On diffusion in heterogeneous media

Abstract

Diffusion in heterogeneous solid media has been investigated for over forty years. However, the derived equations for bulk (or effective) diffusivity used similarity argument between diffusion and other physical properties such as electrical and thermal conductivity, and hence either implicitly or explicitly assumed that the concentrations are continuous across phase boundaries. That is, these derived relations, which have permeated through the literature and textbooks, can only be applied when the partition coefficients of the component between every pair of phases in the medium is 1, which is rarely the case. In this work, we include the effect of partitioning between different phases and present the method to derive the equations to relate bulk diffusivity to individual-phase diffusivities in heterogeneous media.