Linear stability analysis of planar liquid sheet with unequal gas velocities confined between two solid walls

Abstract

A first order stability analysis of planar sheet of liquid flowing inbetween two gas streams with unequal non zero velocities and confined between two solid walls is presented here. A para metric study is conducted to understand the effects of gas velocities and liquid sheet to wall distance on the growth rate, wave number corresponding to maximum growth rate and cut off wave number. Unequal velocity on either sides of the liquid sheet results in two modes of break up viz. the para-sinuous (gas liquid interface phase difference is close to zero) and para-varicose (gas liquid interface difference is close to π) modes. Due to high velocities of both the phases, all the flows are assumed to be inviscid. Both the phases are initially assumed to be irrotational and incompressible. Due to the inviscid nature, the flow is considered to be irrotational in subsequent time as well and therefore can be represented as potential flow. First order analysis gives critical wave number wave number resulting in maximum gro...