Homogenization of the generalized Poisson–Nernst–Planck problem in two-phase medium: The corrector due to nonlinear interface condition

Abstract

The paper deals with homogenization of the generalized Poisson–Nernst–Planck problem stated in the disconnected domain composed of solid and pore phases. The nonlinear cross-diffusion transport equations are coupled with the Stokes flow model. At the interface between two phases, field variables are discontinuous allowing jumps, and nonlinear interface conditions describing electro-chemical reactions are taken into consideration. The first-order asymptotic corrector corresponding to the non-periodic interface data is derived rigorously and justified by residual error estimates within the homogenization procedure.