General Properties of the Nernst-Planck-Poisson-Boltzmann System Describing Electrocapillary Effects in Porous Media

The Nernst-Planck-Poisson-Boltzmann system describes the evolution of ionic concentrations and electrocapillarity effects in porous media. The aim of this paper is a theoretical study of various drift-diffusion modellings. The well-posedness of the systems is proved and some qualitative properties of the global solution are shown to be satisfied (energy law, entropy law in the weak sense of Lyapunov functions, stationary states, Maxwellian distribution, influence of an external electric field). Moreover, some explicit solutions are established in the one-dimensional case.