Reversal permanent charge and reversal potential: case studies via classical Poisson–Nernst–Planck models

In this work, we are interested in effects of a simple profile of permanent charges on ionic flows. We determine when a permanent charge produces current reversal. We adopt the classical Poisson–Nernst–Planck (PNP) models of ionic flows for this study. The starting point of our analysis is the recently developed geometric singular perturbation approach for PNP models. Under the setting in the paper for case studies, we are able to identify a single governing equation for the existence and the value of the permanent charge for a current reversal. A number of interesting features are established. The related topic on reversal potential can be viewed as a dual problem and is briefly examined in this work too.