Stochastic theory of transport in inhomogeneous media

Abstract

Diffusive transport in porous media is analysed herein as a stochastic process by means of a formalism for self-correlated random walks. The usual effective diffusivity representation is rigorously justified upon passing to the continuum limit of the concentration field, and it is demonstrated that for random networks the resulting tortuosity is a process parameter dependent (weakly) on temperature, pressure and the diffusing species, and not a porous medium property alone. The predicted values of the tortuosity are found to be in the range of about 6-8 for pore size distributions typical of catalyst particles, and 30 and upwards for those corresponding to carbonaceous materials, consistent with experimental evidence.