Understanding the evolution of dilute emulsions with single-drop breakup experiments in isotropic turbulence

In this work we investigate the breakup of drops much larger than the Kolmogorov scale in homogeneous isotropic turbulence. We use a novel GPU code to perform thousands of independent direct numerical simulations of single drops at different Weber numbers, and gather statistics of the breakup process, in particular, the breakup time and the daughter drops-size distribution. This extensive database reveals that for small Weber numbers the survival time of single drops resemble a memoryless process characterised by a single parameter, the breakup rate. This quantity depends exponentially on the inverse of the Weber number, matching the celebrated model of Coulaloglou and Tavlarides (Chem. Eng. Sci, 1977), but not on the Reynolds number of the drop. These results show that breakup is possible for drops smaller than the maximum stable diameter, but that it becomes exponentially less likely as the drop diameter decreases. In the absence of coalescence and for sufficiently high Reynolds number, this non-vanishing breakup probability leads to and endless fragmentation process in the inertial range of isotropic turbulence, suggesting that, in real flows, drop-size distributions reach a statistically steady state in time scales much larger than previously thought. We provide an estimate of these time-scales, and show how the asymptotic evolution of dilute emulsions can be modelled with a stochastic approach based on the data gathered in our simulations.