Bubble breakup probability in turbulent flows

Abstract

Bubbles drive gas and chemical transfers in various industrial and geophysical context, in which flows are typically turbulent. A knowledge of the bubble size distributions is then necessary to quantify mass fluxes across interfaces. In a turbulent flow, every bubble might break, depending on both the ratio between inertial and capillary forces at its scale, namely the Weber number We. For inhomogeneous and unstationary flows, the residence time within a turbulent region will also determine the break-up probability. In this work, we use a stochastic linear model, whose parameters have been measured using direct numerical simulations, to infer the breakup probability of bubbles in turbulence as function of the Weber number and the residence time. Our model shows that bubble breakup is a memoryless process, whose breakup rate varies exponentially with $\textrm{We}^{-1}$. This linear model successfully reproduces breakup rates previously measured experimentally.Comment: 4 figures + A supplementary Materia