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

Micro channels are widely used in many industrial applications as they offer the ability to work in small volumes, consume low energy and less time, and reduce costs. Another important application of microfluidics is to generate micro droplets of one phase in another immiscible phase and use them as reaction vessels. In order to generate droplets from these fluids, the interface needs to be stimulated. Electrohydrodynamics is an effective method for stimulating the interface in micro channels. The aim of this study is to analytically investigate the stability of the interface between a hydrodynamically passive fluid (air) and a viscoelastic polymer under the effect of an electric field applied either parallel or normal to the interface. By this analysis, the conditions for the interface deflection which is the first step of generating droplets are determined. The fluids are assumed to be immiscible, incompressible, and leaky-dielectric. The effect of using a passive fluid instead of an active one under the normal electric field, and the effect of the direction of the applied electric field are analyzed. As a result, it is found that the Weissenberg number for the system with passive fluid has an opposite effect on the maximum growth rate. Other dimensionless parameters such as the conductivity ratio, the dimensionless electric number, and the thickness ratio show the same trend in both the maximum growth rate, and the critical wave number. Moreover, for the given set of parameters, the system is always stable when a parallel electric field is applied. The neutral curves are also presented. For some values of dimensionless parameters, the solution failed and singularity occurred when the thickness ratio is 0.5 for the normal electric field. For the parallel electric field; no singularity occurred.