Nonlinear electrokinetics at large voltages

The classical theory of electrokinetic phenomena assumes a dilute solution of point-like ions in chemical equilibrium with a surface whose double-layer voltage is of order the thermal voltage, k(B)T/e = 25 mV. In nonlinear 'induced-charge' electrokinetic phenomena, such as ac electro-osmosis, several volts approximate to 100 k(B)T/e are applied to the double layer, and the theory breaks down and cannot explain many observed features. We argue that, under such a large voltage, counterions 'condense' near the surface, even for dilute bulk solutions. Based on simple models, we predict that the double-layer capacitance decreases and the electro-osmotic mobility saturates at large voltages, due to steric repulsion and increased viscosity of the condensed layer, respectively. The former suffices to explain observed high-frequency flow reversal in ac electro-osmosis; the latter leads to a salt concentration dependence of induced-charge flows comparable to experiments, although a complete theory is still lacking.