Temporal instability of a capillary jet with a source of mass

Abstract

The temporal linear instability of an inviscid capillary liquid jet with a source of mass is investigated. Two different spatial mass distributions are considered. In the first case, mass is added uniformly everywhere in the jet. In the second case, mass is added uniformly in the radial direction, but allowed to change along the axial direction. The problem is solved using a one-dimensional approximation for the capillary jet. An analytical solution for the steady basic flow of a jet with a small source of mass is obtained. The dispersion relation and the growth rate of the disturbances are obtained analytically for small source terms. The influence of the mass addition on the instability characteristics, the breakup time, and the breakup length of a jet are presented. It is shown that the mass addition decreases the rate of growth of the disturbances. The mass addition increases the breakup time and decreases the breakup length. Also, the sizes of the generated drops increase with increasing the source of mass.