Abstract
In this paper, instabilities and breakup phenomena of a viscous liquid column jet in an inviscid stationary surrounding gas are analytically investigated, when the jet flows through a coaxial cylindrical sheath. Under a long wave approximation, axisymmetric non-linear evolution equations of the jet and surrounding gas are derived and numerically solved under a spatially periodic boundary condition. Validity and limitation of the approximation are examined in the linear regime in comparison with exact three-dimensional instabilities. It is shown in the non-linear analysis that there exist three types of breakup modes: the Rayleigh mode in which the surface tension instability is dominant and the breakup is caused by pinching, the first wind-induced mode in which blobs connected by threads are produced by increased aerodynamic instability and the second wind-induced mode in which the jet surface deforms to be spiked like a cusp without pinching and droplets are to be produced from a tip of the cusp. The existing regions of these modes are examined in the parameter space of the Weber number and the sheath radius for different Reynolds numbers and density ratios.
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