Hostname: page-component-8448b6f56d-wq2xx Total loading time: 0 Render date: 2024-04-18T02:44:26.571Z Has data issue: false hasContentIssue false
  • English
  • Français

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: ldeike@princeton.edu
Get access Rights & Permissions [Opens in a new window]

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
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

Afshar-Mohajer, N., Li, C., Rule, A.M., Katz, J. & Koehler, K. 2018 A laboratory study of particulate and gaseous emissions from crude oil and crude oil-dispersant contaminated seawater due to breaking waves. Atmos. Environ. 179, 177–186.CrossRefGoogle Scholar
Aiyer, A.K., Yang, D., Chamecki, M. & Meneveau, C. 2019 A population balance model for large eddy simulation of polydisperse droplet evolution. J. Fluid Mech. 878, 700–739.Google Scholar
Andersson, R. & Andersson, B. 2006 On the breakup of fluid particles in turbulent flows. AIChE J. 52 (6), 2020–2030.CrossRefGoogle Scholar
Ayati, A.A., Farias, P.S.C., Azevedo, L.F.A. & de Paula, I.B. 2017 Characterization of linear interfacial waves in a turbulent gas-liquid pipe flow. Phys. Fluids 29 (6), 062106.CrossRefGoogle Scholar
Baba, E. 1969 A new component of viscous resistance of ships. J. Soc. Nav. Archit. Japan 1969 (125), 23–34.CrossRefGoogle Scholar
Bagué, A., Fuster, D., Popinet, S., Scardovelli, R. & Zaleski, S. 2010 Instability growth rate of two-phase mixing layers from a linear eigenvalue problem and an initial-value problem. Phys. Fluids 22 (9), 092104.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
Blenkinsopp, C.E. & Chaplin, J.R. 2010 Bubble size measurements in breaking waves using optical fiber phase detection probes. IEEE J. Ocean. Engng 35 (2), 388–401.CrossRefGoogle Scholar
Cahn, J.W. & Hilliard, J.E. 1959 Free energy of a nonuniform system. III. Nucleation in a two-component incompressible fluid. J. Chem. Phys. 31 (3), 688–699.CrossRefGoogle Scholar
Canu, R., Puggelli, S., Essadki, M., Duret, B., Menard, T., Massot, M., Reveillon, J. & Demoulin, F.X. 2018 Where does the droplet size distribution come from? Intl J. Multiphase Flow 107, 230–245.CrossRefGoogle Scholar
Chan, W.H.R., Johnson, P.L., Moin, P. & Urzay, J. 2021 The turbulent bubble break-up cascade. Part 2. Numerical simulations of breaking waves. J. Fluid Mech. 912, A43.CrossRefGoogle Scholar
Chan, W.H.R., Mirjalili, S., Jain, S.S., Urzay, J., Mani, A. & Moin, P. 2019 Birth of microbubbles in turbulent breaking waves. Phys. Rev. Fluids 4 (10), 100508.CrossRefGoogle Scholar
Chen, S. & Doolen, G.D. 1998 Lattice boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 30 (1), 329–364.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.Google ScholarPubMed
Deike, L., Ghabache, E., Liger-Belair, G., Das, A.K., Zaleski, S., Popinet, S. & Seon, T. 2018 The dynamics of jets produced by bursting bubbles. Phys. Rev. Fluids 3 (1), 013603.CrossRefGoogle Scholar
Deike, L., Lenain, L. & Melville, W.K. 2017 Air entrainment by breaking waves. Geophys. Res. Lett. 44, 3779–3787.Google Scholar
Deike, L. & Melville, W.K. 2018 Gas transfer by breaking waves. Geophys. Res. Lett. 45 (19), 10–482.Google 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
Deike, L., Popinet, S. & Melville, W.K. 2015 Capillary effects on wave breaking. J. Fluid Mech. 769, 541–569.CrossRefGoogle Scholar
Desjardins, O., Moureau, V. & Pitsch, H. 2008 An accurate conservative level set/ghost fluid method for simulating turbulent atomization. J. Comput. Phys. 227 (18), 8395–8416.CrossRefGoogle Scholar
Dodd, M.S. & Ferrante, A. 2016 On the interaction of Taylor length scale size droplets and isotropic turbulence. J. Fluid Mech. 806, 356–412.CrossRefGoogle Scholar
Duret, B., Luret, G., Reveillon, J., Ménard, T., Berlemont, A. & Demoulin, F.-X. 2012 Dns analysis of turbulent mixing in two-phase flows. Intl J. Multiphase Flow 40, 93–105.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
Essadki, M., De Chaisemartin, S., Laurent, F. & Massot, M. 2018 High order moment model for polydisperse evaporating sprays towards interfacial geometry description. SIAM J. Appl. Maths 78 (4), 2003–2027.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
Galinat, S., Masbernat, O., Guiraud, P., Dalmazzone, C. & Noı, C. 2005 Drop break-up in turbulent pipe flow downstream of a restriction. Chem. Engng Sci. 60 (23), 6511–6528.CrossRefGoogle Scholar
Galinat, S., Risso, F., Masbernat, O. & Guiraud, P. 2007 Dynamics of drop breakup in inhomogeneous turbulence at various volume fractions. J. Fluid Mech. 578, 85–94.CrossRefGoogle Scholar
Garrett, C., Li, M. & Farmer, D. 2000 The connection between bubble size spectra and energy dissipation rates in the upper ocean. J. Phys. Oceanogr. 30 (9), 2163–2171.Google Scholar
Gopalan, B. & Katz, J. 2010 Turbulent shearing of crude oil mixed with dispersants generates long microthreads and microdroplets. Phys. Rev. Lett. 104 (5), 054501.CrossRefGoogle ScholarPubMed
Han, L., Luo, H. & Liu, Y. 2011 A theoretical model for droplet breakup in turbulent dispersions. Chem. Engng Sci. 66 (4), 766–776.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.Google ScholarPubMed
Keeling, R.F. 1993 On the role of large bubbles in air-sea gas exchange and supersaturation in the ocean. J. Mar. Res. 51 (2), 237–271.CrossRefGoogle Scholar
Kolmogorov, A. 1949 On the breakage of drops in a turbulent flow. Dokl. Akad. Navk SSSR 66, 825–828.Google 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.Google ScholarPubMed
Liang, J.H., McWilliams, J.C., Sullivan, P.P. & Baschek, B. 2011 Modeling bubbles and dissolved gases in the ocean. J. Geophys. Res. 116, C03015.Google Scholar
Liao, Y. & Lucas, D. 2009 A literature review of theoretical models for drop and bubble breakup in turbulent dispersions. Chem. Engng Sci. 64 (15), 3389–3406.Google Scholar
Loewen, M.R. & Melville, W.K. 1994 An experimental investigation of the collective oscillations of bubble plumes entrained by breaking waves. J. Acoust. Soc. Am. 95 (3), 1329–1343.CrossRefGoogle Scholar
Loisy, A. & Naso, A. 2017 Interaction between a large buoyant bubble and turbulence. Phys. Rev. Fluids 2, 014606.CrossRefGoogle Scholar
Lu, J. & Tryggvason, G. 2008 Effect of bubble deformability in turbulent bubbly upflow in a vertical channel. Phys. Fluids 20 (4), 040701.CrossRefGoogle Scholar
Lu, J. & Tryggvason, G. 2013 Dynamics of nearly spherical bubbles in a turbulent channel upflow. J. Fluid Mech. 732, 166.CrossRefGoogle Scholar
Luo, H. & Svendsen, H.F. 1996 Theoretical model for drop and bubble breakup in turbulent dispersions. AIChE J. 42 (5), 1225–1233.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
Marcotte, F., Michon, G.-J., Séon, T. & Josserand, C. 2019 Ejecta, corolla, and splashes from drop impacts on viscous fluids. Phys. Rev. Lett. 122 (1), 014501.CrossRefGoogle ScholarPubMed
Martinez-Bazan, C., Montanes, J.L. & Lasheras, J.C. 1999 a 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., Montanes, J.L. & Lasheras, J.C. 1999 b On the breakup of an air bubble injected into a fully developed turbulent flow. Part 2. Size pdf of the resulting daughter bubbles. J. Fluid Mech. 401, 183–207.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
Melville, W.K. 1996 The role of surface-wave breaking in air-sea interaction. Annu. Rev. Fluid Mech. 28 (1), 279–321.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
Mukherjee, S., Safdari, A., Shardt, O., Kenjereš, S. & Van den Akker, H.E.A. 2019 Droplet–turbulence interactions and quasi-equilibrium dynamics in turbulent emulsions. J. Fluid Mech. 878, 221–276.CrossRefGoogle Scholar
Nambiar, D.K.R., Kumar, R., Das, T.R. & Gandhi, K.S. 1992 A new model for the breakage frequency of drops in turbulent stirred dispersions. Chem. Engng Sci. 47 (12), 2989–3002.CrossRefGoogle Scholar
Naso, A. & Prosperetti, A. 2010 The interaction between a solid particle and a turbulent flow. New J. Phys. 12 (3), 033040.CrossRefGoogle Scholar
Perrard, S., Rivière, A., Mostert, W. & Deike, L. 2021 Bubble deformation by a turbulent flow. J. Fluid Mech. (submitted) arXiv:2011.1054.Google Scholar
Pope, S.B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Popinet, S. 2003 Gerris: a tree-based adaptive solver for the incompressible euler equations in complex geometries. J. Comput. Phys. 190 (2), 572–600.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
Qi, Y., Masuk, A.U.M. & Ni, R. 2020 Towards a model of bubble breakup in turbulence through experimental constraints. Intl J. Multiphase Flow 132, 103397.CrossRefGoogle Scholar
Qian, D., McLaughlin, J.B., Sankaranarayanan, K., Sundaresan, S. & Kontomaris, K. 2006 Simulation of bubble breakup dynamics in homogeneous turbulence. Chem. Engng Commun. 193 (8), 1038–1063.Google Scholar
Ravelet, F., Colin, C. & Risso, F. 2011 On the dynamics and breakup of a bubble rising in a turbulent flow. Phys. Fluids 23 (10), 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
Revuelta, A., Rodríguez-Rodríguez, J. & Martínez-Bazán, C. 2006 Bubble break-up in a straining flow at finite Reynolds numbers. J. Fluid Mech. 551, 175–184.CrossRefGoogle Scholar
Risso, F. 2000 The mechanisms of deformation and breakup of drops and bubbles. Multiphase Sci. Technol. 12 (1).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
Rojas, G. & Loewen, M.R. 2007 Fiber-optic probe measurements of void fraction and bubble size distributions beneath breaking waves. Exp. Fluids 43 (6), 895–906.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.J., Mostert, W., Perrard, S. & Deike, L. 2019 Bubble pinch-off in turbulence. Proc. Natl Acad. Sci. USA 116 (51), 25412–25417.CrossRefGoogle ScholarPubMed
Scardovelli, R. & Zaleski, S. 1999 Direct numerical simulation of free-surface and interfacial flow. Annu. Rev. Fluid Mech. 31 (1), 567–603.CrossRefGoogle Scholar
Scott, D.W. 2015 Multivariate Density Estimation: Theory, Practice, and Visualization. John Wiley & Sons.CrossRefGoogle Scholar
Shakeri, M., Tavakolinejad, M. & Duncan, J.H. 2009 An experimental investigation of divergent bow waves simulated by a two-dimensional plus temporal wave marker technique. J. Fluid Mech. 634, 217–243.CrossRefGoogle Scholar
Shan, X. & Chen, H. 1993 Lattice Boltzmann model for simulating flows with multiple phases and components. Phys. Rev. E 47 (3), 1815.CrossRefGoogle ScholarPubMed
Soligo, G., Roccon, A. & Soldati, A. 2019 Breakage, coalescence and size distribution of surfactant-laden droplets in turbulent flow. J. Fluid Mech. 881, 244–282.CrossRefGoogle Scholar
Spandan, V., Verzicco, R. & Lohse, D. 2018 Physical mechanisms governing drag reduction in turbulent Taylor–Couette flow with finite-size deformable bubbles. J. Fluid Mech. 849, R3.CrossRefGoogle Scholar
Thoraval, M.-J., Takehara, K., Etoh, T.G., Popinet, S., Ray, P., Josserand, C., Zaleski, S. & Thoroddsen, S.T. 2012 von kármán vortex street within an impacting drop. Phys. Rev. Lett. 108, 264506.CrossRefGoogle Scholar
Toutant, A., Labourasse, E., Lebaigue, O. & Simonin, O. 2008 Dns of the interaction between a deformable buoyant bubble and a spatially decaying turbulence: a priori tests for les two-phase flow modelling. Comput. Fluids 37 (7), 877–886.CrossRefGoogle Scholar
Tryggvason, G., Bunner, B., Esmaeeli, A., Juric, D., Al-Rawahi, N., Tauber, W., Han, J., Nas, S. & Jan, Y.-J. 2001 A front-tracking method for the computations of multiphase flow. J. Comput. Phys. 169 (2), 708–759.CrossRefGoogle Scholar
Tsouris, C. & Tavlarides, L.L. 1994 Breakage and coalescence models for drops in turbulent dispersions. AIChE J. 40 (3), 395–406.CrossRefGoogle Scholar
Unverdi, S.O. & Tryggvason, G. 1992 A front-tracking method for viscous, incompressible, multi-fluid flows.Google 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. 2020 Fragmentation versus cohesion. J. Fluid Mech. 898.CrossRefGoogle Scholar
Wallace, D.W.R. & Wirick, C.D. 1992 Large air–sea gas fluxes associated with breaking waves. Nature 356 (6371), 694.CrossRefGoogle Scholar
Wang, T., Wang, J. & Jin, Y. 2003 A novel theoretical breakup kernel function for bubbles/droplets in a turbulent flow. Chem. Engng Sci. 58 (20), 4629–4637.CrossRefGoogle Scholar
Wang, Z., Yang, J. & Stern, F. 2016 High-fidelity simulations of bubble, droplet and spray formation in breaking waves. J. Fluid Mech. 792, 307–327.CrossRefGoogle Scholar