DGLSM based study of temporal instability and formation of satellite drop in a capillary jet breakup

Abstract

Temporal instability of a cylindrical capillary jet is analyzed numerically for different liquid Reynolds numbers (Re=1,10,100),disturbance wave numbers (0<k≤1), and ratio of viscosity of continuous and dispersed phase (η=0.01,0.1,1). Simulations are done using an in-house code based on dual grid Level Set Method. Properties as well as physical interpretations of level set functions are used for characterization of temporal evolution and breakup of a liquid jet, the growth rate of disturbance, the breakup time and its location, and the diameter of primary as well as satellite drop. An excellent agreement of the numerical results with the published analytical as well as experimental results is presented. For higher viscosity ratio system (η=1), satellite drops are generated owing to multiple breakup sequences around the neck region of a highly deformed ligament. The breakup mechanism is self-repeating in the sense that every pinch off is always associated with the formation of a neck, the neck undergoes pinch off, and the process repeats. With increasing Re, for all the values of wave numbers, it is found that the growth rate increases; whereas, breakup time decreases. With an increase in the viscosity ratio, the growth rate decreases and breakup time increases accompanied by marginal change in the drop size. Contribution of the total volume of the jet to the satellite (primary) drop decreases (increases) with increasing k, decreasing Re and decreasing η. The present work leads to a better understanding of mechanism of capillary jet breakup and subsequent formation of main, satellite and sub-satellite drops, due to temporal growth of surface perturbation.