Temporal and spatial instability of a compound jet in a surrounding gas

Droplet generated from the rupture of a compound liquid jet can be used to produce encapsulated droplets which have applications in a wide variety of industrial processes. In this paper, we examine the instability of a two dimensional axisymmetric inviscid compound jet falling vertically downwards in a surrounding gas under the influence of gravity. The steady state equations are derived using an asymptotic method and the linear instability, including temporal and spatial instability, is determined using a multiple scales approach. The results are analysed to investigate how the gas-to-shell density ratio affects key features of the jet including theoretical breakup lengths.