Impact of finite ion size, Born energy difference and dielectric decrement on the electroosmosis of multivalent ionic mixtures in a nanotube

Abstract

The electroosmotic flow (EOF) in a nanotube is analyzed by considering the finite ion size and dielectric decrement effects. The ion transport is governed by the modified Nernst-Planck equation, which takes into account the ion steric repulsion, Born energy difference, and dielectrophoretic force. The dielectric permittivity is considered to depend on the ionic concentration and ion size. The governing equations for fluid flow, ion transport, and electric field are solved numerically in their full form. The steric interaction is accounted, based on the Boublik–Mansoori–Carnahan–Starling–Leland (BMCSL) model, which considers the nonuniform ion size for monovalent as well as multivalent salts. We made a quantitative comparison with the standard PNP model for the lower range of charge density and highlighted the impact of ion size and dielectric decrement effects. For a highly charged surface, the impact due to finite ion size is non-negligible when the Debye length is in the order of the nanotube radius. However, the dielectric decrement is found to have a strong impact on a higher range of surface charge density or bulk ionic concentration. The EOF and the ion selectivity of the mixed electrolyte solution of different counterion size are considered in the present study. Present study provides an in-depth analysis of EOF through a cylindrical nanotube beyond the dilute solution and low charge density limits, which has not been addressed before.