  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.
