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Sub-Hinze scale bubble production in turbulent bubble break-up

Published online by Cambridge University Press:  29 April 2021

Aliénor Rivière Open the ORCID record for Aliénor Rivière [Opens in a new window] ,
Wouter Mostert Open the ORCID record for Wouter Mostert [Opens in a new window] ,
Stéphane Perrard Open the ORCID record for Stéphane Perrard [Opens in a new window]  and
Luc Deike Open the ORCID record for Luc Deike [Opens in a new window]
Aliénor Rivière
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ08544, United States LPENS, Département de Physique, Ecole Normale Supérieure, PSL University, 75005Paris, France
Wouter Mostert
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ08544, United States
Stéphane Perrard
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ08544, United States LPENS, Département de Physique, Ecole Normale Supérieure, PSL University, 75005Paris, France
Luc Deike*
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ08544, United States High Meadows Environmental Institute, Princeton University, Princeton, NJ08544, USA
*
†Email address for correspondence: [email protected]
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Abstract

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.

JFM classification

Drops and Bubbles: Bubble dynamics Multiphase and Particle-laden Flows: Multiphase flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 917 , 25 June 2021 , A40
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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