  We consider the Poisson-Nernst-Planck system which is well-accepted for
describing dilute electrolytes as well as transport of charged species in
homogeneous environments. Here, we study these equations in porous media whose
electric permittivities show a contrast compared to the electric permittivity
of the electrolyte phase. Our main result is the derivation of convenient
low-dimensional equations, that is, of effective macroscopic porous media
Poisson-Nernst-Planck equations, which reliably describe ionic transport. The
contrast in the electric permittivities between liquid and solid phase and the
heterogeneity of the porous medium induce strongly oscillating electric
potentials (fields). In order to account for this special physical scenario, we
introduce a modified asymptotic multiple-scale expansion which takes advantage
of the nonlinearly coupled structure of the ionic transport equations. This
allows for a systematic upscaling resulting in a new effective porous medium
formulation which shows a new transport term on the macroscale. Solvability of
all arising equations is rigorously verified. This emergence of a new transport
term indicates promising physical insights into the influence of the microscale
material properties on the macroscale. Hence, systematic upscaling strategies
provide a source and a prospective tool to capitalize intrinsic scale effects
for scientific, engineering, and industrial applications.
