A two-stage droplet breakup model based on the maximum entropy formalism

The maximum entropy formalism (MEF) is employed to develop a model for predicting the size and velocity distributions of daughter droplets resulting from the breakup of an isolated droplet. In this work, the single-stage MEF model developed in Kuo and Trujillo [Phys. Fluids 34(1), 013315 (2022)] is revisited and improved upon by extending it to a two-stage MEF breakup model. This extension is based on the observation of two distinct morphological stages of breakup of the parent droplet, which lead to two distinct contributions to the daughter droplet distributions. The two-stage MEF model yields enhanced predictions of the size and velocity distributions of daughter droplets under conditions characterized by low Ohnesorge numbers (<0.1) and Weber numbers ranging from near-critical (12.6) to 350, compared with the single-stage MEF model. For cases with very high Weber numbers (>350), and cases with high Ohnesorge numbers (>0.1), the single-stage MEF is shown to be sufficient in predicting droplet size distributions. Finally, the two-stage MEF model is shown to improve velocity distribution predictions by accounting for the non-uniform breakup and deceleration of the parent droplet. Comparison to the standard TAB model results in significant improvements for the prediction of drop size over all cases considered.