The formation of satellite droplets by unstable binary drop collisions

Experimental investigations on the process of satellite droplet formation by unstable binary drop collisions are presented. The experiments are carried out using two monodisperse streams of drops of equal size. A systematic variation of the parameters influencing the collisions leads to an extended version of the stability nomogram which involves the numbers of satellite droplets formed by stretching separation after off-center collisions. The time scales for the formation of liquid filaments and their breakup into the satellites are measured and, in the case that a single satellite is formed, the satellite size is measured by means of a phase-Doppler anemometer. Furthermore, a theoretical model for the breakup of cylindrical liquid filaments in head-on and off-center collisions is presented. The model is based on a linear stability analysis of the filament formed after the collision. The critical wavelength associated with the largest deformation energy is calculated and identified with the disturbance which eventually breaks the filament and determines the number of satellites formed. Comparisons with experiments by Ashgriz and Poo [J. Fluid Mech. 221, 183 (1990)] for the head-on and near-head-on cases yield agreement of the numbers of satellites formed.