Electrodiffusive transport in charged porous media: From the particle-level scale to the macroscopic scale using volume averaging

Abstract

The Poisson-Nernst-Planck (PNP) system of equations can be used to describe electro-diffusive multi-ion transport through uncharged porous materials. Phenomenological formulations have been proposed for charged porous media (e.g. clays), usually disregarding links to the particle level scale. However using volume averaging of microscale governing equations, we derive a new set of up-scaled generalized (macroscopic) PNP equations that are valid for both charged and uncharged porous materials. These equations consistently account for non-homogeneous ionic distributions at the microscale, but reduce standard phenomenological PNP equations for the special case of uncharged porous materials. With..