Experimental observations and modeling of sub-Hinze bubble production by turbulent bubble break-up

TL;DR

This study investigates how large air cavities break up into smaller bubbles in turbulence, revealing the role of capillary instability and modeling the process with a population balance approach that matches experimental observations.

Contribution

It provides new experimental data on bubble break-up at various sizes relative to the Hinze scale and introduces a population model incorporating inertial deformation and capillary instability.

Findings

Small bubble size distribution follows a d^{-3/2} power law.

Capillary instability is responsible for creating small bubbles.

The population model accurately reproduces experimental bubble size evolution.

Abstract

We present experiments on large air cavities spanning a wide range of sizes relative to the Hinze scale $d_\mathrm{H}$, the scale at which turbulent stresses are balanced by surface tension, disintegrating in turbulence. For cavities with initial sizes $d_0$ much larger than $d_\mathrm{H}$ (probing up to $d_0 / d_\mathrm{H} = 8.3$), the size distribution of bubbles smaller than $d_\mathrm{H}$ follows $N(d) \propto d^{-3/2}$, with $d$ the bubble diameter. The capillary instability of ligaments involved in the deformation of the large bubbles is shown visually to be responsible for the creation of the small ones. Turning to dynamical, three-dimensional measurements of individual break-up events, we describe the break-up child size distribution and the number of child bubbles formed as a function of $d_0 / d_\mathrm{H}$. Then, to model the evolution of a population of bubbles produced by turbulent bubble break-up, we propose a population balance framework in which break-up involves two physical processes: an inertial deformation to the parent bubble that sets the size of large child bubbles, and a capillary instability that sets the size of small child bubbles. A Monte Carlo approach is used to construct the child size distribution, with simulated stochastic break-ups constrained by our experimental measurements and the understanding of the role of capillarity in small bubble production. This approach reproduces the experimental time evolution of the bubble size distribution during the disintegration of large air cavities in turbulence.