Bubble breakup probability in turbulent flows

Abstract

Bubbles drive gas and chemical transfers in various industrial and geophysical contexts, in which flows are typically turbulent. As gas and chemical transfers are bubble size dependent, their quantification requires a prediction of bubble breakup. The most common idea, introduced by Kolmogorov and Hinze, is to consider a sharp limit between breaking and non breaking bubbles, given by $\mathrm{We}_c\approx 1$, where the Weber number $\mathrm{We}$ is the ratio between inertial and capillary forces at the bubble scale. Yet, due to the inherent stochasticity of the flow every bubble might in reality break. In this work, we use a stochastic linear model previously developed to infer the breakup probability of bubbles in turbulence as function of both We and the residence time. This allows us to introduce a definition of the critical Weber number accounting for the time spent by bubbles within a turbulent region. We show that bubble breakup is a memoryless process, whose breakup rate varies exponentially with $\mathrm{We}^{-1}$. The linear model successfully reproduces experimental breakup rates from the literature. We show that the stochastic nature of bubble breakup is central when the residence time of bubbles is smaller than ten correlation times of turbulence at the bubble scale: the transition between breaking and non breaking bubbles is smooth and most bubbles can break. For large residence times, the original vision of Kolmogorov and Hinze is recovered.