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Research Article

Bubble pinch-off in turbulence

Daniel J. Ruth, Wouter Mostert, Stéphane Perrard, and View ORCID ProfileLuc Deike
  1. aDepartment of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544;
  2. bDépartement de Physique, Ecole Normale Supérieure, PSL (Paris Sorbonne Lettres) Research University, 75005 Paris, France;
  3. cPrinceton Environmental Institute, Princeton University, Princeton, NJ 08544

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PNAS December 17, 2019 116 (51) 25412-25417; first published December 2, 2019; https://doi.org/10.1073/pnas.1909842116
Daniel J. Ruth
aDepartment of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544;
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Wouter Mostert
aDepartment of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544;
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Stéphane Perrard
aDepartment of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544;
bDépartement de Physique, Ecole Normale Supérieure, PSL (Paris Sorbonne Lettres) Research University, 75005 Paris, France;
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Luc Deike
aDepartment of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544;
cPrinceton Environmental Institute, Princeton University, Princeton, NJ 08544
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  • ORCID record for Luc Deike
  • For correspondence: ldeike@princeton.edu
  1. Edited by David A. Weitz, Harvard University, Cambridge, MA, and approved November 3, 2019 (received for review June 7, 2019)

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Significance

As a bubble breaks apart, the final pinching culminates in a singularity. We investigate the pinch-off of a bubble in turbulence and demonstrate that the turbulent flow field freezes during the pinching process, opening the route for a self-similar collapse close to the one predicted for unperturbed configuration. The role of the turbulent flow field is, therefore, to set the complex initial conditions, which can lead to oscillations of the neck shape during the collapse and the eventual escape from self-similarity with the appearance of a kink-like interfacial structure. This work can be seen as a prototype for understanding the route to finite-time singularities in realistic multiscale systems where random perturbations are present, with both fundamental and practical implications.

Abstract

Although bubble pinch-off is an archetype of a dynamical system evolving toward a singularity, it has always been described in idealized theoretical and experimental conditions. Here, we consider bubble pinch-off in a turbulent flow representative of natural conditions in the presence of strong and random perturbations, combining laboratory experiments, numerical simulations, and theoretical modeling. We show that the turbulence sets the initial conditions for pinch-off, namely the initial bubble shape and flow field, but after the pinch-off starts, the turbulent time at the neck scale becomes much slower than the pinching dynamics: The turbulence freezes. We show that the average neck size, d¯, can be described by d¯∼(t−t0)α, where t0 is the pinch-off or singularity time and α≈0.5, in close agreement with the axisymmetric theory with no initial flow. While frozen, the turbulence can influence the pinch-off through the initial conditions. Neck shape oscillations described by a quasi–2-dimensional (quasi-2D) linear perturbation model are observed as are persistent eccentricities of the neck, which are related to the complex flow field induced by the deformed bubble shape. When turbulent stresses are less able to be counteracted by surface tension, a 3-dimensional (3D) kink-like structure develops in the neck, causing d¯ to escape its self-similar decrease. We identify the geometric controlling parameter that governs the appearance of these kink-like interfacial structures, which drive the collapse out of the self-similar route, governing both the likelihood of escaping the self-similar process and the time and length scale at which it occurs.

  • turbulence
  • singularity
  • self-similarity
  • interface

Footnotes

  • ↵1To whom correspondence may be addressed. Email: ldeike{at}princeton.edu.
  • Author contributions: D.J.R. and L.D. designed research; D.J.R., W.M., S.P., and L.D. performed research; D.J.R., W.M., and L.D. analyzed data; and D.J.R., W.M., S.P., and L.D. wrote the paper.

  • The authors declare no competing interest.

  • This article is a PNAS Direct Submission.

  • Data deposition: Data and code to reproduce plots are available at http://arks.princeton.edu/ark:/88435/dsp014f16c5691.

  • This article contains supporting information online at https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1909842116/-/DCSupplemental.

  • Copyright © 2019 the Author(s). Published by PNAS.

This open access article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND).

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Bubble pinch-off in turbulence
Daniel J. Ruth, Wouter Mostert, Stéphane Perrard, Luc Deike
Proceedings of the National Academy of Sciences Dec 2019, 116 (51) 25412-25417; DOI: 10.1073/pnas.1909842116

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Bubble pinch-off in turbulence
Daniel J. Ruth, Wouter Mostert, Stéphane Perrard, Luc Deike
Proceedings of the National Academy of Sciences Dec 2019, 116 (51) 25412-25417; DOI: 10.1073/pnas.1909842116
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  • Applied Physical Sciences
Proceedings of the National Academy of Sciences: 116 (51)
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  • Article
    • Abstract
    • Frozen Turbulence during Pinch-Off
    • Experimental Collapse with a Turbulent Background
    • Escape from Self-Similarity Close to Singularity
    • Control of Kink Formation by the Turbulence
    • Conclusion
    • Materials and Methods
    • Acknowledgments
    • Footnotes
    • References
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