Existence of a maximum flow rate in electro-osmotic systems

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 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 then, this is 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. In addition, we find that standard hydrodynamic theory quantitatively agrees with the simulation results for charged nanoscale systems for sufficiently small charge densities and ion charges, if the correct slip boundaries are applied.