Electrohydrodynamic stability of ivlin-Ericksen viscoelastic liquid sheet streaming in an inviscid gas medium

Abstract

This work is an attempt to study the linear electrohydrodynamic temporal instability of a viscoelastic liquid sheet of Rivlin-Ericksen type streaming with relative velocity in a surrounded inviscid gas medium theoretically and numerically. The governing equation of motion and continuity in ad dition to Maxwell’s equations, and the suitable boundary conditions at the fluid interfaces are linearized, and the method of normal modes analysis has been utilized to obtain the differential equations describing the liq uid and gas media and the electric field. The solution of theses differential equations have been solved, and the constants of integration are determined using the boundary conditions at both interfaces. The dispersion relations between the growth rate and wave number have been derived for both cases and antisymmetric and symmetric disturbances have been derived. The ob tained dispersion relations are very complicated and possible to study the stability of the considered system analytically. Then, we first write these dispersion relations in non-dimensional forms, and solve then numerically using Muller method via new technique using Mathematics program. The effects of each of the electric field, Weber number, Ohnesorge number, gas to liquid density ratio, and viscoelasticity parameter on the disturbances growth rate of two, and three-dimensional cases have been studied in de tail.