Electric field effects on the ionic relaxation in a finite slab adsorbing cell

This paper is a natural continuation of the study done in Scarfone et al (2026 Electric field effects on the ionic relaxation in a semi-infinite adsorbing cell J. Phys. A: Math. Theor. 59 205201). We analyze the distribution of mobile charges for a slab geometry with well-defined thickness under selectively adsorbing surfaces. For simplicity, only positive charges are considered mobile. The full scenario is characterized by bulk drift and diffusion, together with selective charge adsorption at the surfaces. The problem is addressed within the Poisson–Nernst–Planck model framework, in which the continuity equation for the mobile charges is coupled to Poisson’s equation, while the Langmuir balance equation governs selective adsorption at the surface. The time evolution of the system in the presence of an external power supply, as well as the dependence of the longest relaxation time on the applied potential difference, are also analyzed.