Linear stability of co-flowing liquid–gas jets

Abstract

A temporal, inviscid, linear stability analysis of a liquid jet and the co-flowing gas stream surrounding the jet has been performed. The basic liquid and gas velocity profiles have been computed self-consistently by solving numerically the appropriate set of coupled Navier–Stokes equations reduced using the slenderness approximation. The analysis in the case of a uniform liquid velocity profile recovers the classical Rayleigh and Weber non-viscous results as limiting cases for well-developed and very thin gas boundary layers respectively, but the consideration of realistic liquid velocity profiles brings to light new families of modes which are essential to explain atomization experiments at large enough Weber numbers, and which do not appear in the classical stability analyses of non-viscous parallel streams. In fact, in atomization experiments with Weber numbers around 20, we observe a change in the breakup pattern from axisymmetric to helicoidal modes which are predicted and explained by our theory as having an hydrodynamic origin related to the structure of the liquid-jet basic velocity profile. This work has been motivated by the recent discovery by Gañán-Calvo (1998) of a new atomization technique based on the acceleration to large velocities of coaxial liquid and gas jets by means of a favourable pressure gradient and which are of emerging interest in microfluidic applications (high-quality atomization, micro-fibre production, biomedical applications, etc.).