Bubble breakup probability in turbulent flows

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, a robust quantification requires a prediction of bubble breakup. The most common idea, introduced independently by Kolmogorov in 1949 and Hinze in 1955, is to consider a sharp limit between breaking and non breaking bubbles, given by We c ≈ 1 , where the Weber number We is the ratio between inertial and capillary forces at the bubble scale. In the statistically stationary state, We c sets the maximum bubble size. 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, extending the stationary description. We show that bubble breakup is a memoryless process, whose breakup rate varies exponentially with 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.