A volume averaging approach for asymmetric diffusion in porous media (original) (raw)
Related papers
Diffusion in anisotropic porous media
Transport in Porous Media, 1987
An experimental system was constructed in order to measure the two distinct components of the effective diffusivity tensor in transversely isotropic, unconsolidated porous media. Measurements were made for porous media consisting of glass spheres, mica particles, and disks made from mylar sheets. Both the particle geometry and the void fraction of the porous media were determined experimentally, and theoretical calculations for the two components of the effective diffusivity tensor were carried out. The comparison between theory and experiment clearly indicates that the void fraction and particle geometry are insufficient to characterize the process of diffusion in anisotropic porous media
Diffusion in isotropic and anisotropic porous systems: Three-dimensional calculations
Transport in Porous Media, 1993
Effective diffusion coefficients were calculated numerically for three-dimensional unit cells representative of different unconsolidated porous media. These numerical results were compared with the experimental results of Kim for packed beds of glass spheres, mica particles, and an artificial porous medium composed of mylar disks. These three-dimensional numerical results confirm that the porosity is the essential parameter for the determination of the effective diffusion coefficient in the case of unconsolidated isotropic systems. In the case of anisotropic systems, better agreement is obtained between numerical predictions and actual data when the unit cell is three-dimensional rather than twodimensional. This emphasizes the fact that three-dimensional unit cells feature more realistic geometrical properties which are needed to accurately describe anisotropic systems.
A Theory of Diffusion and Reaction in Porous Media
The process of diffusion and heterogeneous reaction is analyzed using the method of volume averaging. Closure is obtained in terms of the solution of two associated transport equations used to predict the spatial deviation of the concentration.
On diffusion, dispersion and reaction in porous media
Chemical Engineering Science, 2011
The upscaling process of mass transport with chemical reaction in porous media is carried out using the method of volume averaging under diffusive and dispersive conditions. We study cases in which the (first-order) reaction takes place in the fluid that saturates the porous medium or when the reaction occurs at the solid-fluid interface. The upscaling process leads to average transport equations, which are expressed in terms of effective medium coefficients for (diffusive or dispersive) mass transport and reaction that are computed by solving the associated closure problems. Our analysis shows that these effective coefficients depend, in general, upon the nature and magnitude of the microscopic reaction rate as well as of the essential geometrical structure of the solid matrix and the flow rate. This study also shows that if the reaction rate at the microscale is arbitrarily large, the capabilities of the upscaled models are hindered, which is in agreement with the breakdown of the physical sense of the microscale formulation.
Bulk and surface diffusion in porous media: An application of the surface-averaging theorem
Chemical Engineering Science, 1993
A general treatment of bulk and surface diffusion is presented in terms of the method of volume averaging. In addition to the spatial-averaging theorem, the analysis requires the surface-averaging theorem, which is derived using only routine three-space vector analysis. The closure problem is formulated and overall effective diffusivities are calculated using Chang's unit cell, which leads to Maxwell's model.
Biophysical Journal, 1992
The effect of spatially varying diffusivity and solubility on the efficiency of intramembrane transport is investigated by obtaining solutions to the generalized lateral diffusion equation in which both the diffusion coefficient, D(r), and the partition coefficient, K(r), are functions of position. The meantime to capture by a sink, tc, of particles diffusing in a plane is obtained analytically for the case of a sink surrounded by gradients in D(r) and K(r) with radially symmetrical geometry. It is shown that for particles originating at random locations, tc is shortened dramatically, if in an annular region around the sink, D and K are significantly greater than in the remainder of the plane. Similarly, a viscous boundary layer-surrounding a sink is demonstrated to represent a significant barrier for diffusing particles. To investigate more complex geometries, a finite difference numencal integration method is used and is shown to provide comparable results for tc with modest computational power. The same methodc is used to calculate the tc for particles originating at a source that is joined to the sink by a channel. The increase in the rate with which particles travel from a source to a sink when they are joined by a high diffusivity and/or solubility channel is illustrated by several numerical examples and by graphical representations that show the equilibrium particle density (and hence the effective particle flow) in the presence of different sink, source, and channel combinations. These results are discussed in terms of fluidity domains and other membrane heterogeneities.
Diffusion in complementary pore spaces
Adsorption, 2016
The rate of mass transfer is among the key numbers determining the efficiency of nanoporous materials in their use for matter upgrading by heterogeneous catalysis or mass separation. Transport enhancement by pore space optimization is, correspondingly, among the main strategies of efficiency promotion. Any such activity involves probing and testing of the appropriate routes of material synthesis and post-synthesis modification just as the exploration of the transport characteristics of the generated material. Modelling and molecular simulation is known to serve as a most helpful tool for correlating these two types of activities and their results. The present paper reports about a concerted research activity comprising these three types of activities. Recent progress in producing pore space replicas enabled focusing, in these studies, on ''complementary'' pore spaces, i.e. on pairs of material, where the pore space of one sample did just coincide with the solid space of the other. We report about the correlations in mass transfer as observable, in this type of material, by pulsed field gradient NMR diffusion studies, with reference to the prediction as resulting from a quite general, theoretical treatment of mass transfer in complementary pore spaces.
Mathematical modeling of anomalous diffusion in porous media
Fractional Differential Calculus, 2011
Analysis of diffusion in a complex environment shows that the conventional diffusion equation based on Fick's law fails to model the anomalous character of the diffusive mass transport observed in the field and laboratory experiments. New mathematical models of diffusive transport, different from Fick's law, were proposed and validated in literature. In the present paper the examples of the equations that can be used for describing the anomalous mass transport are presented and some important properties of these equations are discussed. Two regimes of anomalous diffusion are identified. One regime, which is called sub-diffusion, is characterized by the slower propagation of the concentration front, so that the squared distance of the front passage requires longer time than in the case of the classical Fickian diffusion. The second regime (called super-diffusion) is characterized by the higher diffusion rate, so that the particles will pass the specified distance faster than in the case of classical Fickian diffusion. Both regimes can be modeled by non-local diffusion equation with temporal and spatial fractional derivatives. It is shown that equation with spatially variable diffusivity proposed by O'Shaughnessy and Procaccia (1985), which provides a relatively good model of diffusion on a regular fractal, is less applicable for describing the effects of sub and super diffusion that may take place in a fractured porous medium or any other complex medium.
Water Resources Research, 2013
Diffusive mass transfer into and out of intragranular micropores (''intragranular diffusion'') plays an important role in the transport of some groundwater contaminants. We are interested in understanding the combined effect of pore-scale advection and intragranular diffusion on solute transport at the effective porous medium scale. We have developed a 3-D pore-scale numerical model of fluid flow and solute transport that incorporates diffusion into and out of intragranular pore spaces. A series of numerical experiments allow us to draw comparisons between macroscopic measures computed from the pore-scale simulations (such as breakthrough curves) and those predicted by multirate mass transfer formulations that assume complete local mixing at the pore scale. In this paper we present results for two model systems, one with randomly packed uniform spherical grains and a second with randomly packed spheres drawn from a binary grain size distribution. Non-Fickian behavior was observed at all scales considered, and most cases were better represented by a multirate mass transfer model even when there was no distinct secondary porosity (i.e., no intragranular diffusion). This suggests that pore-scale diffusive mass transfer processes between preferential flow paths and relatively immobile zones within the primary porosity may have significant impact on transport, particular in low-concentration tails. The application of independently determined mass transfer rate parameters based on an assumption of well-mixed concentrations at the pore scale tends to overestimate the amount of mass transfer that occurs in heterogeneous pore geometries in which preferential flow leads to incomplete pore-scale lateral mixing.
Diffusion coefficient in biomembrane critical pores
Journal of Bioenergetics and Biomembranes, 2017
Diffusion is fundamental to the random movement of solutes in solution throughout biological systems. Theoretical studies of diffusing solutes across cell membranes confined in a microscopic size of pores have been an interesting subject in life and medical sciences. When a solute is confined in a critical area of membrane pores, which shows a quite different behavior compared to the homogeneous-bulk fluid whose transport is isotropic in all directions. This property has novel features, which are of considerable physiological interest.