Homogenization of electro-diffusive transport in complex media

Abstract

Electro-diffusive transports in complex media are fundamental processes that occur naturally in the physical world, such as ion transport through biological ion channels of the cell membrane, transport in rocks, water purification etc. Mainly motivated by the ion transport through ion channels, in this talk we present a homogenization result for a nonlinear drift-diffusion system for multiple charged species in porous media. Furthermore, we derive an effective, dimension-reduced model for diffusive-reactive transport in two bulk regions, which are connected by an array of small channels located in a thin membrane, in the limit when the membrane reduces to an interface. The results are based on the derivation of estimates for the solutions uniformly with respect to the microscopic scale of the domain and two-scale convergence type arguments.