  We consider a nonlinear drift-diffusion system for multiple charged species
in a porous medium in 2D and 3D with periodic microstructure. The system
consists of a transport equation for the concentration of the species and
Poisson's equation for the electric potential. The diffusion terms depend
nonlinearly on the concentrations. We consider non-homogeneous Neumann boundary
condition for the electric potential. The aim is the rigorous derivation of an
effective (homogenized) model in the limit when the scale parameter $\epsilon$
tends to zero. This is based on uniform $\textit{a priori}$ estimates for the
solutions of the microscopic model. The crucial result is the uniform
$L^\infty$-estimate for the concentration in space and time. This result
exploits the fact that the system admits a nonnegative energy functional which
decreases in time along the solutions of the system. By using weak and strong
(two-scale) convergence properties of the microscopic solutions, effective
models are derived in the limit $\epsilon \to 0$ for different scalings of the
microscopic model.
