Enhanced zeta potentials caused by surface ion mobilities

TL;DR

This paper investigates how surface ion mobilities influence electro-osmotic flow, revealing that zeta potentials can be amplified beyond surface charges, especially in concentrated solutions or with large slip lengths.

Contribution

It introduces an effective slip boundary condition accounting for surface ion mobility and derives equations linking electrostatic properties to zeta potential enhancement.

Findings

Zeta potential can exceed surface charge, amplifying electro-osmotic flow.

Surface ion mobility is determined solely by electrostatic properties.

Amplification is strongest with large slip lengths and in concentrated solutions.

Abstract

The electro-hydrodynamics near conducting walls is revisited. Attention is focused on the impact of an explicit diffuse Stern layer, which permittivity and viscosity differ from the bulk values, on the velocity of an electro-osmotic plug flow. To solve this problem we propose an approach of mapping the flow in the Stern layer to the surface dividing the Stern and diffuse layer, where an effective electro-hydrodynamic slip boundary condition is imposed. The latter implies that an effective surface charge is responding to the applied field and characterized by a mobility parameter $\mu \geq 1$. We derive analytic equations for $\mu$ and demonstrate that it is determined only by electrostatic properties of the electric double layer. These equations are then used to calculate electrokinetic (zeta) potentials of surfaces. We show that the zeta potential generally exceeds the surface one, which implies an amplification of the electro-osmotic flow. This effect is most pronounced if the hydrodynamic slip length is large and/or in concentrated solutions.