Electro-hydrodynamic instability in a microchannel between a Newtonian and a non-Newtonian liquid

We perform linear stability analysis of the interface between a Newtonian fluid and a non-Newtonian fluid, assumed to obey the Upper Convective Maxwell model, flowing in a channel due to a pressure gradient subject to an electric field applied normal to the interface. The fluids are assumed to be immiscible, incompressible and leaky dielectric. A detailed parametric study of the effects of the system parameters, such as Weissenberg number, Reynolds number, applied potential and physical and electrical properties of the fluids, is conducted. It is found that increasing the applied voltage could be stabilizing or destabilizing depending on the electrical properties of the liquids, and increasing the Weissenberg number decreases the maximum growth rate without changing the corresponding wavenumber and increases the critical wavenumber. The effect of the height ratio of the liquids is analyzed through neutral curves for given electric numbers, i.e. applied potential. The critical wavenumber decreases with height ratio and converges to a value for all the electric numbers considered.