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We study bubble break-up in homogeneous and isotropic turbulence by direct numerical simulations of the two-phase incompressible Navier–Stokes equations. We create the turbulence by forcing in physical space and introduce the bubble once a statistically stationary state is reached. We perform a large ensemble of simulations to investigate the effect of the Weber number (the ratio of turbulent and surface tension forces) on bubble break-up dynamics and statistics, including the child bubble size distribution, and discuss the numerical requirements to obtain results independent of grid size. We characterize the critical Weber number below which no break-up occurs and the associated Hinze scale $$d_h$$ . At Weber number close to stable conditions (initial bubble sizes $$d_0\approx d_h$$ ), we observe binary and tertiary break-ups, leading to bubbles mostly between $$0.5d_h$$ and $$d_h$$ , a signature of a production process local in scale. For large Weber numbers ( $$d_0> 3d_h$$ ), we observe the creation of a wide range of bubble radii, with numerous child bubbles between $$0.1d_h$$ and $$0.3d_h$$ , an order of magnitude smaller than the parent bubble. The separation of scales between the parent and child bubble is a signature of a production process non-local in scale. The formation mechanism of these sub-Hinze scale bubbles relates to rapid large deformation and successive break-ups: the first break-up in a sequence leaves highly deformed bubbles which will break again, without recovering a spherical shape and creating an array of much smaller bubbles. We discuss the application of this scenario to the production of sub-Hinze bubbles under breaking waves.
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Experimental observations and modelling of sub-Hinze bubble production by turbulent bubble break-up
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.
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- Award ID(s):
- 1844932
- PAR ID:
- 10388588
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 951
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2022.604
