We perform the periodic homogenization (i. e. e ¿ 0) of the non-stationary Nernst-Planck-Poisson system using two-scale convergence, where e is a suitable scale parameter. The objective is to investigate the influence of variable choices of scaling in e of the microscopic system of partial differential equations on the structure of the (upscaled) limit model equations. Due to the specific nonlinear coupling of the underlying equations, special attention has to be paid when passing to the limit in the electric drift term. As a direct result of the homogenization procedure, various classes of upscaled model equations are obtained.
Keywords: Homogenization, two-scale convergence, porous media, Nernst-Planck-Poisson
system, colloidal transport
|Name||Preprints des Instituts für Angewandte Mathematik der Universität Erlangen-Nürnberg|