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 phenomena, ranging from heat and mass transfer at the ocean-atmosphere interface to pathogen transmission. The inherent nonlinearity of the equations governing the ligament destabilization leads 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. The simulations are grouped in a large ensemble, each corresponding to a random initial configuration. The resulting probability distributions reveal three stable drop sizes, generated via a sequence of two distinct stages of breakup. Four different distributions are tested, volume-based Poisson, Gaussian, Gamma, and Log-Normal. Depending on the time, range of droplet sizes and criteria for success, each distribution has successes and failures. However, the Log-Normal distribution roughly describes the data when fitting both the primary peak and the tail of the distribution while the number of droplets generated is the highest, while the Gamma and Log-Normal distributions perform equally well when fitting the tail. The study demonstrates a precisely controllable and reproducible framework, which can be employed to investigate the mechanisms responsible for the polydispersity of drop sizes found in complex fluid fragmentation scenarios.