Abstract
We analytically examine the nonlinear instability and breakup phenomena of a viscous compound liquid jet which consists of core and surrounding annular phases. Applying the long wave approximations to both phases, a set of reduced nonlinear equations is derived for large deformations of the jet. Breakup phenomena are numerically examined when sinusoidal disturbances are fed at the end of the semi-infinite jet. Typical breakup profiles are shown for the surface tension ratios and Reynolds numbers. In particular, for sufficiently small Reynolds number, the core phase is found to be choked at a bottle neck of the jet, which is followed by ballooning of the annular phase in the upstream. It is shown that there exit the most unstable frequencies of input disturbances for each parameters of the surface tension, viscosity and amplitudes of disturbances. From variations of the breakup time and distance for such frequencies, it is expected that there exists a critical Weber number, above which the jet becomes convectively unstable and below which absolutely unstable.
