A numerical study supplemented with theoretical analysis on streaming potential in a soft nanochannel influenced by ion partitioning and mobile surface charge-dependent wall slip

Abstract

We consider the pressure-driven flow of an electrolyte in a soft channel with a hydrophobic charged surface coated with a diffuse polyelectrolyte layer (PEL) with constant volumetric charge density. The objectives are to enhance the streaming potential and electrochemical energy conversion efficiency in the modulated soft channel as well as to examine the influence of surface charge mobility-dependent slip velocity on the electrokinetics. The laterally mobile adsorbed surface charge modifies the slip velocity condition, which is coupled with the induced streaming potential. The ion partitioning effect arises due to the step change in dielectric constant between the PEL and the electrolyte that modifies the distribution of ions, which is incorporated through the Born energy difference of ions. The nonlinear coupled set of equations governing the electrokinetics in a soft channel is solved numerically through a control volume approach. A simplified model based on the Debye–Hückel approximation under certain limiting conditions is also derived, which compares well with the present numerical model for a lower range of charge density and non-overlapping Debye layers. We find that a modulation of a nanochannel by coating a PEL of lower dielectric constant on hydrophobic charged walls can significantly enhance the streaming current and energy conversion efficiency. In contrast with existing studies, we find that the mobile surface charge can have a positive impact on the electrochemical energy conversion efficiency in a soft nanochannel. The mobility of the surface charge attenuates the streaming current in a PEL-free channel and can enhance the streaming current for a suitable choice of PEL volumetric charge density.