Statistics of drops generated from ensembles of randomly corrugated ligaments*

The size of drops generated by the capillary-driven disintegration of liquid ligaments plays a fundamental role in several important natural and industrial phenomena. The inherent non-linearities of the equations governing ligament destabilization lead to significant differences in the resulting drop sizes, owing to small fluctuations in the myriad initial conditions. Previous experiments and simulations reveal a variety of drop size distributions, corresponding to competing underlying physical interpretations. Here, we perform numerical simulations of individual ligaments, the deterministic breakup of which is triggered by random initial surface corrugations. Stochasticity is incorporated by simulating a large ensemble of such ligaments, each realization corresponding to a random but unique initial configuration. The resulting probability distributions reveal three stable drop sizes, generated via a sequence of two distinct breakup stages. The probability of the large sizes is described by volume-weighted Poisson and Log-Normal distributions for the first and second breakup stages, respectively. The study demonstrates a quantitatively precise, statistically robust and reproducible framework for studying drop sizes resulting from complex liquid fragmentation phenomena.