Scaling relations in shear electroconvective vortices

Abstract

This paper is devoted to the quantitative understanding of the electroosmotic slip velocity, which is the most essential physical quantity of shear electroconvective (SEC) microfluidics. It is well known that SEC instability caused by the electroosmotic slip velocity is triggered near the permselective membranes. Here, we present for the first time the unifying scaling relations of the electroosmotic slip velocity and overlimiting transport in SEC flow under the moderate voltage. The interplaying effects of the salt flux gradient and voltage result in a slip velocity that loses the pressure flow effect. Determined by both the applied potential and the electrolyte physical properties, the slip velocity is shown to scale as V4/3κ2/3, which deviates significantly from the relation of V2 reported in classical theory [I. Rubinstein and B. Zaltzman, “Equilibrium electroconvective instability,” Phys. Rev. Lett. 114(11), 114502 (2015)]. Since the convection flux and the electromigration flux reached an asymptotic equilibrium, a universal scaling κVPe1/3 was obtained for the overlimiting transport. Detailed direct numerical simulations in conjunction with existing experimental data [R. Kwak et al., “Shear flow of an electrically charged fluid by ion concentration polarization: Scaling laws for electroconvective vortices,” Phys. Rev. Lett. 110, 114501 (2013)] corroborate this novel scaling. Our theory provides a unified view and a perfect interpretation of the existing SEC microfluidics.