Effects of membrane polarization, steric repulsion and ion-solvent interactions on electroosmosis through a conical nanopore

Abstract

The impact of solid polarization of a dielectric membrane on ion transport in a conical nanopore drilled through a membrane is studied by considering ions as finite-sized dielectric charged spheres. The excess polarization of the hydrated ions creates a dielectric decrement. A mean-field-based approach is adopted by modifying the Nernst-Planck equation to incorporate the ion steric interactions, the Born force, and the dielectrophoretic force arising due to the spatial variation of electrolyte permittivity. The viscosity of the medium is considered to vary with the local ionic concentration through the Bachelor-Green equation, which leads to a reduction in the mobility of ions near a charged surface. Governing equations are solved numerically through the control volume method along with a pressure-correction-based iterative algorithm. The solid polarization of the membrane, which is often neglected in existing studies, is found to have a strong impact on the volume flux, conductance, selectivity, and ion current rectification in the conical nanopore. The ion saturation in the vicinity of the charged surface, as governed by the present modified model, creates a pronounced alteration in the electrokinetics compared to that predicted by the standard Poisson-Nernst-Planck (PNP-model) based on the point charge consideration of ions. This discrepancy due to ion steric repulsion and ion-solvent interactions is pronounced at a higher ionic concentration as well as a highly polarizable surface. A close agreement between the predictions of the present modified model and the existing experimental data, compared with that of the standard PNP model, is encouraging. The present modified model provides an accurate analysis of the electroosmotic flow and ion transport in a dielectric charged conical nanopore beyond the low charge density and dilute solution limits.