Effect of the direction of the electric field on the interfacial instability between a passive fluid and a viscoelastic polymer

Abstract

In this paper, we study the linear stability of the interface between an Upper Convective Maxwell fluid and a hydrodynamically passive fluid subject to an electric field applied either parallel or normal to the flat interface between the two fluids. The fluids are leaky-dielectric and we apply surface-coupled model. We solve the model equations analytically and study the dispersion and neutral curves for various parameters representing the applied potential, the fluid’s elasticity, the physical and the electrical properties of the fluids, and the heights of the fluids in the presence of both normal and parallel electric fields. It is found that the critical wavenumber is independent of the Weissenberg number. However, increasing the Weissenberg number increases the maximum growth rate for both the normal and the parallel fields. The critical wavenumber increases with the dimensionless applied voltage for the normal field. Lastly for the normal field, for some values of the dimensionless parameters, the growth rate reached very large values representing some type of singularity as has been observed in the literature. However, for the same values of the parameters no singularity is observed for the parallel field.