Nonlinear ionic diffusion through charged polymeric gels

Abstract

The problem associated with the diffusion of ions through a charged macromolecular gel is investigated. The model consists of Poisson's equation for the electric potential and a diffusion equation for the concentration of diffusing ions. This nonlinear system is reduced using homogenization to a simple linear macroscopic diffusion equation where the diffusion coefficients are found from the solution of a nonlinear problem at the microstructural level. The latter is solved numerically to illustrate the dependence of the diffusion coefficients on valency and concentration. The equations analyzed here are also very similar to those that arise in the study of semiconductors, specifically, in a no-recombination model of charge carriers.