Electro-osmosis at inhomogeneous charged surfaces: hydrodynamic versus electric friction

Electrokinetic methods are efficient in probing the electrostatic surface properties of charged systems. However, anomalies observed in experiments indicate that the classical electrokinetic theory should be reconsidered. Using Green's function methods and hydrodynamic simulations, we investigate electro-osmosis driven by electric-field-induced ion motion near a charged planar substrate with smooth or rough boundary. First, a reformulation of electro-osmotic theory for planar charged surfaces employing Green's functions shows that the Helmholtz-Smoluchowski (HS) relation between electrostatic potential and solvent velocity is exact for smooth surfaces, even in the presence of ion correlations. Deviations from HS theory are caused by combined hydrodynamic and electric surface friction, as our hydrodynamic simulations of ions at smooth and corrugated charged surfaces in lateral electric fields demonstrate. Within the simulations, hydrodynamic interactions are treated in the continuum limit and the presence of a no-slip boundary condition at the surface is taken into account. While electrofriction is relevant in highly charged system and/or for multivalent ions, hydrodynamic friction is dominant in systems with moderate surface charge density and/or low ionic valency. We also derive the effective electrokinetic surface charge from the electro-osmotic solvent profiles, which is substantially reduced when compared with the bare value and shows qualitative agreement with the experimental tendency.