Studies on Ionic Flows via Poisson–Nernst–Planck Systems with Bikerman’s Local Hard-Sphere Potentials under Relaxed Neutral Boundary Conditions

Abstract

We examine the qualitative properties of ionic flows through ion channels via a quasi-one-dimensional Poisson–Nernst–Planck model under relaxed neutral boundary conditions. Bikerman’s local hard-sphere potential is included in the model to account for finite ion size effects. Our main interest is to examine the boundary layer effects (due to the relaxation of electroneutrality boundary conditions) on both individual fluxes and current–voltage relations systematically. Critical values of potentials are identified that play significant roles in studying internal dynamics of ionic flows. It turns out that the finite ion size can either enhance or reduce the ionic flow under different nonlinear interplays between the physical parameters in the system, particularly, boundary concentrations, boundary potentials, boundary layers, and finite ion sizes. Much more rich dynamics of ionic flows through membrane channels is observed.