Diffusion in Spatially Varying Porous Media Seminar

We discuss the problem of diffusion in a porous medium with a spatially varying porosity. The particular microstructure we consider here comprises a collection of impenetrable spheres, though the methods developed are general. We present two different approaches for calculating the effective diffusion coefficient as a function of the microstructure. 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.