Regimes of streaming potential in cylindrical nano-pores in presence of finite sized ions and charge induced thickening: an analytical approach

Abstract

We obtain approximate analytical expressions for the streaming potential and the effective viscosity in a pure pressure-driven flow through a cylindrical pore with electrokinetic interactions, duly accounting for the finite size effects of the ionic species (steric effects) and charge-induced thickening. Our analytical results show a remarkable agreement with the numerical solution even for high surface potentials and small channel radii. We demonstrate a consistent increment in the predicted value of the streaming potential and effective viscosity when finite size effects of the ionic species are accounted for. In addition to this, we account for the radial variation of in the viscosity of the fluid due to charge-induced thickening. We show that this so-called viscoelectric effect leads to a decrease in the induced streaming potential especially at high steric factors and high surface potentials. However, the viscoelectric effect, which is prominent at high zeta potential and narrow channels, does not cause significant changes in the electrokinetic conversion efficiency. These results shed light on the interesting confluence of the steric factor, the channel radius, the electrical double layer screening length, and the surface charge density in conjunction with the charge induced thickening, and thus provide ion-size dependent analytical framework for accurate system design and better interpretation of electrokinetic data.