Modeling of electro-diffusive ion transport through charged porous materials using a multiscale iterative approach

摘要

The electro-diffusive transport behavior of ions through charged porous media is commonly described by phenomenological theories, directly formulated on the observation scale of the macroscopic material and disregarding the underlying physical principles known on the particle scale. In this paper, to remedy this deficit, a new approach is presented, by derivation of a generalized macroscopic mathematical framework valid for both charged and uncharged porous media, on the basis of classical Poisson and Nernst-Planck equations. Due to the distinctive nonlinearity of the sought-after quantities, an iterative, numerical two-scale homogenization scheme is employed for evaluation of the resulting governing equations, giving finally access to the effective macroscopic diffusion coefficients and fixed charge concentration as functions of the electrolyte background concentration and of the surface charge. While this methodology can be applied for a large number of different pore geometries, we restrict ourselves, for the time being, to linear cylindrical pores, to demonstrate the capability of the presented approach. For the chosen setup and boundary conditions, the applied two-scale model reveals deviations of the effective macroscopic diffusion coefficients from corresponding self-diffusion coefficients amounting to up to 12%. These results corroborate the relevance of the presented approach.