Instability of pressure driven viscous fluid streams in a microchannel under a normal electric field

This paper investigates analytically and experimentally electrohydrodynamic instability of the interface between two viscous fluids with different electrical properties under constant flow rates in a microchannel. In the three-dimensional analytical model, the two-layer system is subjected to an electric field normal to the interface between the two fluids. There is no assumption on the magnitude of the ratio of fluid to electric time scales, and thus the linear Poisson-Boltzmann equation are solved using separation of variable method for densities of bulk charge and surface charge. The electric field and fluid dynamics are coupled only at the interface through the tangential and normal interfacial stress balance equations. In the experiments, two immiscible fluids, aqueous NaHCO₃ (the high electrical mobility fluid) and silicone oil (polydimethylsiloxane, the low electrical mobility fluid) are pumped into a microchannel made in polymethyl methacrylate) (PMMA) substrate. The normal electric field is added using a high voltage power supply. The results showed that the external electric field and increasing width of microchannel destabilize the interface between the immiscible fluids. At the same time, the viscosity of the high electrical mobility fluid and flow rates of fluids has a stabilizing effect. The experimental results and the analytical results show a reasonable agreement.