Diffusion in porous media of a random structure

Abstract

The present paper deals with diffusion in a porous solid, which is considered as a discrete random medium composed of random structural elements (pores) chaotically connected with each other. Each structural element is characterized by the passage time distribution function calculated with taking into account the correlations of flows passing through the neighboring pores. The analysis of a nonstationary diffusion process, after transition to the limit of times much exceeding the mean passage time of a single pore, enables to obtain general expressions connecting the effective diffusivity in a porous medium with the statistical parameters of structural elements. At the same time the values are calculated which characterize the deviation of the concentration distribution in a porous medium from the gaussian one obtained as a solution of the quasi-homogeneous diffusion equation. To make the general expressions more concrete it is necessary to introduce a model of structural elements (pores) which determines the passage time distribution. The models of straight and corrugated pores considered yield expressions for the effective diffusion coefficient in the Fick and Knudsen regions. A similar analysis of the nonstationary diffusion accompanied by the first order reaction allows to get the expression for the effective rate constant of the catalytic reaction in a porous medium.