# Interfacial transport with mobile surface charges and consequences for ionic transport in carbon nanotubes

## TL;DR

This study investigates how mobile surface charges influence ionic and fluid transport at interfaces, revealing modifications to boundary conditions and transport efficiencies, especially in carbon nanotubes, with implications for electrokinetic applications.

## Contribution

It introduces a model accounting for finite surface charge mobility affecting interfacial transport and modifies hydrodynamic boundary conditions in electrokinetic systems.

## Key findings

- Surface charge mobility reduces slip length inversely with surface charge.
- Mobility moderates interfacial slippage effects on transport.
- Non-linear electrostatic effects are crucial for accurate predictions.

## Abstract

In this paper, we explore the effect of a finite surface charge mobility on the interfacial transport: conductance, streaming currents, electro- and diffusio-osmotic flows. We first show that the surface charge mobility modifies the hydrodynamic boundary condition for the fluid, which introduces a supplementary term depending on the applied electric field. In particular, the resulting slip length is found to decrease inversely with the surface charge. We then derive expressions for the various transport mobilities, high-lighting that the surface charge mobility merely moderates the amplification effect of interfacial slippage, to the noticeable exception of diffusio-osmosis and surface conductance. Our calculations, obtained within Poisson-Boltzmann framework, highlight the importance of non-linear electrostatic contributions to predict the small concentration/large charge limiting regimes for the transport mobilities. We discuss these predictions in the context of recent electrokinetic experiments with carbon nanotubes.