Ionic transfer in charged porous media. Periodic homogenization and parametric study on 2D microstructures

In this paper we propose a macroscopic model for ionic diffusion in saturated porous media, taking into account the electrical double layer phenomenon. This model is established by periodic homogenization technique of Nernst–Planck and Poisson–Boltzmann equations at Debye length. The electrical double layer potential appears explicitly in the homogenized ionic diffusion equation and in the homogenized diffusion tensor expression. A numerical parametric study is conducted on more or less complex periodic microstructure to highlight the influence of electrocapillary interactions on the homogenized diffusion tensor and ionic transfer.