Justification of a New Original Homogenized Model for Ionic Diffusion in Porous Media

Abstract

In this work, a new original justification of an homogenized model for ionic diffusion in porous media is proposed. The approach used enables to specify clearly the domain of validity of this homogenized model, involving a source term characterizing the electrical double layer effect at the macroscale. This homogenized model is obtained from the formal periodic homogenization of a Nernst–Planck–Poisson system at the pore scale accounting for conductivity of the solid phase which is generally neglected. The Poisson equation is defined in both fluid and solid phases and the discontinuity of fluxes at the solid–fluid interface is modeled by a jump of the electrical field, linked to the surface electrical charge of the solid interface. Numerical simulations are carried out at the scale of the unit cell to underscore the influence of the contrast on the electrical permittivity between fluid and solid phases. The comparison of the concentrations and the electrical potential given at the macroscale by the homogenized model and by a direct pore scale model reveals the accuracy of the homogenized model which is very simple to use.