Effects of ion sizes on Poisson–Nernst–Planck systems with multiple ions

Abstract

In this work, we analyze a one‐dimensional version of steady‐state Poisson–Nernst–Planck models for ionic flow through a membrane channel including ionic interactions modeled by the density functional theory. The model includes an arbitrary number of positively changed ions with the same valences and one negatively charged ion and ignores the permanent charge. The model can be viewed as a singularly perturbed differential system; therefore, our analysis is mainly based on the geometric singular perturbation theory. The existence and the uniqueness result for small ion sizes are established, and treating the sizes as small parameters, we also derive an approximation of the individual flux, the – (current–voltage) relation and the individual flux difference. Critical potentials are identified, and their roles in characterizing ionic flow properties are studied.