Modeling and deriving porous media Stokes-Poisson-Nernst-Planck equations by a multi-scale approach (Q357466)

The author presents the derivation of the Poisson-Nernst-Planck (PNP) equations which describe electrolytes in porous media. On the interface between solid and liquid phase is imposed the Lipschitz continuity. In order to study the limit problem, in the framework of homogenization theory, the two-scale convergence method is performed with a periodic description of the medium, which statistically represents the microstructure. Finally the author extends this approach by including a fluid flow for small velocities and small length scales. Coupling together fluid flow and porous media equations the periodic formulation of Stokes-Poisson-Nernst-Planck system is achieved by a convective term and suitable boundary conditions.