Existence of a maximum flow rate in electro-osmotic systems

TL;DR

This paper demonstrates the existence of a maximum electro-osmotic flow rate in ionic systems influenced by wall-fluid friction, supported by theoretical derivations and molecular dynamics simulations, highlighting the importance of slip boundary conditions.

Contribution

The work introduces a theoretical prediction of a maximum flow rate in electro-osmotic systems and validates it through molecular dynamics simulations, emphasizing the role of slip length and electrostatic screening.

Findings

Maximum flow rate exists under certain conditions.

Hydrodynamic slip length correlates with electrostatic screening.

Theory aligns with simulations for small charge densities.

Abstract

In this work, we investigate the effect of the hydrodynamic wall-fluid friction in electro-osmotic flows. First, we present the solution to the electro-hydrodynamic equation for the electro-osmotic velocity profile, which is derived for an ionic system composed of cations immersed in uncharged solvent particles. The system (solution and walls) is kept electrically neutral using negatively charged walls and will here be referred to as a "counterion-only" system. The theory predicts the existence of a counterion concentration that results in a maximum electro-osmotic flow rate, but only if the wall-fluid friction, or equivalently the slip length, is correlated with the system electrostatic screening length. Through equilibrium molecular dynamics simulations we precisely determine the hydrodynamic slip from the wall-fluid friction, and this is then used as input to the theoretical predictions. Comparison between the theory and independent non-equilibrium molecular dynamics simulation data confirms the existence of the maximum. Also, we find that standard hydrodynamic theory quantitatively agrees with simulation results for charged nanoscale systems for sufficiently small charge densities and ion charges, if the correct slip boundaries are applied.