Diffusion in spatially varying porous media

TL;DR

This paper investigates how diffusion behaves in porous media with spatially varying porosity, using two different analytical approaches to calculate the effective diffusion coefficient and comparing their results.

Contribution

It introduces and compares deterministic and stochastic methods for calculating effective diffusion in microstructured porous media with spatially varying porosity.

Findings

Good agreement between the two approaches in example configurations

Methods are generalizable beyond the specific microstructure analyzed

Provides a framework for analyzing diffusion in complex porous structures

Abstract

The problem of diffusion in a porous medium with a spatially varying porosity is considered. The particular microstructure analyzed comprises a collection of impenetrable spheres, though the methods developed are general. Two different approaches for calculating the effective diffusion coefficient as a function of the microstructure are presented. The first is a deterministic approach based on the method of multiple scales; the second is a stochastic approach for small volume fraction of spheres based on matched asymptotic expansions. We compare the two approaches, and we show good agreement between them in a number of example configurations.