The aim of this paper is to study the properties of Nernst-Planck-Poisson system describing the evolution of ionic concentrations in porous media. In particular, the well-posedness character of the system is proved and some qualitative properties of the global solution are established (energy and entropy laws, stationary states, Boltzmann distribution, influence of an external electrical field). We prove also that a superficial accumulation of ions occurs when an important external electrical field is applied.
Gagneux, G., & Millet, O. (2016). A survey on properties of Nernst-Planck-Poisson system. Application to ionic transport in porous media. Applied Mathematical Modelling, 40(2), 846–858. https://doi.org/10.1016/j.apm.2015.06.013