Non-linear boundary condition for non-ideal electrokinetic equations in porous media

This paper studies the partial differential equation describing charge distribution of an electrolyte in a porous medium. Realistic non-ideal effects are incorporated through mean spherical approximation (MSA) model which takes into account finite size ions and screening effects. The main novelty is consideration non-constant surface density on pore walls. Indeed, chemical equilibrium reaction considered boundary to represent dissociation ionizable sites solid thus given as non-linear function electrostatic potential. Even ideal case, resulting system new variant famous Poisson–Boltzmann equation, still has monotone structure under quantitative assumptions physical parameters. In MSA brings additional non-linearities break down system. We prove existence, sometimes uniqueness, solution. Some numerical experiments performed 2d compare this with that for constant charge.