Electrohydrodynamic instability of a dielectric compressible liquid sheet streaming into an ambient stationary compressible gas

Abstract

The effect of compressibility of fluids on the linear electrohydrodynamic instability of a dielectric liquid sheet issued from a nozzle into an ambient dielectric stationary gas in the presence of a horizontal electric field is investigated. It is found that increasing the Mach number from subsonic to transonic causes the maximum growth rate and the dominant wavenumber of the disturbances to increase, and the increase is higher in the presence of the electric field. Liquid compressibility has been found to have a minimal effect on instability. At constant wavenumber and electric field values, the growth rate of disturbances increases as the gas Mach number tends to 1, and then begins to decrease with further increase in the gas Mach number. At small values of wavenumber, antisymmetrical disturbances grow faster than symmetrical ones, while the growth rate of both types of disturbances approach each other at large wavenumbers, which increases by increasing the electric field values. At small Weber numbers, antisymmetrical disturbances exhibit a higher maximum growth rate and a lower dominant wavenumber than symmetrical disturbances. However, the maximum growth rate and dominant wavenumber of the two types of disturbances are almost identical when both Weber number and electric field values become large. An increase in the gas to liquid density ratio enhances the instability, and this effect is enhanced for high electric field values. Surface tension and electric fields always oppose and increase the development of instability, respectively; and they have opposite effects for long wavelengths and high Weber numbers.