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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Simultaneous measurements of deforming Hinze-scale bubbles with surrounding turbulence
We experimentally investigate the breakup mechanisms and probability of Hinze-scale bubbles in turbulence. The Hinze scale is defined as the critical bubble size based on the critical mean Weber number, across which the bubble breakup probability was believed to have an abrupt transition from being dominated by turbulence stresses to being suppressed completely by the surface tension. In this work, to quantify the breakup probability of bubbles with sizes close to the Hinze scale and to examine different breakup mechanisms, both bubbles and their surrounding tracer particles were simultaneously tracked. From the experimental results, two Weber numbers, one calculated from the slip velocity between the two phases and the other acquired from local velocity gradients, are separated and fitted with models that can be linked back to turbulence characteristics. Moreover, we also provide an empirical model to link bubble deformation to the two Weber numbers by extending the relationship obtained from potential flow theory. The proposed relationship between bubble aspect ratio and the Weber numbers seems to work consistently well for a range of bubble sizes. Furthermore, the time traces of bubble aspect ratio and the two Weber numbers are connected using the linear forced oscillator model. Finally, having access to the distributions of these two Weber numbers provides a unique way to extract the breakup probability of bubbles with sizes close to the Hinze scale.
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- PAR ID:
- 10212191
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 910
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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