Scale Analysis of Electrodiffusion Through Porous Media

Abstract

This paper is a fundamental analytical and numerical study of the electrical current effect on the diffusion of ions through porous media. The analytical part is based on scale analysis in the limit where the electrical current is the dominant drive force for ionic diffusion The scales of this regime are compared with the known scales of pure diffusion, where the dominant drive force is the concentration gradient. The new dimensionless group B that marks the transition between classical diffusion and electrodiffusion is identified: B is the ratio of the two characteristic time scales, the time of electrodiffusion divided by the time of pure diffusion. The numerical part is based on the Nernst-Planck equation for continuity, which is nondimensionalized based on the correct scales revealed by scale analysis. Numerical simulations conducted for several practical examples (e.g., extraction of an ionic species from a contaminated block) validate the predictions based on scale analysis, and confirm the correctness of both methods.