Eur. Phys. J. E (2004) 15: 443-455
https://doi.org/10.1140/epje/i2004-10076-2

Three-dimensional electrohydrodynamic temporal instability of a moving dielectric liquid sheet emanated into a gas medium

Department of Mathematics and Computer Science, Faculty of Science, United Arab Emirates University, P.O. Box 17551, Al Ain, United Arab Emirates

^* e-mail: M.Elsayed@uaeu.ac.ae

Received: 20 April 2004
Accepted: 19 October 2004
Published online: 20 December 2004

Abstract

A linear electrohydrodynamic instability analysis is presented for an inviscid dielectric liquid sheet emanated into an inviscid dielectric gas medium in the presence of a horizontal electric field. The influence of Weber number, gas-to-liquid density ratio, and the applied electric field on the evolution of two-, and three-dimensional disturbances of symmetrical and antisymmetrical types is studied. It is found, for antisymmetrical waves, that two-dimensional disturbances always prevail over three-dimensional disturbances, regardless of Weber number or gas-to-liquid density ratio values, especially for long waves; while for short waves, both two- and three-dimensional disturbances grow at approximately the same rate. It is also found, for symmetrical waves, that two-dimensional disturbances always dominate the instability process at low Weber number, and when the Weber number is large, symmetrical three-dimensional disturbances become more unstable than two-dimensional ones for long waves. The effect of increasing the gas-to-liquid density ratio is to promote the dominance of long three-dimensional symmetrical waves over their two-dimensional counterpart. Finally, the equilibrium Weber number at which the growth rates of two- and three-dimensional modes are equal is discussed for both symmetrical- and antisymmetrical-disturbances cases.-1