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

Abstract

We present experiments on large air cavities spanning a wide range of sizes relative to the Hinze scale $d_{H}$ , the scale at which turbulent stresses are balanced by surface tension, disintegrating in turbulence. For cavities with initial sizes $d_0$ much larger than $d_{H}$ (probing up to $d_0/d_{H} = 8.3$ ), the size distribution of bubbles smaller than $d_{H}$ 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 bubbles. 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 $d_0/d_{H}$ . 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.

Role of viscosity in turbulent drop break-up

“…2021; Ruth et al. 2022), with a very small and a very large drop being formed, with similar results for . However, at a high viscosity ratio, the distribution is close to a bell shape (similar to the shape of the distribution at lower for the same viscosity ratio) corresponding to two lobes of equal size, just prior to the fragmentation into tiny droplets of the snake like shape seen in figure 1.…”

“…The U-shape is therefore often used in population balance models, as it allows us to recreate a rapid sequence as long as the model for the successive break-up times is adequate (see Ruth et al. 2022). A discussion on the bell shape is provided by Martínez-Bazán et al.…”

“…2022; Ruth et al. 2022), with a shape that is not a direct result of the first break-up, as rapid break-ups follow the initial one, leading to a broad sub-Hinze population.…”

“…2019; Gaylo, Hendrickson & Yue 2021; Ruth et al. 2022). A large variety of break-up mechanisms have been introduced (Balachandar & Eaton 2010), with most models for droplet break-up in a turbulent flow considering a single mechanism with drop interaction with a single turbulent eddy, or a continuum of turbulence scales, with fluctuations at the size of the drop being the most effective part of the process (Hinze 1955; Luo & Svendsen 1996; Liao & Lucas 2009; Lalanne, Masbernat & Risso 2019).…”

Bubbles spray aerosols: Certitudes and mysteries

“…We have (with Q ( u > ℓ) ∼ u −10/3 ), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$$\begin{equation*} \partial _tQ(R)\delta R\sim \frac{1}{t(R)}\int _\ell ^\infty {\rm d}u\, Q(u)\delta p(R\vert u) , \end{equation*} $$\end{document} where p ( R | u ) ∼ 1 × ( u / R ) −1 is the fraction of an elongated bubble of size u actually producing one (typically, at most a few) bubble of size R . Therefore, for R < ℓ, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$$\begin{equation*} \partial _tQ(R)\sim \frac{1}{t(R)}\int _\ell ^\infty {\rm d}u\, \frac{Q(u)}{u}\sim \ell ^{-10/3}R^{-3/2}, \end{equation*} $$\end{document} consistent with the recent experiments in ( 10 , 65 ).…”