On Diffusion in Heterogeneous Media

On Diffusion in Heterogeneous Media

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.

非均相固体介质中的扩散已经被研究了四十多年。然而，所推导的体（或有效）扩散系数方程利用了扩散与其他物理性质（如电导率和热导率）之间的相似性论据，因此隐含或明确地假设浓度在相界处是连续的。也就是说，这些贯穿于文献和教科书中的推导关系，只有当介质中每对相之间的组分分配系数为1时才能应用，而这种情况很少见。在这项工作中，我们考虑了不同相之间分配的影响，并提出了推导方程的方法，以将非均相介质中的体扩散系数与各相扩散系数联系起来。