Linear instability analysis of planar non-Newtonian liquid sheets in two gas streams of unequal velocities

Abstract

Linear stability theory is applied to study the breakup process of a non-Newtonian liquid sheet subjected to non-zero unequal gas flow on both sides of the liquid sheet. The unequal non-zero velocities of the gas streams on both sides are considered in this temporal instability analysis. The dispersion relation between the growth rate of disturbances and the wave number of disturbances is derived. Then a parametric study of the instability of the liquid sheet is made. The emphasis of the paper is to study the effects of various velocities of the upper and lower gas streams. It is found that the larger velocity difference across each interface enhances the instability of the sheets. But the enhanced extent could be different. The instability is primarily determined by the larger one between the velocity differences across the two liquid–gas interfaces for para-sinuous mode and the smaller one for the para-varicose mode. The influences of the density ratio, surface tension and liquid viscosity on the instability of the planar sheet are also included in this paper.