas diffusion layer of polymer electrolyte membrane fuel cells (PEMFCs) play a critically important and multiple role as reactant gas distributor, medium for electron and water transport. The most commonly used GDL material is either carbon cloth or carbon paper. Scanning electron microscopic analysis reveals that the GDL microstructure resembles the structure of randomly laid out fibres. Almost all publications on PEMFC models have treated diffusive transport of chemical species through the porous gas diffusion layer (GDL) using correlations originally derived for isotropic granular porous media. Unfortunately, the GDL microstructure does not resemble such a structure. This paper questions the validity of effective diffusivity models used in PEMFC literature and shows that the choice of diffusivity model has significant impact on the prediction of local species fluxes and composition, and consequently on local current densities. (author)

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.

The use of a diffuse interface model to estimate effective transport properties for two-phase flows in porous media

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

A thermal mixing model of crossflow in tube bundles for use with the porous body approximation

International Nuclear Information System (INIS)

Ashcroft, J.; Kaminski, D.A.

1996-06-01

Diffusive thermal mixing in a heated tube bundle with a cooling fluid in crossflow was analyzed numerically. From the results of detailed two-dimensional models, which calculated the diffusion of heat downstream of one heated tube in an otherwise adiabatic flow field, a diffusion model appropriate for use with the porous body method was developed. The model accounts for both molecular and turbulent diffusion of heat by determining the effective thermal conductivity in the porous region. The model was developed for triangular shaped staggered tube bundles with pitch to diameter ratios between 1.10 and 2.00 and for Reynolds numbers between 1,000 and 20,000. The tubes are treated as nonconducting. Air and water were considered as working fluids. The effective thermal conductivity was found to be linearly dependent on the tube Reynolds number and fluid Prandtl number, and dependent on the bundle geometry. The porous body thermal mixing model was then compared against numerical models for flows with multiple heated tubes with very good agreement

Two-demensional analysis of heat and mass transfer in porous media using the strongly implicit procedure

Science.gov (United States)

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.

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.)

An Iterative Implicit Scheme for Nanoparticles Transport with Two-Phase Flow in Porous Media

KAUST Repository

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.

Understanding generalized inversions of nuclear magnetic resonance transverse relaxation time in porous media

Science.gov (United States)

Mitchell, J.; Chandrasekera, T. C.

2014-12-01

The nuclear magnetic resonance transverse relaxation time T2, measured using the Carr-Purcell-Meiboom-Gill (CPMG) experiment, is a powerful method for obtaining unique information on liquids confined in porous media. Furthermore, T2 provides structural information on the porous material itself and has many applications in petrophysics, biophysics, and chemical engineering. Robust interpretation of T2 distributions demands appropriate processing of the measured data since T2 is influenced by diffusion through magnetic field inhomogeneities occurring at the pore scale, caused by the liquid/solid susceptibility contrast. Previously, we introduced a generic model for the diffusion exponent of the form -ant_e^k (where n is the number and te the temporal separation of spin echoes, and a is a composite diffusion parameter) in order to distinguish the influence of relaxation and diffusion in CPMG data. Here, we improve the analysis by introducing an automatic search for the optimum power k that best describes the diffusion behavior. This automated method is more efficient than the manual trial-and-error grid search adopted previously, and avoids variability through subjective judgments of experimentalists. Although our method does not avoid the inherent assumption that the diffusion exponent depends on a single k value, we show through simulation and experiment that it is robust in measurements of heterogeneous systems that violate this assumption. In this way, we obtain quantitative T2 distributions from complicated porous structures and demonstrate the analysis with examples of ceramics used for filtration and catalysis, and limestone of relevance to the construction and petroleum industries.

Radionuclide transport in fractured porous media -- Analytical solutions for a system of parallel fractures with a constant inlet flux

International Nuclear Information System (INIS)

Chen, C.T.; Li, S.H.

1997-01-01

Analytical solutions are developed for the problem of radionuclide transport in a system of parallel fractures situated in a porous rock matrix. A constant flux is used as the inlet boundary condition. The solutions consider the following processes: (a) advective transport along the fractures; (b) mechanical dispersion and molecular diffusion along the fractures; (c) molecular diffusion from a fracture to the porous matrix; (d) molecular diffusion within the porous matrix in the direction perpendicular to the fracture axis; (e) adsorption onto the fracture wall; (f) adsorption within the porous matrix, and (g) radioactive decay. The solutions are based on the Laplace transform method. The general transient solution is in the form of a double integral that is evaluated using composite Gauss-Legendre quadrature. A simpler transient solution that is in the form of a single integral is also presented for the case that assumes negligible longitudinal dispersion along the fractures. The steady-state solutions are also provided. A number of examples are given to illustrate the effects of various important parameters, including: (a) fracture spacing; (b) fracture dispersion coefficient; (c) matrix diffusion coefficient; (d) fracture width; (e) groundwater velocity; (f) matrix retardation factor; and (g) matrix porosity

Determination of the macroscopic chloride diffusivity in cementitious by porous materials coupling periodic homogenization of Nernst-Planck equation with experimental protocol

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.

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.

Scaling of chaos in strongly nonlinear lattices.

Science.gov (United States)

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.

Diffusion of Finite-Size Particles in Confined Geometries

KAUST Repository

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.

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)

Higher-order Solution of Stochastic Diffusion equation with Nonlinear Losses Using WHEP technique

KAUST Repository

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.

Higher-order Solution of Stochastic Diffusion equation with Nonlinear Losses Using WHEP technique

KAUST Repository

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.

Exact solutions of the Navier-Stokes equations generalized for flow in porous media

Science.gov (United States)

Daly, Edoardo; Basser, Hossein; Rudman, Murray

2018-05-01

Flow of Newtonian fluids in porous media is often modelled using a generalized version of the full non-linear Navier-Stokes equations that include additional terms describing the resistance to flow due to the porous matrix. Because this formulation is becoming increasingly popular in numerical models, exact solutions are required as a benchmark of numerical codes. The contribution of this study is to provide a number of non-trivial exact solutions of the generalized form of the Navier-Stokes equations for parallel flow in porous media. Steady-state solutions are derived in the case of flows in a medium with constant permeability along the main direction of flow and a constant cross-stream velocity in the case of both linear and non-linear drag. Solutions are also presented for cases in which the permeability changes in the direction normal to the main flow. An unsteady solution for a flow with velocity driven by a time-periodic pressure gradient is also derived. These solutions form a basis for validating computational models across a wide range of Reynolds and Darcy numbers.

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.

On full-tensor permeabilities of porous media from numerical solutions of the Navier-Stokes equation

KAUST Repository

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.

Error-diffusion binarization for joint transform correlators

Science.gov (United States)

Inbar, Hanni; Mendlovic, David; Marom, Emanuel

1993-02-01

A normalized nonlinearly scaled binary joint transform image correlator (JTC) based on a 1D error-diffusion binarization method has been studied. The behavior of the error-diffusion method is compared with hard-clipping, the most widely used method of binarized JTC approaches, using a single spatial light modulator. Computer simulations indicate that the error-diffusion method is advantageous for the production of a binarized power spectrum interference pattern in JTC configurations, leading to better definition of the correlation location. The error-diffusion binary JTC exhibits autocorrelation characteristics which are superior to those of the high-clipping binary JTC over the whole nonlinear scaling range of the Fourier-transform interference intensity for all noise levels considered.

The instability of nonlinear surface waves in an electrified liquid jet

International Nuclear Information System (INIS)

Moatimid, Galal M

2009-01-01

We investigate the weakly nonlinear stability of surface waves of a liquid jet. In this work, the liquids are uniformly streaming through two porous media and the gravitational effects are neglected. The system is acted upon by a uniform tangential electric field, that is parallel to the jet axis. The equations of motion are linearly treated and solved in the light of nonlinear boundary conditions. Therefore, the boundary-value problem leads to a nonlinear characteristic second-order differential equation. This characterized equation has a complex nature. The nonlinearity is kept up to the third degree. It is used to judge the behavior of the surface evolution. According to the linear stability theory, we derive the dispersion relation that accounts for the growth waves. The stability criterion is discussed analytically and a stability picture is identified for a chosen sample system. Several special cases are recovered upon appropriate data choices. In order to derive the Ginsburg-Landau equation for the general case, in the nonlinear approach, we used the method of multiple timescales with the aid of the Taylor expansion. This equation describes the competition between nonlinearity and the linear dispersion relation. As a special case for non-porous media where there is no streaming, we obtained the well-known nonlinear Schroedinger equation as it has been derived by others. The stability criteria are expressed theoretically in terms of various parameters of the problem. Stability diagrams are obtained for a set of physical parameters. We found new instability regions in the parameter space. These regions are due to the nonlinear effects.

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

Diffusion of Finite-Size Particles in Confined Geometries

KAUST Repository

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.

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

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

Separation of irradiance and reflectance from observed color images by logarithmical nonlinear diffusion process

Science.gov (United States)

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.

Hydrodynamic dispersion within porous biofilms

KAUST Repository

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.

Analytical and numerical models of transport in porous cementitious materials

International Nuclear Information System (INIS)

Garboczi, E.J.; Bentz, D.P.

1990-01-01

Most chemical and physical processes that degrade cementitious materials are dependent on an external source of either water or ions or both. Understanding the rates of these processes at the microstructural level is necessary in order to develop a sound scientific basis for the prediction and control of the service life of cement-based materials, especially for radioactive-waste containment materials that are required to have service lives on the order of hundreds of years. An important step in developing this knowledge is to understand how transport coefficients, such as diffusivity and permeability, depend on the pore structure. Fluid flow under applied pressure gradients and ionic diffusion under applied concentration gradients are important transport mechanisms that take place in the pore space of cementitious materials. This paper describes: (1) a new analytical percolation-theory-based equation for calculating the permeability of porous materials, (2) new computational methods for computing effective diffusivities of microstructural models or digitized images of actual porous materials, and (3) a new digitized-image mercury intrusion simulation technique

On the viscous dissipation modeling of thermal fluid flow in a porous medium

KAUST Repository

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

Fractal diffusion equations: Microscopic models with anomalous diffusion and its generalizations

International Nuclear Information System (INIS)

Arkhincheev, V.E.

2001-04-01

To describe the ''anomalous'' diffusion the generalized diffusion equations of fractal order are deduced from microscopic models with anomalous diffusion as Comb model and Levy flights. It is shown that two types of equations are possible: with fractional temporal and fractional spatial derivatives. The solutions of these equations are obtained and the physical sense of these fractional equations is discussed. The relation between diffusion and conductivity is studied and the well-known Einstein relation is generalized for the anomalous diffusion case. It is shown that for Levy flight diffusion the Ohm's law is not applied and the current depends on electric field in a nonlinear way due to the anomalous character of Levy flights. The results of numerical simulations, which confirmed this conclusion, are also presented. (author)

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 ...

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

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.

Modeling of heat transfer within porous multi-constituent materials

International Nuclear Information System (INIS)

Niezgoda, M.

2012-01-01

The CEA works a great deal with porous materials - carbon composites, ceramics - and aims to optimize their properties for specific uses. These materials can be composed of several constituents and generally has a complex structure with pore size of several tens of micrometers. It is used in large-scale systems that are bigger than its own characteristic scale in which they are considered as equivalent to a homogeneous medium for the simulation of its behavior in its using environment without taking into account its local morphology. We are especially interested in the effective thermal diffusivity of heterogeneous materials that we estimate as a function of temperature with the help of an inverse method by considering they are homogeneous. The identification of the diffusivity of porous and/or semi-transparent materials is made difficult because of the strong conducto-radiative coupling can quickly occur when the temperature increases. We have thus modeled the coupled conductive and radiative heat transfer as a function of the temperature within porous multi-constituent materials from their morphology discretized into a set of homogeneous voxels. We have developed a methodology that consists in starting from a 3D-microstructure of the studied materials obtained by tomography. The microstructures constitute the numerical support to this modeling that renders it possible, on the one hand, to simulate any kind of numerical thermal experiments, especially the flash method whose the results render it possible to estimate the thermal diffusivity, and on the other hand, to reproduce the thermal behavior of our materials in their using conditions. (author) [fr

Simulation results for a multirate mass transfer modell for immiscible displacement of two fluids in highly heterogeneous porous media

Science.gov (United States)

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

Efficiency in supercritical fluid chromatography with different superficially porous and fully porous particles ODS bonded phases.

Science.gov (United States)

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

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.

DISPL-1, 2. Order Nonlinear Partial Differential Equation System Solution for Kinetics Diffusion Problems

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

Size effects in non-linear heat conduction with flux-limited behaviors

Science.gov (United States)

Li, Shu-Nan; Cao, Bing-Yang

2017-11-01

Size effects are discussed for several non-linear heat conduction models with flux-limited behaviors, including the phonon hydrodynamic, Lagrange multiplier, hierarchy moment, nonlinear phonon hydrodynamic, tempered diffusion, thermon gas and generalized nonlinear models. For the phonon hydrodynamic, Lagrange multiplier and tempered diffusion models, heat flux will not exist in problems with sufficiently small scale. The existence of heat flux needs the sizes of heat conduction larger than their corresponding critical sizes, which are determined by the physical properties and boundary temperatures. The critical sizes can be regarded as the theoretical limits of the applicable ranges for these non-linear heat conduction models with flux-limited behaviors. For sufficiently small scale heat conduction, the phonon hydrodynamic and Lagrange multiplier models can also predict the theoretical possibility of violating the second law and multiplicity. Comparisons are also made between these non-Fourier models and non-linear Fourier heat conduction in the type of fast diffusion, which can also predict flux-limited behaviors.

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....

Measuring adsorption, diffusion and flow in chemical engineering: applications of magnetic resonance to porous media

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.

On full-tensor permeabilities of porous media from numerical solutions of the Navier-Stokes equation

KAUST Repository

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.

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

Interface conditions for fast-reaction fronts in wet porous mineral materials: the case of concrete carbonation

NARCIS (Netherlands)

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

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.

PIV study of flow through porous structure using refractive index matching

Science.gov (United States)

Häfeli, Richard; Altheimer, Marco; Butscher, Denis; Rudolf von Rohr, Philipp

2014-05-01

An aqueous solution of sodium iodide and zinc iodide is proposed as a fluid that matches the refractive index of a solid manufactured by rapid prototyping. This enabled optical measurements in single-phase flow through porous structures. Experiments were also done with an organic index-matching fluid (anisole) in porous structures of different dimensions. To compare experiments with different viscosities and dimensions, we employed Reynolds similarity to deduce the scaling laws. One of the target quantities of our investigation was the dissipation rate of turbulent kinetic energy. Different models for the dissipation rate estimation were evaluated by comparing isotropy ratios. As in many other studies also, our experiments were not capable of resolving the velocity field down to the Kolmogorov length scale, and therefore, the dissipation rate has to be considered as underestimated. This is visible in experiments of different relative resolutions. However, being near the Kolmogorov scale allows estimating a reproducible, yet underestimated spatial distribution of dissipation rate inside the porous structure. Based on these results, the model was used to estimate the turbulent diffusivity. Comparing it to the dispersion coefficient obtained in the same porous structure, we conclude that even at the turbulent diffusivity makes up only a small part of mass transfer in axial direction. The main part is therefore attributed to Taylor dispersion.

Numerical Analysis of a Class of THM Coupled Model for Porous Materials

Science.gov (United States)

Liu, Tangwei; Zhou, Jingying; Lu, Hongzhi

2018-01-01

We consider the coupled models of the Thermo-hydro-mechanical (THM) problem for porous materials which arises in many engineering applications. Firstly, mathematical models of the THM coupled problem for porous materials were discussed. Secondly, for different cases, some numerical difference schemes of coupled model were constructed, respectively. Finally, aassuming that the original water vapour effect is neglectable and that the volume fraction of liquid phase and the solid phase are constants, the nonlinear equations can be reduced to linear equations. The discrete equations corresponding to the linear equations were solved by the Arnodli method.

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.

Hydromagnetic Flow and Heat Transfer over a Porous Oscillating Stretching Surface in a Viscoelastic Fluid with Porous Medium.

Science.gov (United States)

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.

Linear and nonlinear susceptibilities from diffusion quantum Monte Carlo: application to periodic hydrogen chains.

Science.gov (United States)

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.

Self diffusion in tungsten

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.)

Characterization of thermal, hydraulic, and gas diffusion properties in variably saturated sand grades

DEFF Research Database (Denmark)

Deepagoda Thuduwe Kankanamge Kelum, Chamindu; Smits, Kathleen; Ramirez, Jamie

2016-01-01

porous media transport properties, key transport parameters such as thermal conductivity and gas diffusivity are particularly important to describe temperature-induced heat transport and diffusion-controlled gas transport processes, respectively. Despite many experimental and numerical studies focusing...... transport models (thermal conductivity, saturated hydraulic conductivity, and gas diffusivity). An existing thermal conductivity model was improved to describe the distinct three-region behavior in observed thermal conductivity–water saturation relations. Applying widely used parametric models for saturated......Detailed characterization of partially saturated porous media is important for understanding and predicting vadose zone transport processes. While basic properties (e.g., particle- and pore-size distributions and soil-water retention) are, in general, essential prerequisites for characterizing most...

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)

The rate of diffusion into advanced gas cooled reactor moderator bricks: an equivalent cylinder model

International Nuclear Information System (INIS)

Kyte, W.S.

1980-01-01

The graphite moderator bricks which make up the moderator of an advanced gas-cooled nuclear reactor (AGR) are of many different and complex shapes. Many physico-chemical processes that occur within these porous bricks include a diffusional step and thus to model these processes it is necessary to solve the diffusion equation (with chemical reaction) in a porous medium of complex shape. A finite element technique is applied to calculating the rate at which nitrogen diffuses into and out of the porous moderator graphite during operation of a shutdown procedure for an AGR. However, the finite element method suffers from several disadvantages that undermine its general usefulness for calculating rates of diffusion in AGR moderator cores. A model which overcomes some of these disadvantages is presented (the equivalent cylinder model) and it is shown that this gives good results for a variety of different boundary and initial conditions

Mechanics of adsorption-deformation coupling in porous media

Science.gov (United States)

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.

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)

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.

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...

Multiphase radon generation and transport in porous materials

International Nuclear Information System (INIS)

Rogers, V.C.; Nielson, K.K.

1991-01-01

Radon generation and transport in porous materials involve solid, liquid, and gas phases in the processes of emanation, diffusion, advection, absorption, and adsorption. Oversimplifications, such as representing moist soil systems by air-phase emanation and transport models, cause theoretical inconsistencies and biases in resulting calculations. Detailed Rn rate balance equations for solid, liquid, and gas phases were analyzed and combined using phase equilibrium constants to derive a single diffusive-advective rate balance equation in the traditional form. The emanation, diffusion, and permeability coefficients in the new equation have expanded definitions and interpretations to include Rn phase transfer. Radon adsorption was characterized by an exponential moisture dependence, and diffusion and permeability constants utilized previous moisture relationships. Correct boundary and interface conditions were defined, and the unified theoretical approach was applied to field data from a diffusion-dominated system and to laboratory data from an advection-dominated system. Measured 222 Rn fluxes and concentrations validated the modeled values within the measurement variability in both applications

Transport Phenomena in Porous Media Aspects of MicroMacro Behaviour

CERN Document Server

Ichikawa, Yasuaki

2012-01-01

This monograph presents an integrated perspective of the wide range of phenomena and processes applicable to the study of transport of species in porous materials. In order to formulate the entire range of porous media and their uses, this book gives the basics of continuum mechanics, thermodynamics, seepage and consolidation and diffusion, including multiscale homogenization methods. The particular structure of the book has been chosen because it is essential to be aware of the true properties of porous materials particularly in terms of nano, micro and macro mechanisms.  This book is of pedagogical and practical importance to the fields covered by civil, environmental, nuclear and petroleum engineering and also in chemical physics and geophysics as it relates to radioactive waste disposal, geotechnical engineering, mining and petroleum engineering and chemical engineering.

Study of diffusion of wave packets in a square lattice under external fields along the discrete nonlinear Schrödinger equation

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.

Diffusion, Coulombic interactions and multicomponent ionic transport of charged species in saturated porous media

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...

Porous Core-Shell Nanostructures for Catalytic Applications

Science.gov (United States)

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.

Analysis of discrete reaction-diffusion equations for autocatalysis and continuum diffusion equations for transport

Energy Technology Data Exchange (ETDEWEB)

Wang, Chi-Jen [Iowa State Univ., Ames, IA (United States)

2013-01-01

In this thesis, we analyze both the spatiotemporal behavior of: (A) non-linear “reaction” models utilizing (discrete) reaction-diffusion equations; and (B) spatial transport problems on surfaces and in nanopores utilizing the relevant (continuum) diffusion or Fokker-Planck equations. Thus, there are some common themes in these studies, as they all involve partial differential equations or their discrete analogues which incorporate a description of diffusion-type processes. However, there are also some qualitative differences, as shall be discussed below.

Frost fatigue and spring recovery of xylem vessels in three diffuse-porous trees in situ.

Science.gov (United States)

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.

Dynamic characterization of partially saturated engineered porous media and gas diffusion layers using hydraulic admittance

Science.gov (United States)

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.

Introduction to porous media micro-mechanics; Introduction a la micromecanique des milieux poreux

Energy Technology Data Exchange (ETDEWEB)

Dormieux, L.; Bourgeois, E.

2002-07-01

The study of porous materials can be considered at two different scales: the microscopic scale characterized by the size of the pores and by the domains occupied by the solid and the fluids, and the macroscopic scale which is controlled by the size of the structures under study (backfilling, foundations, dams, oil reservoirs or sedimentary basins). An alternative way, explored since about 30 years, consists in searching the formulation of macroscopic laws in the framework of a scale change approach. This is the point of view considered in this book which proposes a micro-mechanical approach of the modeling of porous environments based on various techniques of homogenization of the heterogenous materials with a random or periodical microstructure: 1 - macroscopic description of porous environments (space scales, skeleton deformation and kinematics, kinematics of fluid components, conservation laws, internal stresses); 2 - scale change techniques (representative elementary volume, averaging operation, application to conservation laws); 3 - Darcy transport (phenomenological approach of the Darcy law, Darcy law interpretation at the microscopic scale, fluid and solid phases interaction, flows inside a rigid porous environment, application); 4 - diffusive transport of a fluid component (solute transport equation, modeling of the macroscopic diffusive flux by scale change, application to pollutant diffusion); 5 - linear poro-elastic behaviour (first approach: empty sphere model, generalisation, estimation of poro-elastic characteristics); 6 - evolution problems in poro-elasticity (problem formulation, resolution, study of poro-elastic consolidation, tide response of an underwater massif, modeling of the formation of a syncline, study of the folding back of a sheet, numerical resolution of coupled problems, realization of a Scilab script); 7 - conclusion. (J.S.)

Development of Numerical Technique to Analyze the Flow Characteristics of Porous Media Using Lattice Boltzmann Method

Energy Technology Data Exchange (ETDEWEB)

Kim, Hyung Min [Kyonggi Univ., Suwon (Korea, Republic of)

2016-11-15

The performance of proton exchange membrane fuel cells (PEMFC) is strongly related to the water flow and accumulation in the gas diffusion layer (GDL) and catalyst layer. Understanding the behavior of fluid from the characteristics of the media is crucial for the improvement of the performance and design of the GDL. In this paper, a numerical method is proposed to calculate the design parameters of the GDL, i.e., permeability, tortuosity, and effective diffusivity. The fluid flow in a channel filled with randomly packed hard spheres is simulated to validate the method. The flow simulation was performed by lattice Boltzmann method with bounce back condition for the solid volume fraction in the porous media, with different values of porosities. Permeability, which affects the flow, was calculated from the average pressure drop and the velocity in the porous media. Tortuosity, calculated by the ratio the average path length of the randomly injected massless particles to the thickness of the porous media, and the resultant effective diffusivity were in good agreement with the theoretical model. The suggested method can be used to calculate the parameters of real GDL accurately without any modification.

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

Recent topics in non-linear partial differential equations 4

CERN Document Server

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.

A unified nonlocal strain gradient plate model for nonlinear axial instability of functionally graded porous micro/nano-plates reinforced with graphene platelets

Science.gov (United States)

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.

Diffusive counter dispersion of mass in bubbly media.

Science.gov (United States)

Goldobin, Denis S; Brilliantov, Nikolai V

2011-11-01

We consider a liquid bearing gas bubbles in a porous medium. When gas bubbles are immovably trapped in a porous matrix by surface-tension forces, the dominant mechanism of transfer of gas mass becomes the diffusion of gas molecules through the liquid. Essentially, the gas solution is in local thermodynamic equilibrium with vapor phase all over the system, i.e., the solute concentration equals the solubility. When temperature and/or pressure gradients are applied, diffusion fluxes appear and these fluxes are faithfully determined by the temperature and pressure fields, not by the local solute concentration, which is enslaved by the former. We derive the equations governing such systems, accounting for thermodiffusion and gravitational segregation effects, which are shown not to be neglected for geological systems-marine sediments, terrestrial aquifers, etc. The results are applied for the treatment of non-high-pressure systems and real geological systems bearing methane or carbon dioxide, where we find a potential possibility of the formation of gaseous horizons deep below a porous medium surface. The reported effects are of particular importance for natural methane hydrate deposits and the problem of burial of industrial production of carbon dioxide in deep aquifers.

Stability, diffusion and interactions of nonlinear excitations in a many body system

Science.gov (United States)

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.

Diffusion and saponification inside porous cellulose triacetate fibers.

Science.gov (United States)

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.

Synthesis of hierarchical porous materials with ZSM-5 structures via template-free sol–gel method

Directory of Open Access Journals (Sweden)

Wei Han et al

2007-01-01

Full Text Available Interests are focused on preparation of hierarchical porous materials with zeolite structures by using soft or rigid templates in order to solve diffusion and mass transfer limitations resulting from the small pore sizes of zeolites. Here we develop a convenient template-free sol–gel method to synthesize hierarchical porous materials with ZSM-5 structures. This method involves hydrothermal recrystallization of the xerogel converted from uniform ZSM-5 sol by a vacuum drying process. By utilizing this method we can manipulate the size of zeolite nanocrystals as building units of porous structures based on controlling temperature of recrystallization, consequently obtain hierarchical porous materials with different intercrystalline pore sizes and ZSM-5 structures.

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)

Radionuclide transport in fractured porous media -- Analytical solutions for a system of parallel fractures with a kinetic solubility-limited dissolution model

International Nuclear Information System (INIS)

Li, S.H.; Chen, C.T.

1997-01-01

Analytical solutions are developed for the problem of radionuclide transport in a system of parallel fractures situated in a porous rock matrix. A kinetic solubility-limited dissolution model is used as the inlet boundary condition. The solutions consider the following processes: (a) advective transport in the fractures, (b) mechanical dispersion and molecular diffusion along the fractures, (c) molecular diffusion from a fracture to the porous matrix, (d) molecular diffusion within the porous matrix in the direction perpendicular to the fracture axis, (e) adsorption onto the fracture wall, (f) adsorption within the porous matrix, and (g) radioactive decay. The solutions are based on the Laplace transform method. The general transient solution is in the form of a double integral that is evaluated using composite Gauss-Legendre quadrature. A simpler transient solution that is in the form of a single integral is also presented for the case that assumes negligible longitudinal dispersion along the fractures. The steady-state solutions are also provided. A number of examples are given to illustrate the effects of the following important parameters: (a) fracture spacings, (b) dissolution-rate constants, (c) fracture dispersion coefficient, (d) matrix retardation factor, and (e) fracture retardation factor

A New Approach and Solution Technique to Solve Time Fractional Nonlinear Reaction-Diffusion Equations

Directory of Open Access Journals (Sweden)

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.

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)

Homogenization of a locally-periodic medium with areas of low and high diffusivity

NARCIS (Netherlands)

Noorden, van T.L.; Muntean, A.

2010-01-01

We aim at understanding transport in porous materials including regions with both high and low diffusivities. For such scenarios, the transport becomes structured (here: micro- macro). The geometry we have in mind includes regions of low diffusivity arranged in a locally-periodic fashion. We choose

The movement of solutes through aqueous fissures in micro-porous rock during borehole experiments

International Nuclear Information System (INIS)

Glueckauf, E.

1981-02-01

When a tracer is injected for a short period into a solution flowing through a fissure in micro-porous rock, that tracer is not only carried along by the aqueous stream, but its local concentration is also markedly affected by hydro-dynamic dispersion and by sideway diffusion and adsorption in the micro-porous rock. The process has been simulated by computer calculations and these have made it possible to obtain from the concentration-time curves observed in borehole experiments an assessment of the physical parameters involving the water velocity and the hydro-dynamic dispersion in the fissure, and the diffusion and adsorption in the micro-porous rock. With these parameters it was then possible to recalculate quantitatively the local concentration-time history. However, in actual borehole experiments, the velocity of the water stream in the fissure is not known, and numerous side effects can distort the shape of the observed tracer curves. In order to test the theoretical interpretation more thoroughly, it is therefore proposed to carry out a laboratory experiment which simulates the borehole test under strictly defined conditions. (author)

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

On the Mass and Heat Transfer in the Porous Electrode of a Fuel Cell

Energy Technology Data Exchange (ETDEWEB)

Revuelta Bayod, A.

2004-07-01

In the first part of this report a reduced model of the mass transport in the PEMFC cathode gas diffusion layer is formulated ro an interrogated flow field design of the cathode bipolar plate. The non-dimensional formulation of the problem allows to identify the leading parameters which determines the fundamental species distribution and flow field structure. The effect of the forced convection of the gases into the porous electrode, caused by the interrogated flow field, is quantified through the Peclet numbers of the active species, and the non-dimensional polarization curves are obtained. In the second part, the diffusion-thermal instability is analyzed in a porous gas diffusion layer (GDL) of a fuel cell. The investigation presented provides an initial guideline to future theoretical and experimental investigations on one aspect of the fuel cell performance not previously considered, with impact on the fuel cell life-time. Starting from the simples possible 1D-model of the flow into the porous electrode, the steady solution of the model is presented an analyzed depending on a minimum number of non-dimensional parameters. From this steady solution, a linear stability analysis is formulated, taking into account the temporal-spatial perturbations transversal to the gas flow direction, and the marginal stability regions are determined from the corresponding dispersion relation. (Author) 33 refs.

Large-time behavior of solutions to a reaction-diffusion system with distributed microstructure

NARCIS (Netherlands)

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

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...

Non-Boussinesq Dissolution-Driven Convection in Porous Media

Science.gov (United States)

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.

A variational theory for frictional flow of fluids in inhomogeneous porous systems

Energy Technology Data Exchange (ETDEWEB)

Sieniutycz, Stanislaw [Faculty of Chemical Engineering, Warsaw University of Technology, 00-645 Warsaw, 1 Warynskiego Street (Poland)

2007-04-15

For nonlinear steady paths of a fluid in an inhomogeneous isotropic porous medium a Fermat-like principle of minimum time is formulated which shows that the fluid streamlines are curved by a location dependent hydraulic conductivity. The principle describes an optimal nature of nonlinear paths in steady Darcy's flows of fluids. An expression for the total resistance of the path leads to a basic analytical formula for an optimal shape of a steady trajectory. In the physical space an optimal curved path ensures the maximum flux or shortest transition time of the fluid through the porous medium. A sort of 'law of bending' holds for the frictional fluid flux in Lagrange coordinates. This law shows that - by minimizing the total resistance - a ray spanned between two given points takes the shape assuring that its relatively large part resides in the region of lower flow resistance (a 'rarer' region of the medium). Analogies and dissimilarities with other systems (e.g. optical or thermal ones) are also discussed. (author)

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)

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)

Model of two-temperature convective transfer in porous media

Science.gov (United States)

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.

Adaptive moving grid methods for two-phase flow in porous media

KAUST Repository

Dong, Hao

2014-08-01

In this paper, we present an application of the moving mesh method for approximating numerical solutions of the two-phase flow model in porous media. The numerical schemes combine a mixed finite element method and a finite volume method, which can handle the nonlinearities of the governing equations in an efficient way. The adaptive moving grid method is then used to distribute more grid points near the sharp interfaces, which enables us to obtain accurate numerical solutions with fewer computational resources. The numerical experiments indicate that the proposed moving mesh strategy could be an effective way to approximate two-phase flows in porous media. © 2013 Elsevier B.V. All rights reserved.

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.)

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)

Fabrication and formation mechanism of poly (L-lactic acid ultrafine multi-porous hollow fiber by electrospinning

Directory of Open Access Journals (Sweden)

Q. Z. Yu

2013-01-01

Full Text Available Poly(L-lactic acid (PLLA ultrafine multi-porous hollow fibers are fabricated by electrospinning with methylene dichloride as solvent. The Kirkendall effect has been widely applied for the fabrication of hollow structure in metals and inorganic materials. In this study, a conceptual extension is proposed for the formation mechanism: the development of porous hollow fiber undergoes three stages. The initial stage is the generation of small voids or pits on the surface of the fiber via surface diffusion and phase separation; the second stage is the formation of multi-pores penetrating the core of the fiber through the interaction of Kirkendall effect, surface diffusion and phase separation; the third stage is dominated by surface diffusion of the core material along the pore surface. To explore the formation conditions, the factors including ambient temperature, relativity humidity (R. H., molecular weight and fiber diameter are studied. The longitudinal and cross sectional morphologies of these fibers are examined by scanning electron micrograph (SEM. The results show that the prerequisite for the formation of uniform porous hollow PLLA fibers include moderate ambient temperature (10~20°C and appropriate molecular weight for the PLLA, as well as the diameter of the fiber in the range of several micrometers to about 100 nanometers.

Chemically reactive and naturally convective high speed MHD fluid flow through an oscillatory vertical porous plate with heat and radiation absorption effect

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

IN-SITU MEASURING METHOD OF RADON AND THORON DIFFUSION COEFFICIENT IN SOIL

Directory of Open Access Journals (Sweden)

V.S. Yakovleva

2014-06-01

Full Text Available A simple and valid in-situ measurement method of effective diffusion coefficient of radon and thoron in soil and other porous materials was designed. The analysis of numerical investigation of radon and thoron transport in upper layers of soil revealed that thoron flux density from the earth surface does not depend on soil gas advective velocity and varies only with diffusion coefficient changes. This result showed the advantages of thoron using versus radon using in the suggested method. The comparison of the new method with existing ones previously developed. The method could be helpful for solving of problems of radon mass-transport in porous media and gaseous exchange between soil and atmosphere.

Nonlinear theory of collisionless trapped ion modes

International Nuclear Information System (INIS)

Hahm, T.S.; Tang, W.M.

1996-01-01

A simplified two field nonlinear model for collisionless trapped-ion-mode turbulence has been derived from nonlinear bounce-averaged drift kinetic equations. The renormalized thermal diffusivity obtained from this analysis exhibits a Bohm-like scaling. A new nonlinearity associated with the neoclassical polarization density is found to introduce an isotope-dependent modification to this Bohm-like diffusivity. The asymptotic balance between the equilibrium variation and the finite banana width induced reduction of the fluctuation potential leads to the result that the radial correlation length decreases with increasing plasma current. Other important conclusions from the present analysis include the predictions that (i) the relative density fluctuation level δn/n 0 is lower than the conventional mixing length estimate, Δr/L n (ii) the ion temperature fluctuation level δT i /T i significantly exceeds the density fluctuation level δn/n 0 ; and (iii) the parallel ion velocity fluctuation level δv iparallel /v Ti is expected to be negligible

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

Science.gov (United States)

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

2017-02-01

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

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

Science.gov (United States)

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

2014-12-15

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

A multi-scale computational scheme for anisotropic hydro-mechanical couplings in saturated heterogeneous porous media

NARCIS (Netherlands)

Mercatoris, B.C.N.; Massart, T.J.; Sluys, L.J.

2013-01-01

This contribution discusses a coupled two-scale framework for hydro-mechanical problems in saturated heterogeneous porous geomaterials. The heterogeneous nature of such materials can lead to an anisotropy of the hydro-mechanical couplings and non-linear effects. Based on an assumed model of the

Percolation-enhanced nonlinear scattering from semicontinuous metal films

Science.gov (United States)

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.

Electron diffusion in tokamaks due to electromagnetic fluctuations

International Nuclear Information System (INIS)

Horton, W.; Choi, D.-I.; Yushmanov, P.N.; Parail, V.V.

1987-01-01

Calculations for the stochastic diffusion of electrons in Tokamaks due to a spectrum of electromagnetic drift fluctuations are presented. The parametric dependence of the diffusion coefficient on the amplitude and phase velocity of the spectrum, and the bounce frequency for the electrons is studied. The wavenumber spectrum is taken to be a low order (5 x 5) randomly-phased, isotropic, monotonic spectrum extending from k sub(perpendicular to min) ≅ ωsub(ci)/Csub(s) to k sub(perpendicular to max) ≅ 3ωsub(pe)/C with different power laws of decrease φsub(k) ≅ φ 1 /ksup(m), 1 ≤ m ≤ 3. A nonlinear Ohm's law is derived for the self-consistent relation between the electrostatic and parallel vector potentials. The parallel structure of the fluctuations is taken to be such that ksup(nl)sub(parallel to)Vsub(e) < ωsub(k) due to the nonlinear perpendicular motion of the electrons described in the nonlinear Ohm's law. The diffusion coefficient scales approximately as the neo-Alcator and Merezhkin-Mukhovatov empirical formulas for plasma densities below a critical density. (author)

Effect of wetting properties on the kinetics of drying of porous media

International Nuclear Information System (INIS)

Shahidzadeh-Bonn, N; Azouni, A; Coussot, P

2007-01-01

The influence of the wetting properties of a model porous medium on the evaporation rate of water contained in the sample is studied experimentally. For a hydrophilic porous medium, drying is mainly controlled by the liquid film covering the solid grains and capillary rise inside the pores, leading to a constant drying rate and a homogeneous desaturation of the whole sample in time. For a hydrophobic porous medium, a drying front penetrates into the sample in the early stages of evaporation and the drying rate is found to strongly depend on the boundary conditions and wetting heterogeneities. In the presence of an air flow along the free surface of the sample, the drying rate varies as the square root of time, indicating a diffusive transport mechanism. Without air flow, a power law behaviour for the drying rate as a function of time is observed with an exponent of 0.75 ± 0.03. This is likely to be due to competition between diffusion through the vapour phase and local capillary rise of the liquid due to wetting heterogeneities. A surprising consequence is that for the late stages of drying, the total evaporated mass may become larger without air flow than with air flow. (fast track communication)

Contaminant flow and transport simulation in cracked porous media using locally conservative schemes

KAUST Repository

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

Determination of oxygen effective diffusivity in porous gas diffusion layer using a three-dimensional pore network model

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.

Enhancement of aspirin capsulation by porous particles including iron hydrous oxide

International Nuclear Information System (INIS)

Saito, Kenji; Koishi, Masumi; Hosoi, Fumio; Makuuchi, Keizo.

1986-01-01

Polymer-coated porous particles containing aspirin as a drug were prepared and the release of rate of aspirin was studied. The impregnation of aspirin was carried out by post-graft polymerization, where methyl methacrylate containing aspirin was treated with porous particles including iron oxide, pre-irradiated with γ-ray form Co-60. Release of aspirin from modified particles was examined with 50 % methanol solution. The amount of aspirin absorbed in porous particles increased by grafting of methyl methacrylate. The particles treated with iron hydrous oxide sols before irradiation led to the increment of aspirin absorption. Diffusion of aspirin through the polymer matrix and the gelled layer was the limiting process in the aspirin release from particles. The rate of aspirin released from modified particles including iron hydrous oxide wasn't affected by the grafting of methyl methacrylate. (author)

Interfacial reactions between DBD and porous catalyst in dry methane reforming

Science.gov (United States)

Kameshima, Seigo; Mizukami, Ryo; Yamazaki, Takumi; Prananto, Lukman A.; Nozaki, Tomohiro

2018-03-01

Interaction between dielectric barrier discharge (DBD) and porous catalyst in dry methane reforming (CH4  +  CO2  =  2H2  +  2CO) was studied. Coke formation behavior and coke morphology, as well as material conversion and selectivity, over the cross-section of porous pellets was investigated comprehensively by SEM analysis, Raman spectroscopy and pulsed reforming diagnosis, showing DBD and porous pellet interaction is possible only in the interfacial region (the external surface of the pellet): neither generation of DBD nor the diffusion of plasma generated reactive species in the internal micropores is possible. Coke formation and gasification mechanism in nonthermal plasma catalysis of DMR were discussed based on the catalyst effectiveness factor: low-temperature plasma catalysis is equivalent to the high-temperature thermal catalysis.

Airflow Pattern and Performance Analysis of Diffuse Ceiling Ventilation in an Office Room using CFD Study

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...

Molecular exchange of n-hexane in zeolite sieves studied by diffusion-diffusion and T{sub 1}-diffusion nuclear magnetic resonance exchange spectroscopy

Energy Technology Data Exchange (ETDEWEB)

Neudert, Oliver; Stapf, Siegfried; Mattea, Carlos, E-mail: carlos.mattea@tu-ilmenau.de [Fachgebiet Technische Physik II/Polymerphysik, Institute of Physics, Technische Universitaet Ilmenau, PO Box 100 565, 98684 Ilmenau (Germany)

2011-03-15

Molecular exchange properties and diffusion of n-hexane embedded in a bimodal pore structure with characteristic length scales in the order of nano and micrometres, respectively, formed by packing of zeolite particles, are studied. Two-dimensional (2D) nuclear magnetic resonance (NMR) diffusion correlation experiments together with relaxation-diffusion correlation experiments are performed at low magnetic field using a single-sided NMR scanner. The exchange time covers a range from 10{sup -3} to 10{sup -1} s. The molecular exchange properties are modulated by transport inside the zeolite particles. Different exchange regimes are observed for molecules starting from different positions inside the porous sample. The influence of the spin-lattice relaxation properties of the fluid molecules inside the zeolite particles on the signal intensity is also studied. A Monte Carlo simulation of the exchange process is performed and is used to support the analysis of the experimental data.

Non-Darcy Mixed Convection in a Doubly Stratified Porous Medium with Soret-Dufour Effects

Directory of Open Access Journals (Sweden)

D. Srinivasacharya

2014-01-01

Full Text Available This paper presents the nonsimilarity solutions for mixed convection heat and mass transfer along a semi-infinite vertical plate embedded in a doubly stratified fluid saturated porous medium in the presence of Soret and Dufour effects. The flow in the porous medium is described by employing the Darcy-Forchheimer based model. The nonlinear governing equations and their associated boundary conditions are initially cast into dimensionless forms and then solved numerically. The influence of pertinent parameters on dimensionless velocity, temperature, concentration, heat, and mass transfer in terms of the local Nusselt and Sherwood numbers is discussed and presented graphically.

Pore and surface diffusion in multicomponent adsorption and liquid chromatography systems

International Nuclear Information System (INIS)

Ma, Z.; Whitley, R.D.; Wang, N.H.L.

1996-01-01

A generalized parallel pore and surface diffusion model for multicomponent adsorption and liquid chromatography is formulated and solved numerically. Analytical solution for first- and second-order central moments for a pulse on a plateau input is used as benchmarks for the numerical solutions. Theoretical predictions are compared with experimental data for two systems: ion-exchange of strontium, sodium, and calcium in a zeolite and competitive adsorption of two organics on activated carbon. In a linear isotherm region of single-component systems, both surface and pore diffusion cause symmetric spreading in breakthrough curves. In a highly nonlinear isotherm region, however, surface diffusion causes pronounced tailing in breakthrough curves; the larger the step change in concentration, the more pronounced tailing, in contrast to relatively symmetric breakthroughs due to pore diffusion. If only a single diffusion mechanism is assumed in analyzing the data of parallel diffusion systems, a concentration-dependent apparent surface diffusivity or pore diffusivity results; for a convex isotherm, the apparent surface diffusivity increases, whereas the apparent pore diffusivity decreases with increasing concentration. For a multicomponent nonlinear system, elution order can change if pore diffusion dominates for a low-affinity solute, whereas surface diffusion dominates for a high-affinity solute

Size-controllable synthesis of nanosized-TiO2 anatase using porous Vycor glass as template

International Nuclear Information System (INIS)

Mazali, I.O.; Filho, A.G. Souza; Viana, B.C.; Filho, J. Mendes; Alves, O.L.

2006-01-01

In this paper we report the synthesis and characterization of TiO 2 nanocrystal dispersed into a porous Vycor glass. We have obtained very small TiO 2 nanocrystals in the anatase form. The nanocrystal size is controlled via the mass increment only thus preventing the growth through the coalescence process. The nanocrystal size was monitored through transmission electron microscope and Raman scattering. The coalescence control is attributed due to the obtention of nanocrystals dispersed into the host and to the terminal bonds present in the porous which act as an anchor thus resulting in a low diffusion of the nanocrystals through the porous network

Simultaneous heat and moisture transfer in porous elements: transfer function method

International Nuclear Information System (INIS)

Souza, H.A. de.

1985-01-01

The presence of moisture in a porous element may strongly affect the transfer of heat through this element due to the processes which occur associated with the phase changes at the boundary surfaces and internally in the wall body. In addition, the structural properties of the element may also be meaningfully affected. The formulation of mathematical models for the simultaneous heat and mass transfer in porous elements results in a pair of nonlinear coupled equations for the temperature and moisture content distributions, in the material. It is supposed, in this work, that the actual variation of the properties of the porous medium is small in the range of variables which describe the specific problem to be analyzed. This enables us to work with linearized equations, making possible the use of linear solution methods. In this context, the present work deals with a linear procedure for the solution of simultaneous heat and moisture transfer problems in porous elements, sujected to arbitrary boundary conditions. This results in a linear relation between the heat and mass flux densities through the boundary surfaces of the elements and their associated potentials. It is shown that the model is consistent in asymptotical limiting cases; the model is then used for analyzing the drying process of a porous element, subjected to ambient actual conditions. (Author) [pt

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 ...

The Influence of Uniform Suction/Injection on Heat Transfer of MHD Hiemenz Flow in Porous Media

DEFF Research Database (Denmark)

Ghsemi, E; Soleimani, S; Barari, Amin

2012-01-01

The steady two-dimensional laminar forced magneto-hydrodynamic (MHD) Hiemenz flow against a flat plate with variable wall temperature in a porous medium is analyzed. The transformed nonlinear boundary-layer equations are solved analytically by homotopy analysis method (HAM). Results for the veloc...

3D hybrid-porous carbon derived from carbonization of metal organic frameworks for high performance supercapacitors

Science.gov (United States)

Bao, Weizhai; Mondal, Anjon Kumar; Xu, Jing; Wang, Chengyin; Su, Dawei; Wang, Guoxiu

2016-09-01

We report a rational design and synthesis of 3D hybrid-porous carbon with a hierarchical pore architecture for high performance supercapacitors. It contains micropores (<2 nm diameter) and mesopores (2-4 nm), derived from carbonization of unique porous metal organic frameworks (MOFs). Owning to the synergistic effect of micropores and mesopores, the hybrid-porous carbon has exceptionally high ion-accessible surface area and low ion diffusion resistance, which is desired for supercapacitor applications. When applied as electrode materials in supercapacitors, 3D hybrid-porous carbon demonstrates a specific capacitance of 332 F g-1 at a constant charge/discharge current of 500 mA g-1. The supercapacitors can endure more than 10,000 cycles without degradation of capacitance.

Spectral theory and nonlinear functional analysis

CERN Document Server

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.

Sensitive Nonenzymatic Electrochemical Glucose Detection Based on Hollow Porous NiO

Science.gov (United States)

He, Gege; Tian, Liangliang; Cai, Yanhua; Wu, Shenping; Su, Yongyao; Yan, Hengqing; Pu, Wanrong; Zhang, Jinkun; Li, Lu

2018-01-01

Transition metal oxides (TMOs) have attracted extensive research attentions as promising electrocatalytic materials. Despite low cost and high stability, the electrocatalytic activity of TMOs still cannot satisfy the requirements of applications. Inspired by kinetics, the design of hollow porous structure is considered as a promising strategy to achieve superior electrocatalytic performance. In this work, cubic NiO hollow porous architecture (NiO HPA) was constructed through coordinating etching and precipitating (CEP) principle followed by post calcination. Being employed to detect glucose, NiO HPA electrode exhibits outstanding electrocatalytic activity in terms of high sensitivity (1323 μA mM-1 cm-2) and low detection limit (0.32 μM). The excellent electrocatalytic activity can be ascribed to large specific surface area (SSA), ordered diffusion channels, and accelerated electron transfer rate derived from the unique hollow porous features. The results demonstrate that the NiO HPA could have practical applications in the design of nonenzymatic glucose sensors. The construction of hollow porous architecture provides an effective nanoengineering strategy for high-performance electrocatalysts.

Understanding of flux-limited behaviors of heat transport in nonlinear regime

Energy Technology Data Exchange (ETDEWEB)

Guo, Yangyu, E-mail: yangyuhguo@gmail.com [Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Engineering Mechanics and CNMM, Tsinghua University, Beijing 100084 (China); Jou, David, E-mail: david.jou@uab.es [Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Catalonia (Spain); Wang, Moran, E-mail: mrwang@tsinghua.edu [Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Engineering Mechanics and CNMM, Tsinghua University, Beijing 100084 (China)

2016-01-28

The classical Fourier's law of heat transport breaks down in highly nonequilibrium situations as in nanoscale heat transport, where nonlinear effects become important. The present work is aimed at exploring the flux-limited behaviors based on a categorization of existing nonlinear heat transport models in terms of their theoretical foundations. Different saturation heat fluxes are obtained, whereas the same qualitative variation trend of heat flux versus exerted temperature gradient is got in diverse nonlinear models. The phonon hydrodynamic model is proposed to act as a standard to evaluate other heat flux limiters because of its more rigorous physical foundation. A deeper knowledge is thus achieved about the phenomenological generalized heat transport models. The present work provides deeper understanding and accurate modeling of nonlocal and nonlinear heat transport beyond the diffusive limit. - Highlights: • Exploring flux-limited behaviors based on a categorization of existing nonlinear heat transport models. • Proposing phonon hydrodynamic model as a standard to evaluate heat flux limiters. • Providing accurate modeling of nonlocal and nonlinear heat transport beyond the diffusive limit.

Weak chaos in the disordered nonlinear Schroedinger chain: Destruction of Anderson localization by Arnold diffusion

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.

Multipassage diffuser

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

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)

Homogeneous-heterogeneous reactions in curved channel with porous medium

Science.gov (United States)

Hayat, T.; Ayub, Sadia; Alsaedi, A.

2018-06-01

Purpose of the present investigation is to examine the peristaltic flow through porous medium in a curved conduit. Problem is modeled for incompressible electrically conducting Ellis fluid. Influence of porous medium is tackled via modified Darcy's law. The considered model utilizes homogeneous-heterogeneous reactions with equal diffusivities for reactant and autocatalysis. Constitutive equations are formulated in the presence of viscous dissipation. Channel walls are compliant in nature. Governing equations are modeled and simplified under the assumptions of small Reynolds number and large wavelength. Graphical results for velocity, temperature, heat transfer coefficient and homogeneous-heterogeneous reaction parameters are examined for the emerging parameters entering into the problem. Results reveal an activation in both homogenous-heterogenous reaction effect and heat transfer rate with increasing curvature of the channel.

Dynamic aperture and transverse proton diffusion in HERA

International Nuclear Information System (INIS)

Zimmermann, F.

1994-04-01

The dynamic aperture caused by persistent-current nonlinear field errors is an important concern in the design of superconducting hadron storage rings. The HERA proton ring is the second superconducting accelerator in operation. In this lecture note, its measured dynamic aperture is compared with that inferred from comprehensive trackig studies. To understand the difference between prediction and measurement, a semi-analytical method is developed for evaluating transverse diffusion rates due to various processes, such as modulational diffusion or sweeping diffusion this analysis makes use of parameters for high-order resonances in the transverse phase space, which are obtained by normal-form algorithms using differential-algebra software. This semi-analytical results are consistent wit the measurements, and suggest that the actual dynamic aperture is caused by an interplay of tune modulation and nonlinear magnetic fields

Studies on dispersive stabilization of porous media flows

Energy Technology Data Exchange (ETDEWEB)

Daripa, Prabir, E-mail: prabir.daripa@math.tamu.edu; Gin, Craig [Department of Mathematics, Texas A& M University, College Station, Texas 77843 (United States)

2016-08-15

Motivated by a need to improve the performance of chemical enhanced oil recovery (EOR) processes, we investigate dispersive effects on the linear stability of three-layer porous media flow models of EOR for two different types of interfaces: permeable and impermeable interfaces. Results presented are relevant for the design of smarter interfaces in the available parameter space of capillary number, Peclet number, longitudinal and transverse dispersion, and the viscous profile of the middle layer. The stabilization capacity of each of these two interfaces is explored numerically and conditions for complete dispersive stabilization are identified for each of these two types of interfaces. Key results obtained are (i) three-layer porous media flows with permeable interfaces can be almost completely stabilized by diffusion if the optimal viscous profile is chosen, (ii) flows with impermeable interfaces can also be almost completely stabilized for short time, but become more unstable at later times because diffusion flattens out the basic viscous profile, (iii) diffusion stabilizes short waves more than long waves which leads to a “turning point” Peclet number at which short and long waves have the same growth rate, and (iv) mechanical dispersion further stabilizes flows with permeable interfaces but in some cases has a destabilizing effect for flows with impermeable interfaces, which is a surprising result. These results are then used to give a comparison of the two types of interfaces. It is found that for most values of the flow parameters, permeable interfaces suppress flow instability more than impermeable interfaces.

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)

Electron dynamics with radiation and nonlinear wigglers

International Nuclear Information System (INIS)

Jowett, J.M.

1986-06-01

The physics of electron motion in storage rings is described by supplementing the Hamiltonian equations of motion with fluctuating radiation reaction forces to describe the effects of synchrotron radiation. This leads to a description of radiation damping and quantum diffusion in single-particle phase-space by means of Fokker-Planck equations. For practical purposes, most storage rings remain in the regime of linear damping and diffusion; this is discussed in some detail with examples, concentrating on longitudinal phase space. However special devices such as nonlinear wigglers may permit the new generation of very large rings to go beyond this into regimes of nonlinear damping. It is shown how a special combined-function wiggler can be used to modify the energy distribution and current profile of electron bunches

Fem Formulation for Heat and Mass Transfer in Porous Medium

Science.gov (United States)

Azeem; Soudagar, Manzoor Elahi M.; Salman Ahmed, N. J.; Anjum Badruddin, Irfan

2017-08-01

Heat and mass transfer in porous medium can be modelled using three partial differential equations namely, momentum equation, energy equation and mass diffusion. These three equations are coupled to each other by some common terms that turn the whole phenomenon into a complex problem with inter-dependable variables. The current article describes the finite element formulation of heat and mass transfer in porous medium with respect to Cartesian coordinates. The problem under study is formulated into algebraic form of equations by using Galerkin's method with the help of two-node linear triangular element having three nodes. The domain is meshed with smaller sized elements near the wall region and bigger size away from walls.

Nonlinear flow model for well production in an underground formation

Directory of Open Access Journals (Sweden)

J. C. Guo

2013-05-01

Full Text Available Fluid flow in underground formations is a nonlinear process. In this article we modelled the nonlinear transient flow behaviour of well production in an underground formation. Based on Darcy's law and material balance equations, we used quadratic pressure gradients to deduce diffusion equations and discuss the origins of nonlinear flow issues. By introducing an effective-well-radius approach that considers skin factor, we established a nonlinear flow model for both gas and liquid (oil or water. The liquid flow model was solved using a semi-analytical method, while the gas flow model was solved using numerical simulations because the diffusion equation of gas flow is a stealth function of pressure. For liquid flow, a series of standard log-log type curves of pressure transients were plotted and nonlinear transient flow characteristics were analyzed. Qualitative and quantitative analyses were used to compare the solutions of the linear and nonlinear models. The effect of nonlinearity upon pressure transients should not be ignored. For gas flow, pressure transients were simulated and compared with oil flow under the same formation and well conditions, resulting in the conclusion that, under the same volume rate production, oil wells demand larger pressure drops than gas wells. Comparisons between theoretical data and field data show that nonlinear models will describe fluid flow in underground formations realistically and accurately.

Mechanobiology of LDL mass transport in the arterial wall under the effect of magnetic field, part I: Diffusion rate

Energy Technology Data Exchange (ETDEWEB)

Aminfar, Habib, E-mail: hh_aminfar@tabrizu.ac.ir [Faculty of Mechanical Engineering, University of Tabriz, Tabriz (Iran, Islamic Republic of); Mohammadpourfard, Mousa, E-mail: Mohammadpour@tabrizu.ac.ir [Faculty of Chemical and Petroleum Engineering, University of Tabriz, Tabriz 5166616471 (Iran, Islamic Republic of); Khajeh, Kosar, E-mail: k.khajeh.2005@tabrizu.ac.ir [Faculty of Mechanical Engineering, University of Tabriz, Tabriz (Iran, Islamic Republic of)

2017-03-15

It is well-known that the Low Density Lipoprotein (LDL) can accumulate and penetrate into the arterial wall. Here, we have investigated the diffusion rate of macromolecules across the porous layer of blood vessel under the effects of magnetic force. By using a finite volume technique, it was found that magnetic field makes alterations in diffusion rate of LDLs, also surface concentration of macromolecules on the walls. As well, the influence of different value of Re and Sc number in the presence of a magnetic field have shown as nondimensional concentration profiles. Magnetic field considered as a body force, porous layer simulated by using Darcy's law and the blood regarded as nano fluid which was examined as a single phase model. - Highlights: • LDLs mass transfer across the arterial wall under magnetic field has simulated numerically. • Arterial wall assumed as a homogeneous porous layer by using Darcy's law. • Blood containing 4% Vol. Fe{sub 3}O{sub 4} regarded as nanofluid and has examined by single phase model. • Magnetic field significantly affects the diffusion rate of LDLs through porous arterial wall.

Antithrombogenicity of Fluorinated Diamond-Like Carbon Films Coated Nano Porous Polyethersulfone (PES) Membrane

Science.gov (United States)

Prihandana, Gunawan S.; Sanada, Ippei; Ito, Hikaru; Noborisaka, Mayui; Kanno, Yoshihiko; Suzuki, Tetsuya; Miki, Norihisa

2013-01-01

A nano porous polyethersulfone (PES) membrane is widely used for aspects of nanofiltration, such as purification, fractionation and dialysis. However, the low-blood-compatibility characteristic of PES membrane causes platelets and blood cells to stick to the surface of the membrane and degrades ions diffusion through membrane, which further limits its application for dialysis systems. In this study, we deposited the fluorinated-diamond-like-carbon (F-DLC) onto the finger like structure layer of the PES membrane. By doing this, we have the F-DLC films coating the membrane surface without sacrificing the membrane permeability. In addition, we examined antithrombogenicity of the F-DLC/PES membranes using a microfluidic device, and experimentally found that F-DLC drastically reduced the amount of blood cells attached to the surface. We have also conducted long-term experiments for 24 days and the diffusion characteristics were found to be deteriorated due to fouling without any surface modification. On the other hand, the membranes coated by F-DLC film gave a consistent diffusion coefficient of ions transfer through a membrane porous. Therefore, F-DLC films can be a great candidate to improve the antithrombogenic characteristics of the membrane surfaces in hemodialysis systems. PMID:28788333

Porous nanocubic Mn3O4-Co3O4 composites and their application as electrochemical supercapacitors.

Science.gov (United States)

Pang, Huan; Deng, Jiawei; Du, Jimin; Li, Sujuan; Li, Juan; Ma, Yahui; Zhang, Jiangshan; Chen, Jing

2012-09-14

A simple approach has been developed to fabricate ideal supercapacitors based on porous Mn(3)O(4)-Co(3)O(4) nanocubic composite electrodes. We can easily obtain porous corner-truncated nanocubic Mn(3)O(4)-Co(3)O(4) composite nanomaterials without any subsequent complicated workup procedure for the removal of a hard template, seed or by using a soft template. In such a composite, the porous Mn(3)O(4)-Co(3)O(4) enables a fast and reversible redox reaction to improve the specific capacitance. The porous nanocubic Mn(3)O(4)-Co(3)O(4) composite electrode can effectively transport electrolytes and shorten the ion diffusion path, which offers excellent electrochemical performance. These results suggest that such porous Mn(3)O(4)-Co(3)O(4) composite nanocubes are very promising for next generation high-performance supercapacitors.

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.))

Colloid-facilitated radionuclide transport in the fractured rock: effects of decay chain and limited matrix diffusion

International Nuclear Information System (INIS)

Park, J. B.; Park, J. W.; Lee, E. Y.; Kim, C. R.

2002-01-01

Colloid-facilitated radionuclide transport in the fractured rock is studies by considering radioactive decay chain and limited matrix diffusion into surrounding porous media. Semi-analytical solution in the Laplace domain is obtained from the mass balance equation of radionuclides and colloid particles. Numerical inversion of the Laplace solution is used to get the concentration profiles both in a fracture and in rock matrix. There issues are analyzed for the radionuclide concentration in a fracture by 1) formation constant of pseudo-colloid, 2) filtration coefficient of radio-colloid and 3) effective diffusion depth into the surrounding porous rock media

Acoustics of multiscale sorptive porous materials

Science.gov (United States)

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.

Modified Shrinking Core Model for Atomic Layer Deposition of TiO2 on Porous Alumina with Ultrahigh Aspect Ratio

International Nuclear Information System (INIS)

Park, Inhye; Leem, Jina; Lee, Hooyong; Min, Yosep

2013-01-01

When atomic layer deposition (ALD) is performed on a porous material by using an organometallic precursor, minimum exposure time of the precursor for complete coverage becomes much longer since the ALD is limited by Knudsen diffusion in the pores. In the previous report by Min et al. (Ref. 23), shrinking core model (SCM) was proposed to predict the minimum exposure time of diethylzinc for ZnO ALD on a porous cylindrical alumina monolith. According to the SCM, the minimum exposure time of the precursor is influenced by volumetric density of adsorption sites, effective diffusion coefficient, precursor concentration in gas phase and size of the porous monolith. Here we modify the SCM in order to consider undesirable adsorption of byproduct molecules. TiO 2 ALD was performed on the cylindrical alumina monolith by using titanium tetrachloride (TiCl 4 ) and water. We observed that the byproduct (i. e., HCl) of TiO 2 ALD can chemically adsorb on adsorption sites, unlike the behavior of the byproduct (i. e., ethane) of ZnO ALD. Consequently, the minimum exposure time of TiCl 4 (∼16 min) was significantly much shorter than that (∼71 min) of DEZ. The predicted minimum exposure time by the modified SCM well agrees with the observed time. In addition, the modified SCM gives an effective diffusion coefficient of TiCl 4 of ∼1.78 Χ 10 -2 cm 2 /s in the porous alumina monolith

Actinide transport in Topopah Spring Tuff: Pore size, particle size, and diffusion

International Nuclear Information System (INIS)

Buchholtz ten Brink, M.; Phinney, D.L.; Smith, D.K.

1991-04-01

Diffusive transport rates for aqueous species in a porous medium are a function of sorption, molecular diffusion, and sample tortuosity. With heterogeneous natural samples, an understanding of the effect of multiple transport paths and sorption mechanisms is particularly important since a small amount of radioisotope traveling via a faster-than-anticipated transport path may invalidate the predictions of transport codes which assume average behavior. Static-diffusion experiments using aqueous 238 U tracer in tuff indicated that U transport was faster in regions of greater porosity and that apparent diffusion coefficients depended on the scale (m or μm) over which concentration gradients were measured in Topopah Spring Tuff. If a significant fraction of actinides in high-level waste are released to the environment in forms that do not sorb to the matrix, they may be similarly transported along fast paths in porous regions of the tuff. To test this, aqueous diffusion rates in tuff were measured for 238 U and 239 Pu leached from doped glass. Measured transport rates and patterns were consistent in both systems with a dual-porosity transported moeld. In addition, filtration or channelling of actinides associated with colloidal particles may significantly affect the radionuclide transport rate in Topopah Spring tuff. 9 refs., 7 figs

The stability of second sound waves in a rotating Darcy–Brinkman porous layer in local thermal non-equilibrium

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)

High-precision numerical simulation with autoadaptative grid technique in nonlinear thermal diffusion

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

Electron diffusion in tokamaks due to electromagnetic fluctuations

International Nuclear Information System (INIS)

Horton, W.; Choi, D.I.; Yushmanov, P.N.; Parail, V.V.

1986-05-01

Calculations for the stochastic diffusion of electrons in tokamaks due to a spectrum of electromagnetic drift fluctuations are presented. The parametric dependence of the diffusion coefficient on the amplitude and phase velocity of the spectrum, and the bounce frequency for the electrons is studied. The wavenumber spectrum is taken to be a low order (5 x 5) randomly-phased, isotropic, Monotonic spectrum extending from k /sub perpendicular min/ approx. = ω/sub ci//c/sub s/ to k/sub perpendicular max/ approx. = 3ω/sub pe//c with different power laws of decrease phi k approx. = phi 1/k/sup m/, 1 less than or equal to m less than or equal to 3. A nonlinear Ohm's law is derived for the self-consistent relation between the electrostatic and parallel vector potentials. The parallel structure of the fluctuations is taken to be such that k parallel/sup nl/upsilon/sub e/ < w/sub k/ due to the nonlinear perpendicular motion of the electrons described in the nonlinear Ohm's law. The diffusion coefficient scales approximately as the neo-Alcator and Merezhkin-Mukhovatoc empirical formulas for plasma densities above a critical density

Microscopic modeling of the Raman diffusion

International Nuclear Information System (INIS)

Benisti, D.; Morice, O.; Gremillet, L.; Strozzi, D.

2010-01-01

In the typical conditions of density and electronic temperature of the Laser Megajoule (LMJ), a quantitative assessment of the Raman reflectivity requires an accurate calculation of the non-linear movement of each electron submitted to the waves propagating in the plasma. The interaction of a laser beam with a plasma generates an electronic wave shifted in frequency (that can be back-scattered) and an electron plasma wave (OPE). The OPE can give to the electrons a strongly non-linear movement by trapping them in a potential well. This non-linearity of microscopic origin has an impact on the plasma electronic density. We have succeeded in computing this plasma electronic density in a very accurate way by combining the principles of a perturbative approach with those of an adiabatic theory. Results show that the Raman diffusion can grow on temperature and density ranges more important than expected. We have predicted the threshold and the behavior of the Raman diffusion above this threshold as accurately as we had done it with a Vlasov code but by being 10000 times more rapid. (A.C.)

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.

Characterization of transport phenomena in porous transport layers using X-ray microtomography

Science.gov (United States)

Hasanpour, S.; Hoorfar, M.; Phillion, A. B.

2017-06-01

Among different methods available for estimating the transport properties of porous transport layers (PTLs) of polymer electrolyte membrane fuel cells, X-ray micro computed tomography (X-μCT) imaging in combination with image-based numerical simulation has been recognized as a viable tool. In this study, four commercially-available single-layer and dual-layer PTLs are analyzed using this method in order to compare and contrast transport properties between different PTLs, as well as the variability within a single sheet. Complete transport property datasets are created for each PTL. The simulation predictions indicate that PTLs with high porosity show considerable variability in permeability and effective diffusivity, while PTLs with low porosity do not. Furthermore, it is seen that the Tomadakis-Sotirchos (TS) analytical expressions for porous media match the image-based simulations when porosity is relatively low but predict higher permeability and effective diffusivity for porosity values greater than 80%. Finally, the simulations show that cracks within MPL of dual-layer PTLs have a significant effect on the overall permeability and effective diffusivity of the PTLs. This must be considered when estimating the transport properties of dual-layer PTLs. These findings can be used to improve macro-scale models of product and reactant transport within fuel cells, and ultimately, fuel cell efficiency.

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...

Facile preparation of hierarchically porous polymer microspheres for superhydrophobic coating

Science.gov (United States)

Gao, Jiefeng; Wong, Julia Shuk-Ping; Hu, Mingjun; Li, Wan; Li, Robert. K. Y.

2013-12-01

A facile method, i.e., nonsolvent assisted electrospraying, is proposed to fabricate hierarchically porous microspheres. The pore size on the microsphere surface ranges from a few tens to several hundred nanometers. Thermally and nonsolvent induced phase separation as well as breath figure is responsible for the formation of the hierarchical structures with different nano-sized pores. The nonsolvent could not only induce phase separation, but also stabilize the interface between the droplet and air, which can prevent the droplet from strong deformation, and is therefore beneficial to the formation of regular and uniform microspheres. On the other hand, solvent evaporation, polymer diffusion and Coulomb fission during electrospraying influence the morphology of finally obtained products. In this paper, the influence of polymer concentration, the weight ratio between nonsolvent and polymer and the flowing rate on the morphology of the porous microsphere is carefully studied. The hierarchically porous microsphere significantly increases the surface roughness and thus the hydrophobicity, and the contact angle can reach as high as 152.2 +/- 1.2°. This nonsolvent assisted electrospraying opens a new way to fabricate superhydrophobic coating materials.A facile method, i.e., nonsolvent assisted electrospraying, is proposed to fabricate hierarchically porous microspheres. The pore size on the microsphere surface ranges from a few tens to several hundred nanometers. Thermally and nonsolvent induced phase separation as well as breath figure is responsible for the formation of the hierarchical structures with different nano-sized pores. The nonsolvent could not only induce phase separation, but also stabilize the interface between the droplet and air, which can prevent the droplet from strong deformation, and is therefore beneficial to the formation of regular and uniform microspheres. On the other hand, solvent evaporation, polymer diffusion and Coulomb fission during

Evolution of density profiles for reaction-diffusion processes

International Nuclear Information System (INIS)

Ondarza-Rovira, R.

1990-01-01

The purpose of this work is to study the reaction diffusion equations for the concentration of one species in one spatial dimension. Nonlinear diffusion equations paly an important role in several fields: Physics, Kinetic Chemistry, Poblational Biology, Neurophysics, etc. The study of the behavior of solutions, with nonlinear diffusion coefficient, and monomial creation and annihilation terms, is considered. It is found, that when the exponent of the annihilation term is smaller than the one of the creation term, unstable equilibrium solutions may exist, for which solutions above it explode in finite time, but solutions below it decay exponentially. By means of the reduction to quadratures technique, it is found that is possible to obtain travelling wave solution in those cases when the annihilation term is greater than the creation term. This method of solution always permits to know the propagation velocity of the front, even if the concentration cannot be written in closed form. The portraits of the solutions in phase space show the existence of solutions which velocities may be smaller or greater than the ones found analytically. Linear and nonlinear diffusion equations, differ significantly in that the former are of change of solutions are considered. This is reminiscent of the fact that linear diffusion yields infinite propagation speed, even though the speed of the front is finite. When the strength of the annihilation term increases, as compared with that of the creation term, arbitrary initial conditions (studied numerically) relax to stable platforms that move indefinitly with constant speed. (Author)

Modelling and simulation of diffusive processes methods and applications

CERN Document Server

Basu, SK

2014-01-01

This book addresses the key issues in the modeling and simulation of diffusive processes from a wide spectrum of different applications across a broad range of disciplines. Features: discusses diffusion and molecular transport in living cells and suspended sediment in open channels; examines the modeling of peristaltic transport of nanofluids, and isotachophoretic separation of ionic samples in microfluidics; reviews thermal characterization of non-homogeneous media and scale-dependent porous dispersion resulting from velocity fluctuations; describes the modeling of nitrogen fate and transport

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 .

Development of pore interconnectivity/morphology in porous silica films investigated by cyclic voltammetry and slow positron annihilation spectroscopy

International Nuclear Information System (INIS)

Tang, Xiuqin; Xiong, Bangyun; Li, Qichao; Mao, Wenfeng; Xiao, Wei; Fang, Pengfei; He, Chunqing

2015-01-01

Highlights: •Porous silica films were studied by cyclic voltammetry and positron annihilation. •Highly interconnected pores were formed in the film fabricated with more CTAB. •Aligned nanochannels were observed in the porous flim prepared with 25 wt.% CTAB. •I − and Ps diffusion in the films was governed by pore interconnectivity/morphology. •Cyclic voltammetry is feasible to explore pore interconnectivity/morphology. -- Abstract: Cyclic voltammetry and positronium (Ps) 3γ-annihilation spectroscopy were applied to investigate pore interconnectivity/morphology of porous silica films fabricated with various loading of cetyltrimethyl ammonium bromide (CTAB). With increasing the ratio of CTAB up to 15 wt.%, the total charge Q, resulted from I − diffusion across the silica films, increased remarkably, indicative of formation of highly interconnected pores in the films prepared with more porogen. However, it decreased dramatically with further loading CTAB of 25 wt.%. Interestingly, 3γ-annihilation fraction I 3γ due to a triplet-state Ps (ortho-positronium, o-Ps) emission from the silica films showed a similar behavior as a function of CTAB loading. The abnormal decrement in Q and I 3γ in the film fabricated with 25 wt.% CTAB was well explained by formation of long nanochannels aligning parallel to the film surface. The results indicated that the total charge Q and Ps 3γ-annihilation fraction were closely associated with I − and Ps diffusion governed by the pore interconnectivity/morphology of the silica films, which made cyclic voltammetry possible to be a feasible tool to characterize pore interconnectivity/morphology of porous thin films

Development and Characterization of Non-Conventional Micro-Porous Layers for PEM Fuel Cells

Directory of Open Access Journals (Sweden)

Riccardo Balzarotti

2015-07-01

Full Text Available Gas diffusion medium (GDM is a crucial component in proton exchange membrane fuel cells (PEMFCs. Being composed of a gas diffusion layer (GDL with a micro-porous layer (MPL coated onto it, it ensures a proper water management due to the highly hydrophobic materials employed in cell assembly. In current commercial applications, the desired water repellent behaviour is usually obtained by using polytetrafluoroethylene (PTFE. In this work, Fluorolink® P56 (Solvay Specialty Polymers, Milan, Italy, a commercially available, anionic, segmented high molecular weight polyfluorourethane with perfluoropolyether groups was extensively evaluated as an alternative to PTFE for micro-porous layer hydrophobization. A change in polymer used is desirable in order to simplify the production process, both in terms of ink formulation and thermal treatment, as well as to get a higher hydrophobicity and, consequently, more efficient water management. Innovative prepared samples were compared to a PTFE-based GDM, in order to assess differences both from morphological and from an electrochemical point of view.

Effect of Organic Substrates on the Photocatalytic Reduction of Cr(VI by Porous Hollow Ga2O3 Nanoparticles

Directory of Open Access Journals (Sweden)

Jin Liu

2018-04-01

Full Text Available Porous hollow Ga2O3 nanoparticles were successfully synthesized by a hydrolysis method followed by calcination. The prepared samples were characterized by field emission scanning electron microscope, transmission electron microscope, thermogravimetry and differential scanning calorimetry, UV-vis diffuse reflectance spectra and Raman spectrum. The porous structure of Ga2O3 nanoparticles can enhance the light harvesting efficiency, and provide lots of channels for the diffusion of Cr(VI and Cr(III. Photocatalytic reduction of Cr(VI, with different initial pH and degradation of several organic substrates by porous hollow Ga2O3 nanoparticles in single system and binary system, were investigated in detail. The reduction rate of Cr(VI in the binary pollutant system is markedly faster than that in the single Cr(VI system, because Cr(VI mainly acts as photogenerated electron acceptor. In addition, the type and concentration of organic substrates have an important role in the photocatalytic reduction of Cr(VI.

Effect of Organic Substrates on the Photocatalytic Reduction of Cr(VI) by Porous Hollow Ga2O3 Nanoparticles

Science.gov (United States)

Liu, Jin; Gan, Huihui; Wu, Hongzhang; Zhang, Xinlei; Zhang, Jun; Li, Lili; Wang, Zhenling

2018-01-01

Porous hollow Ga2O3 nanoparticles were successfully synthesized by a hydrolysis method followed by calcination. The prepared samples were characterized by field emission scanning electron microscope, transmission electron microscope, thermogravimetry and differential scanning calorimetry, UV-vis diffuse reflectance spectra and Raman spectrum. The porous structure of Ga2O3 nanoparticles can enhance the light harvesting efficiency, and provide lots of channels for the diffusion of Cr(VI) and Cr(III). Photocatalytic reduction of Cr(VI), with different initial pH and degradation of several organic substrates by porous hollow Ga2O3 nanoparticles in single system and binary system, were investigated in detail. The reduction rate of Cr(VI) in the binary pollutant system is markedly faster than that in the single Cr(VI) system, because Cr(VI) mainly acts as photogenerated electron acceptor. In addition, the type and concentration of organic substrates have an important role in the photocatalytic reduction of Cr(VI). PMID:29690548

The entropy dissipation method for spatially inhomogeneous reaction-diffusion-type systems

KAUST Repository

Di Francesco, M.

2008-12-08

We study the long-time asymptotics of reaction-diffusion-type systems that feature a monotone decaying entropy (Lyapunov, free energy) functional. We consider both bounded domains and confining potentials on the whole space for arbitrary space dimensions. Our aim is to derive quantitative expressions for (or estimates of) the rates of convergence towards an (entropy minimizing) equilibrium state in terms of the constants of diffusion and reaction and with respect to conserved quantities. Our method, the so-called entropy approach, seeks to quantify convergence to equilibrium by using functional inequalities, which relate quantitatively the entropy and its dissipation in time. The entropy approach is well suited to nonlinear problems and known to be quite robust with respect to model variations. It has already been widely applied to scalar diffusion-convection equations, and the main goal of this paper is to study its generalization to systems of partial differential equations that contain diffusion and reaction terms and admit fewer conservation laws than the size of the system. In particular, we successfully apply the entropy approach to general linear systems and to a nonlinear example of a reaction-diffusion-convection system arising in solid-state physics as a paradigm for general nonlinear systems. © 2008 The Royal Society.

Hadron–Quark Combustion as a Nonlinear, Dynamical System

Science.gov (United States)

Ouyed, Amir; Ouyed, Rachid; Jaikumar, Prashanth

2018-03-01

The hadron-quark combustion front is a system that couples various processes, such as chemical reactions, hydrodynamics, diffusion, and neutrino transport. Previous numerical work has shown that this system is very nonlinear, and can be very sensitive to some of these processes. In these proceedings, we contextualize the hadron-quark combustion as a nonlinear system, subject to dramatic feedback triggered by leptonic weak decays and neutrino transport.

Lithiation Kinetics in High-Performance Porous Vanadium Nitride Nanosheet Anode

International Nuclear Information System (INIS)

Peng, Xiang; Li, Wan; Wang, Lei; Hu, Liangsheng; Jin, Weihong; Gao, Ang; Zhang, Xuming; Huo, Kaifu; Chu, Paul K.

2016-01-01

Vanadium nitride (VN) is promising in lithium ion battery (LIB) anode due to its high energy density, chemical stability, and corrosion resistivity. Herein, porous VN nanosheets are synthesized hydrothermally followed by an ammonia treatment. The porous nanosheets offer a large interfacial area between the electrode and electrolyte as well as short Li + diffusion path and consequently, the VN nanosheets electrode has high capacity and rate capability as an anode in LIB. The VN anode delivers a high reversible capacity of 455 mAh g −1 at a current density of 100 mA g −1 and it remains at 341 mAh g −1 when the current density is increased to 1 A g −1 . The charge transfer and Li + diffusion kinetics during the lithiation process is studied systematically. A highly stable SEI film is formed during the initial discharging-charging cycles to achieve a long cycle life and sustained capacity at a high level for 250 discharging-charging cycles without deterioration. This work demonstrates the preparation of high-performance LIB anode materials by a simple method and elucidates the lithiation kinetics.

MATHEMATICAL FRAMEWORK OF THE WELL PRODUCTIVITY INDEX FOR FAST FORCHHEIMER (NON-DARCY) FLOWS IN POROUS MEDIA

KAUST Repository

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

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.

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

Matrix Diffusion for Performance Assessment - Experimental Evidence, Modelling Assumptions and Open Issues

Energy Technology Data Exchange (ETDEWEB)

Jakob, A

2004-07-01

In this report a comprehensive overview on the matrix diffusion of solutes in fractured crystalline rocks is presented. Some examples from observations in crystalline bedrock are used to illustrate that matrix diffusion indeed acts on various length scales. Fickian diffusion is discussed in detail followed by some considerations on rock porosity. Due to the fact that the dual-porosity medium model is a very common and versatile method for describing solute transport in fractured porous media, the transport equations and the fundamental assumptions, approximations and simplifications are discussed in detail. There is a variety of geometrical aspects, processes and events which could influence matrix diffusion. The most important of these, such as, e.g., the effect of the flow-wetted fracture surface, channelling and the limited extent of the porous rock for matrix diffusion etc., are addressed. In a further section open issues and unresolved problems related to matrix diffusion are mentioned. Since matrix diffusion is one of the key retarding processes in geosphere transport of dissolved radionuclide species, matrix diffusion was consequently taken into account in past performance assessments of radioactive waste repositories in crystalline host rocks. Some issues regarding matrix diffusion are site-specific while others are independent of the specific situation of a planned repository for radioactive wastes. Eight different performance assessments from Finland, Sweden and Switzerland were considered with the aim of finding out how matrix diffusion was addressed, and whether a consistent picture emerges regarding the varying methodology of the different radioactive waste organisations. In the final section of the report some conclusions are drawn and an outlook is given. An extensive bibliography provides the reader with the key papers and reports related to matrix diffusion. (author)

Stability of quasi-steady deflagrations in confined porous energetic materials

Energy Technology Data Exchange (ETDEWEB)

Alexander M. Telengator; Stephen B. Margolis; Forman A. Williams

2000-03-01

Previous analyses have shown that unconfined deflagrations propagating through both porous and nonporous energetic materials can exhibit a thermal/diffusive instability that corresponds to the onset of various oscillatory modes of combustion. For porous materials, two-phase-flow effects, associated with the motion of the gas products relative to the condensed material, play a significant role that can shift stability boundaries with respect to those associated with the nonporous problem. In the present work, additional significant effects are shown to be associated with confinement, which produces an overpressure in the burned-gas region that leads to reversal of the gas flow and hence partial permeation of the hot gases into the unburned porous material. This results in a superadiabatic effect that increases the combustion temperature and, consequently, the burning rate. Under the assumption of gas-phase quasi-steadiness, an asymptotic model is presented that facilitates a perturbation analysis of both the basic solution, corresponding to a steadily propagating planar combustion wave, and its stability. The neutral stability boundaries collapse to the previous results in the absence of confinement, but different trends arising from the presence of the gas-permeation layer are predicted for the confined problem. Whereas two-phase-flow effects are generally destabilizing in the unconfined geometry, the effects of increasing overpressure and hence combustion temperature associated with confinement are shown to be generally stabilizing with respect to thermal/diffusive instability, analogous to the effects of decreasing heat losses on combustion temperature and stability in single-phase deflagrations.

Solute transport in aggregated and layered porous media

International Nuclear Information System (INIS)

Koch, S.

1993-01-01

This work is a contribution to research in soil physics dealing with solute transport in porous media. The influence of structural inhomogeneities on solute transport is investigated. Detailed experiments at the laboratory scale are used to enlighten distinct processes which cannot be studied separately at field scale. Two main aspects are followed up: (i) to show the influence of aggregation of a porous medium on breakthrough time and spreading of an inert tracer and consequences on the estimation of parameter values of models describing solute transport in aggregated systems, (ii) to investigate the influences on the dispersion process when stratification is perpendicular to the direction of flow. Several concepts of modelling solute transport in soil are discussed. Models based on the convection-dispersion equation (CDE) are emphasized because they are used here to model solute transport experiments conducted with aggregated porous media. Stochastic concepts are introduced to show the limitations of the deterministic CDE approaches. Experiments are done in columns containing two kinds of solid phases and were saturated with water. The solid phases are porous and solid glass beads exhibiting a distinctly unimodal or bimodal pore size distribution. Experimental breakthrough curves (BTCs) are modelled with the CDE, a bicontinuum model with a phenomenological mass transfer rate and a bicontinuum spherical diffusion model. Experiments are also done in columns that are unsaturated containing porous materials that are layered. Flow is made at a steady rate. It is shown that layer boundaries have a severe influence on lateral mixing. They may force streamlines to converge or cause a lateral redistribution of solutes. (author) figs., tabs., 122 refs

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

Optical performance of hybrid porous silicon-porous alumina multilayers

Science.gov (United States)

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.

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 - δui = ui+1Pi(x0, t), (i = 1,...,k, uk+1 := uu) in Ω × (0, T) with boundary conditions ui = 0 on ∂Ω × [0, T). We show that the solution has a global blowup. The exact rate...

Laser-beam-induced current mapping evaluation of porous silicon-based passivation in polycrystalline silicon solar cells

Energy Technology Data Exchange (ETDEWEB)

Rabha, M. Ben; Bessais, B. [Laboratoire de Nanomateriaux et des Systemes pour l' Energie, Centre de Recherches et des Technologies de l' Energie - Technopole de Borj-Cedria BP 95, 2050 Hammam-Lif (Tunisia); Dimassi, W.; Bouaicha, M.; Ezzaouia, H. [Laboratoire de photovoltaique, des semiconducteurs et des nanostructures, Centre de Recherches et des Technologies de l' Energie - Technopole de Borj-Cedria BP 95, 2050 Hammam-Lif (Tunisia)

2009-05-15

In the present work, we report on the effect of introducing a superficial porous silicon (PS) layer on the performance of polycrystalline silicon (pc-Si) solar cells. Laser-beam-induced current (LBIC) mapping shows that the PS treatment on the emitter of pc-Si solar cells improves their quantum response and reduce the grain boundaries (GBs) activity. After the porous silicon treatment, mapping investigation shows an enhancement of the LBIC and the internal quantum efficiency (IQE), due to an improvement of the minority carrier diffusion length and the passivation of recombination centers at the GBs as compared to the reference substrate. It was quantitatively shown that porous silicon treatment can passivate both the grains and GBs. (author)

Soft tissue deformation modelling through neural dynamics-based reaction-diffusion mechanics.

Science.gov (United States)

Zhang, Jinao; Zhong, Yongmin; Gu, Chengfan

2018-05-30

Soft tissue deformation modelling forms the basis of development of surgical simulation, surgical planning and robotic-assisted minimally invasive surgery. This paper presents a new methodology for modelling of soft tissue deformation based on reaction-diffusion mechanics via neural dynamics. The potential energy stored in soft tissues due to a mechanical load to deform tissues away from their rest state is treated as the equivalent transmembrane potential energy, and it is distributed in the tissue masses in the manner of reaction-diffusion propagation of nonlinear electrical waves. The reaction-diffusion propagation of mechanical potential energy and nonrigid mechanics of motion are combined to model soft tissue deformation and its dynamics, both of which are further formulated as the dynamics of cellular neural networks to achieve real-time computational performance. The proposed methodology is implemented with a haptic device for interactive soft tissue deformation with force feedback. Experimental results demonstrate that the proposed methodology exhibits nonlinear force-displacement relationship for nonlinear soft tissue deformation. Homogeneous, anisotropic and heterogeneous soft tissue material properties can be modelled through the inherent physical properties of mass points. Graphical abstract Soft tissue deformation modelling with haptic feedback via neural dynamics-based reaction-diffusion mechanics.

Diffusive limits for linear transport equations

International Nuclear Information System (INIS)

Pomraning, G.C.

1992-01-01

The authors show that the Hibert and Chapman-Enskog asymptotic treatments that reduce the nonlinear Boltzmann equation to the Euler and Navier-Stokes fluid equations have analogs in linear transport theory. In this linear setting, these fluid limits are described by diffusion equations, involving familiar and less familiar diffusion coefficients. Because of the linearity extant, one can carry out explicitly the initial and boundary layer analyses required to obtain asymptotically consistent initial and boundary conditions for the diffusion equations. In particular, the effects of boundary curvature and boundary condition variation along the surface can be included in the boundary layer analysis. A brief review of heuristic (nonasymptotic) diffusion description derivations is also included in our discussion

A scalable variational inequality approach for flow through porous media models with pressure-dependent viscosity

Science.gov (United States)

Mapakshi, N. K.; Chang, J.; Nakshatrala, K. B.

2018-04-01