A rationally-based correlation of mean fragment size for drop secondary breakup

A correlation was derived for the Sauter mean diameter of fragments produced in the bag and multimode drop breakup regimes for drops having Ohnesorge numbers less than 0.1. Development of the correlation focused on the growth of capillary instabilities on the toroidal rim seen during the final stages of bag breakup. The model linked the time scale for drop breakup and the time scale associated with growth of the unstable waves. The instability scale was approximated from the results of linear stability theory for capillary waves on liquid cylinders. The drop breakup scale was based on correlations available in the literature for drops subjected to a rapid (relative to drop deformation time scales) rise in relative velocity. Though development focused on bag breakup, the resultant expression was also shown to correlate the multimode regime data reasonably well.