Recipes for mixing vortices in a microchannel using electric field

Abstract

Application of an electric field on the pressure-driven flow of a fluid inside a microchannel can create mixing vortices. The Coulombic force at electrode–fluid interface generates the additional stress to engender the instability. While the previous studies show the phenomena at the two-layer immiscible or miscible flows, we show the same for a single fluid system. Linear stability analysis (LSA), non-linear simulations, and experiments together uncover the conditions for onset and propagation of such instabilities with Reynolds (Re) and electric field Rayleigh (Raψ) numbers. The LSA uncover that a higher critical field (larger Racψ) is required to destabilize a flow with a higher flow rate (higher Re), highlighting the stabilizing nature of the inertia. Subsequently, the non-linear simulations and experiments uncover that such systems can develop localized steady or unsteady vortices with time in order to dissipate the excess localized electrical energy originating from the applied field. Example cases are shown wherein the size, number, and recirculation strength of the vortices have been tuned inside the microchannel with the variations in the external field intensity and the arrangements of the electrodes for a fixed Re. The study further unveils that while at lower Raψ only be steady vortices may show up for the fluids with higher viscosities, at the significantly higher Raψ the fluids with a lower viscosity may manifest an array of unsteady counter-rotating vortices. Such vortices may translate due to the flow of the fluid inside the confined microfluidic channel to eventually form a “vortex-street” inside the microchannel.