We perform the periodic homogenization (i.e. e¿0) of a non-stationary Stokes–Nernst–Planck–Poisson system using two-scale convergence, where e is a suitable scale parameter. The objective is to investigate the influence of different boundary conditions and variable choices of scalings 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 electrostatic drift term. As a direct result of the homogenization procedure, various classes of upscaled model equations are obtained.
Ray, N., Muntean, A., & Knabner, P. (2012). Rigorous homogenization of a Stokes-Nernst-Planck-Poisson problem for various boundary conditions. Journal of Mathematical Analysis and Applications, 390(1), 374-393. https://doi.org/10.1016/j.jmaa.2012.01.052