Following the drop oscillation breakup mechanism, a theoretical model for drop breakup probability is proposed based on the three-dimensional Maxwell velocity distribution. The model considers both the interfacial energy increase constraint and viscous energy increase constraint. The model shows that for low-viscous drops, the breakup probability is determined by the Weber number (WeL), and for intermediate or high viscous drops, the breakup probability is determined by the combined influence of the Weber number (WeL) and the Ohnesorge number (Oh). By combining the theoretical model of drop breakup time constructed in our previous work, the breakup frequency model is obtained based on the statistical description framework. The accuracy and generality of the model were then validated using the direct experimental data. Moreover, effects of the drop diameter, turbulent energy dissipation rate, and interfacial tension on the predicted drop breakup frequency were analyzed in detail.

Drop breakup experiments were carried out in a stirred tank using the high-speed online camera. Breakup behaviors of drop breakup time, multiple breakage, and breakup rate were investigated. Experimental results show that the drop breakup time is mainly controlled by the interfacial tension and drop diameter, while is almost independent of the rotating speed. Besides, the dispersed phase viscosity has a slight influence on the breakup time. An empirical correlation for the breakup time is proposed and is further verified by comparing with the results of Solsvik and Jakobsen (Chem. Eng. Sci., 2015, 131: 219-234). The percentage of multiple breakage comparing to binary breakup was statistically counted. The results indicated that the dimensionless drop diameter η = d / dmax can be adopted to characterize the proportion of binary breakup. Finally, the breakup rate was experimentally measured and the breakup probability was calculated using the inverse method.