Diffusion in spatially varying porous media

Maria Bruna; S. Jonathan Chapman

doi:10.1137/141001834

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arXiv · 1501.06549

Diffusion in spatially varying porous media

Maria Bruna·S. Jonathan Chapman

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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.

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Maria Bruna, S. Jonathan Chapman. 2015-06-05. Diffusion in spatially varying porous media. https://doi.org/10.1137/141001834

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