Linear Instability Analysis of an Electrified Viscoelastic Liquid Sheet in Compressible Ambient Gas

Abstract

The linear instability analysis of an electrified viscoelastic liquid sheet exposed to a compressible ambient gas in the presence of a transverse electric field is theoretically investigated. The dispersion relations for the sinuous and varicose mode are obtained. The combined effects of Mach number and Euler number on the instability of the liquid sheet are checked. Our results demonstrate that there is a critical Mach number, below which the growth rate increases and above which the growth rate decreases with the increase of the Mach number. A larger Euler number leads to a smaller critical Mach number. The maximum growth rate nearly stays constant for Mach number that is smaller than the critical Mach number at large Euler numbers. Besides, the electric field enhances the instability of charged electrified liquid sheets, and the maximum growth rate is a linear increasing function of the Euler number. Furthermore, the compressibility of the gas flow will weaken the effect of the electric field on the instability of liquid sheets.