Diffusion in spatially varying porous media
Fluid Dynamics
2017-10-12 v2 Statistical Mechanics
Analysis of PDEs
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.
Cite
@article{arxiv.1501.06549,
title = {Diffusion in spatially varying porous media},
author = {Maria Bruna and S. Jonathan Chapman},
journal= {arXiv preprint arXiv:1501.06549},
year = {2017}
}