Hostname: page-component-848d4c4894-x5gtn Total loading time: 0 Render date: 2024-05-06T23:27:55.863Z Has data issue: false hasContentIssue false
  • English
  • Français

Bubble deformation by a turbulent flow

Published online by Cambridge University Press:  09 June 2021

Stéphane Perrard Open the ORCID record for Stéphane Perrard [Opens in a new window] ,
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]  and
Luc Deike Open the ORCID record for Luc Deike [Opens in a new window]
Stéphane Perrard
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ08544, USA LPENS, Département de Physique, Ecole Normale Supérieure, PSL University, 75005Paris, France
Aliénor Rivière
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ08544, USA LPENS, Département de Physique, Ecole Normale Supérieure, PSL University, 75005Paris, France
Wouter Mostert
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ08544, USA Department of Mechanical and Aerospace Engineering, Missouri University of Science and Technology, Rolla, MO65401, USA
Luc Deike*
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ08544, USA High Meadows Environmental Institute, Princeton University, Princeton, NJ08544, USA
*
†Email address for correspondence: ldeike@princeton.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We investigate the modes of deformation of an initially spherical bubble immersed in a homogeneous and isotropic turbulent background flow. We perform direct numerical simulations of the two-phase incompressible Navier–Stokes equations, considering a low-density bubble in the high-density turbulent flow at various Weber numbers (the ratio of turbulent and surface tension forces) using the air–water density ratio. We discuss a theoretical framework for the bubble deformation in a turbulent flow using a spherical harmonic decomposition. We propose, for each mode of bubble deformation, a forcing term given by the statistics of velocity and pressure fluctuations, evaluated on a sphere of the same radius. This approach formally relates the bubble deformation and the background turbulent velocity fluctuations, in the limit of small deformations. The growth of the total surface deformation and of each individual mode is computed from the direct numerical simulations using an appropriate Voronoi decomposition of the bubble surface. We show that two successive temporal regimes occur: the first regime corresponds to deformations driven only by inertial forces, with the interface deformation growing linearly in time, in agreement with the model predictions, whereas the second regime results from a balance between inertial forces and surface tension. The transition time between the two regimes is given by the period of the first Rayleigh mode of bubble oscillation. We discuss how our approach can be used to relate the bubble lifetime to the turbulence statistics and eventually show that at high Weber numbers, bubble lifetime can be deduced from the statistics of turbulent fluctuations at the bubble scale.

JFM classification

Drops and Bubbles: Bubble dynamics Multiphase and Particle-laden Flows: Multiphase flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 920 , 10 August 2021 , A15
Check for updates
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Andersson, R. & Andersson, B. 2006 On the breakup of fluid particles in turbulent flows. AIChE J. 52 (6), 2020–2030.CrossRefGoogle Scholar
Balachandar, S. & Eaton, J.K. 2010 Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech. 42, 111–133.CrossRefGoogle Scholar
Berny, A., Deike, L., Séon, T. & Popinet, S. 2020 Role of all jet drops in mass transfer from bursting bubbles. Phys. Rev. Fluids 5 (3), 033605.CrossRefGoogle Scholar
Brocchini, M. & Peregrine, D.H. 2001 The dynamics of strong turbulence at free surfaces. Part 1. Description. J. Fluid Mech. 449, 225–254.CrossRefGoogle Scholar
Cano-Lozano, J.C., Martinez-Bazan, C., Magnaudet, J. & Tchoufag, J. 2016 Paths and wakes of deformable nearly spheroidal rising bubbles close to the transition to path instability. Phys. Rev. Fluids 1 (5), 053604.CrossRefGoogle Scholar
Caroli, M., de Castro, P.M.M., Loriot, S., Rouiller, O., Teillaud, M. & Wormser, C. 2009 Robust and efficient Delaunay triangulations of points on or close to a sphere. Research Rep. RR-7004. INRIA.CrossRefGoogle Scholar
Cowen, E.A. & Variano, E.A. 2008 A random-jet-stirred turbulence tank. J. Fluid Mech. 604, 1–32.Google Scholar
Deane, G.B. & Stokes, M.D. 2002 Scale dependence of bubble creation mechanisms in breaking waves. Nature 418, 839–844.CrossRefGoogle ScholarPubMed
Deike, L., Ghabache, E., Liger-Belair, G., Das, A.K., Zaleski, S., Popinet, S. & Seon, T. 2018 Dynamics of jets produced by bursting bubbles. Phys. Rev. Fluids 3 (1), 013603.CrossRefGoogle Scholar
Deike, L. & Melville, W.K. 2018 Gas transfer by breaking waves. Geophys. Res. Lett. 45 (19), 10–482.CrossRefGoogle Scholar
Deike, L., Melville, W.K. & Popinet, S. 2016 Air entrainment and bubble statistics in breaking waves. J. Fluid Mech. 801, 91–129.CrossRefGoogle Scholar
Eggers, J. & Villermaux, E. 2008 Physics of liquid jets. Rep. Prog. Phys. 71 (3), 036601.CrossRefGoogle Scholar
Elghobashi, S. 2019 Direct numerical simulation of turbulent flows laden with droplets or bubbles. Annu. Rev. Fluid Mech. 51 (1), 217–244.CrossRefGoogle Scholar
Ern, P., Risso, F., Fabre, D. & Magnaudet, J. 2012 Wake-induced oscillatory paths of bodies freely rising or falling in fluids. Annu. Rev. Fluid Mech. 44, 97–121.CrossRefGoogle Scholar
Fuster, D. & Popinet, S. 2018 An all-mach method for the simulation of bubble dynamics problems in the presence of surface tension. J. Comput. Phys. 374, 752–768.CrossRefGoogle Scholar
Harper, J.F. 1970 On bubbles rising in line at large Reynolds numbers. J. Fluid Mech. 41 (4), 751–758.CrossRefGoogle Scholar
Hinze, J.O. 1955 Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes. AIChE J. 1 (3), 289–295.CrossRefGoogle Scholar
van Hooft, J.A., Popinet, S., van Heerwaarden, C.C., van der Linden, S.J.A., de Roode, S.R. & van de Wiel, B.J.H. 2018 Towards adaptive grids for atmospheric boundary-layer simulations. Boundary-Layer Meteorol. 167 (3), 421–443.CrossRefGoogle ScholarPubMed
Hussein, H.J., Capp, S.P. & George, W.K. 1994 Velocity measurements in high-Reynolds number, momentum-conserving, axisymmetric, turbulent jets. J. Fluid Mech. 258, 31–75.CrossRefGoogle Scholar
Kolmogorov, A.N. 1941 The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR 30, 301.Google Scholar
Lai, C.-Y., Eggers, J. & Deike, L. 2018 Bubble bursting: universal cavity and jet profiles. Phys. Rev. Lett. 121, 144501.CrossRefGoogle ScholarPubMed
Lalanne, B., Masbernat, O. & Risso, F. 2019 A model for drop and bubble breakup frequency based on turbulence spectra. AIChE J. 65 (1), 347–359.CrossRefGoogle Scholar
Lamb, H. 1995 Hydrodynamics, 6th edn. Cambridge University Press.Google Scholar
Lance, M. & Bataille, J. 1991 Turbulence in the liquid phase of a uniform bubbly air–water flow. J. Fluid Mech. 222, 95–118.CrossRefGoogle Scholar
Loisy, A. & Naso, A. 2017 Interaction between a large buoyant bubble and turbulence. Phys. Rev. Fluids 2, 014606.CrossRefGoogle Scholar
Magnaudet, J. & Eames, I. 2000 The motion of high-Reynolds-number bubbles in inhomogeneous flows. Annu. Rev. Fluid Mech. 32 (1), 659–708.CrossRefGoogle Scholar
Martinez-Bazan, C., Montanes, J.L. & Lasheras, J.C. 1999 On the breakup of an air bubble injected into a fully developed turbulent flow. Part 1. Breakup frequency. J. Fluid Mech. 401, 157–182.CrossRefGoogle Scholar
Martinez-Bazan, C., Rodriguez-Rodriguez, J., Deane, G.B., Montañes, J.L. & Lasheras, J.C. 2010 Considerations on bubble fragmentation models. J. Fluid Mech. 661, 159–177.CrossRefGoogle Scholar
Masuk, A.U.M., Salibindla, A., Tan, S. & Ni, R. 2019 V-onset (vertical octagonal noncorrosive stirred energetic turbulence): a vertical water tunnel with a large energy dissipation rate to study bubble/droplet deformation and breakup in strong turbulence. Rev. Sci. Instrum. 90 (8), 085105.CrossRefGoogle ScholarPubMed
Mathai, V., Lohse, D. & Sun, C. 2020 Bubble and buoyant particle–laden turbulent flows. Annu. Rev. Conden. Ma. P. 11, 529–559.CrossRefGoogle Scholar
Maxworthy, T., Gnann, C., Kürten, M. & Durst, F. 1996 Experiments on the rise of air bubbles in clean viscous liquids. J. Fluid Mech. 321, 421–441.CrossRefGoogle Scholar
Miller, C.A. & Scriven, L.E. 1968 The oscillations of a fluid droplet immersed in another fluid. J. Fluid Mech. 32 (3), 417–435.CrossRefGoogle Scholar
Minnaert, M. 1933 On musical air-bubbles and the sound of running water. Phil. Mag. 16 (104), 235–248.CrossRefGoogle Scholar
Moore, D.W. 1965 The velocity of rise of distorted gas bubbles in a liquid of small viscosity. J. Fluid Mech. 23 (4), 749–766.CrossRefGoogle Scholar
Mostert, W. & Deike, L. 2020 Inertial energy dissipation in shallow-water breaking waves. J. Fluid Mech. 890, A12.CrossRefGoogle Scholar
Mostert, W., Popinet, S. & Deike, L. 2021 High-resolution direct simulation of deep water breaking waves: transition to turbulence, bubbles and droplet production. arXiv:2103.05851.Google Scholar
Peregrine, D.H. 1976 Interaction of water waves and currents. Adv. Appl. Mech. 16, 9–117.CrossRefGoogle Scholar
Perrard, S., Lozano-Durán, A., Rabaud, M., Benzaquen, M. & Moisy, F. 2019 Turbulent windprint on a liquid surface. J. Fluid Mech. 873, 1020–1054.CrossRefGoogle Scholar
Phillips, O.M. 1957 On the generation of waves by turbulent wind. J. Fluid Mech. 2 (5), 417–445.CrossRefGoogle Scholar
Pope, S.B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Popinet, S. 2009 An accurate adaptive solver for surface-tension-driven interfacial flows. J. Comput. Phys. 228, 5838–5866.CrossRefGoogle Scholar
Popinet, S. 2015 A quadtree-adaptive multigrid solver for the Serre–Green–Naghdi equations. J. Comput. Phys. 302, 336–358.CrossRefGoogle Scholar
Popinet, S. 2018 Numerical models of surface tension. Annu. Rev. Fluid Mech. 50, 49–75.CrossRefGoogle Scholar
Prosperetti, A. 1980 Free oscillations of drops and bubbles: the initial-value problem. J. Fluid Mech. 100, 333–347.CrossRefGoogle Scholar
Ravelet, F., Colin, C. & Risso, F. 2011 On the dynamics and breakup of a bubble immersed in a turbulent flow. Phys. Fluids 23, 103301.CrossRefGoogle Scholar
Reichl, B.G. & Deike, L. 2020 Contribution of sea-state dependent bubbles to air-sea carbon dioxide fluxes. Geophys. Res. Lett. 47, e2020GL087267.CrossRefGoogle Scholar
Risso, F. 2018 Agitation, mixing, and transfers induced by bubbles. Annu. Rev. Fluid Mech. 50, 25–48.CrossRefGoogle Scholar
Risso, F. & Fabre, J. 1998 Oscillations and breakup of a bubble immersed in a turbulent field. J. Fluid Mech. 372, 323–355.CrossRefGoogle Scholar
Rivière, A., Perrard, S., Mostert, W. & Deike, L. 2021 Sub-hinze scale bubble production in turbulent bubble break-up. J. Fluid Mech. (in press).CrossRefGoogle Scholar
Rosales, C. & Meneveau, C. 2005 Linear forcing in numerical simulations of isotropic turbulence: physical space implementations and convergence properties. Phys. Fluids 17 (9), 095106.CrossRefGoogle Scholar
Ruth, D., Mostert, W., Perrard, S. & Deike, L. 2019 Bubble pinch-off in turbulence. Proc. Natl Acad. Sci. USA 116 (51), 25412–25417.CrossRefGoogle ScholarPubMed
Tennekes, H. 1975 Eulerian and lagrangian time microscales in isotropic turbulence. J. Fluid Mech. 67, 561–567.CrossRefGoogle Scholar
Vejražka, J., Zedníková, M. & Stanovskỳ, P. 2018 Experiments on breakup of bubbles in a turbulent flow. AIChE J. 64 (2), 740–757.CrossRefGoogle Scholar
Veron, F. 2015 Ocean spray. Annu. Rev. Fluid Mech. 47, 507–538.CrossRefGoogle Scholar
Villermaux, E. & Bossa, B. 2009 Single-drop fragmentation determines size distribution of raindrops. Nat. Phys. 5 (9), 697.CrossRefGoogle Scholar
Voronoi, G. 1908 Nouvelles applications des paramètres continus à la théorie des formes quadratiques. J. Reine Angew. Math. 133, 97–178.CrossRefGoogle Scholar
Yuan, H. & Prosperetti, A. 1994 On the in-line motion of two spherical bubbles in a viscous fluid. J. Fluid Mech. 278, 325–349.CrossRefGoogle Scholar