Homogenization of the generalized Poisson–Nernst–Planck problem in two-phase medium: The corrector due to nonlinear interface condition
Victor A. Kovtunenko, Anna V. Zubkova · AIP conference proceedings · 2019
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.