Pumping of electrolytes by electrical forces induced on the diffusion layer: A weakly nonlinear analysis

Pumping of electrolytes in microchannels can be achieved with the use of microelectrodes subjected to AC potentials. Experiments have shown an influence of Faradaic currents in the pumping performance, and theoretical studies for asymmetric electrolytes suggest that induced charges in the diffusion layer play an important role. In this work we consider the case of a diffusion layer induced by an array of electrodes subjected to a traveling wave potential and we include Faradaic currents. Previous theoretical studies considered the case of very small applied voltages, which allowed for two major simplifications: (i) Butler-Volmer (B-V) equation was linearized, and (ii) the presence of gradients in ion concentration was neglected. We extend previous results and used the full nonlinear B-V equation. A comparison with the linear limit shows that the flow rate in both cases coincides for voltages around and below ≈0.25 V. For voltages larger than this, the nonlinear equations show that gradients in ion concentration appear and have an important influence, therefore, the predictions deviate from the linear model. We show that the electrical force in the diffusion layer can induce pumping either in the same or the opposite direction of the applied traveling-wave potential and it could be responsible for the reversal of the flow as observed in experiments.