Hostname: page-component-77c89778f8-7drxs Total loading time: 0 Render date: 2024-07-20T08:21:08.283Z Has data issue: false hasContentIssue false
  • English
  • Français

Experiments on the fragmentation of a buoyant liquid volume in another liquid

Published online by Cambridge University Press:  16 May 2014

M. Landeau ,
R. Deguen  and
P. Olson
M. Landeau*
Affiliation:
Department of Earth and Planetary Sciences, Johns Hopkins University, Baltimore, MD 21218, USA Dynamique des Fluides Géologiques, Institut de Physique du Globe de Paris, Sorbonne Paris Cité, Université Paris Diderot, CNRS UMR 7154, 1 rue Jussieu 75238 Paris CEDEX 5, France
R. Deguen
Affiliation:
Laboratoire de Géologie de Lyon, Université Lyon 1, 2 rue Raphaël Dubois, 69622 Villeurbanne, France Institut de Mécanique des Fluides de Toulouse, Université de Toulouse (INPT, UPS) and CNRS, 2 allée Camille Soula, Toulouse, 31400, France
P. Olson
Affiliation:
Department of Earth and Planetary Sciences, Johns Hopkins University, Baltimore, MD 21218, USA
*
†Email address for correspondence: mlandeau@jhu.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We present experiments on the instability and fragmentation of volumes of heavier liquids released into lighter immiscible liquids. We focus on the regime defined by small Ohnesorge numbers, density ratios of the order of one, and variable Weber numbers. The observed stages in the fragmentation process include deformation of the released fluid by either Rayleigh–Taylor instability (RTI) or vortex ring roll-up and destabilization, formation of filamentary structures, capillary instability, and drop formation. At low and intermediate Weber numbers, a wide variety of fragmentation regimes is identified. Those regimes depend on early deformations, which mainly result from a competition between the growth of RTI and the roll-up of a vortex ring. At high Weber numbers, turbulent vortex ring formation is observed. We have adapted the standard theory of turbulent entrainment to buoyant vortex rings with initial momentum. We find consistency between this theory and our experiments, indicating that the concept of turbulent entrainment is valid for non-dispersed immiscible fluids at large Weber and Reynolds numbers.

JFM classification

Drops and Bubbles: Breakup/coalescence Drops and Bubbles: Drops Convection: Plumes/thermals
Type
Papers
Information
Journal of Fluid Mechanics , Volume 749 , 25 June 2014 , pp. 478 - 518
Copyright
© 2014 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

Adalsteinsson, D., Camassa, R., Harenberg, S., Lin, Z., McLaughlin, R. M., Mertens, K., Reis, J., Schlieper, W. & White, B. 2011 Subsurface trapping of oil plumes in stratification: laboratory investigations. In Monitoring and Modeling the Deepwater Horizon Oil Spill: A Record-Breaking Enterprise (ed. Liu, Y., MacFadyen, A., Ji, Z. G. & Weisberg, R. H.), Geophysical Monograph Series, vol. 195, pp. 257–262. AGU.Google Scholar
Alahyari, A. & Longmire, E. K. 1995 Dynamics of experimentally simulated microbursts. AIAA J. 33 (11), 2128–2136.CrossRefGoogle Scholar
Alahyari, A. A. & Longmire, E. K. 1997 Concentration measurements in experimental microbursts. AIAA J. 35 (3), 569–571.CrossRefGoogle Scholar
Archer, P. J., Thomas, T. G. & Coleman, G. N. 2008 Direct numerical simulation of vortex ring evolution from the laminar to the early turbulent regime. J. Fluid Mech. 598, 201–226.CrossRefGoogle Scholar
Arecchi, F. T., Buah-Bassuah, P. K., Francini, F., Perez-Garcia, C. & Quercioli, F. 1989 An experimental investigation of the break-up of a liquid-drop falling in a miscible fluid. Europhys. Lett. 9 (4), 333–338.Google Scholar
Arecchi, F. T., Buah-Bassuah, P. K. & Perez-Garcia, C. 1991 Fragment formation in the break-up of a drop falling in a miscible liquid. Europhys. Lett. 15 (4), 429–434.CrossRefGoogle Scholar
Baines, W. D. 1975 Entrainment by a plume or jet at a density interface. J. Fluid Mech. 68, 309–320.CrossRefGoogle Scholar
Baines, W. D. & Hopfinger, E. J. 1984 Thermals with large density difference. Atmos. Environ. 18 (6), 1051–1057.Google Scholar
Batchelor, G. K. 1954 Heat convection and buyoancy effects in fluids. Q. J. R. Meteorol. Soc. 80 (345), 339–358.Google Scholar
Batchelor, G. K. 1987 The stability of a large gas bubble rising through liquid. J. Fluid Mech. 184, 399–422.Google Scholar
Baumann, N., Joseph, D. D., Mohr, P. & Renardy, Y. 1992 Vortex rings of one fluid in another in free-fall. Phys. Fluids A 4 (3), 567–580.CrossRefGoogle Scholar
Bellman, R. & Pennington, R. H. 1954 Effects of surface tension and viscosity on Taylor instability. Q. J. Appl. Maths 12 (2), 151–162.CrossRefGoogle Scholar
Bettelini, M. S. G. & Fannelop, T. K. 1993 Underwater plume from an instantaneously started source. Appl. Ocean Res. 15 (4), 195–206.CrossRefGoogle Scholar
Bond, D. & Johari, H. 2010 Impact of buoyancy on vortex ring development in the near field. Exp. Fluids 48 (5), 737–745.CrossRefGoogle Scholar
Bremond, N. & Villermaux, E. 2006 Atomization by jet impact. J. Fluid Mech. 549, 273–306.CrossRefGoogle Scholar
Buah-Bassuah, P. K., Rojas, R., Residori, S. & Arecchi, F. T. 2005 Fragmentation instability of a liquid drop falling inside a heavier miscible fluid. Phys. Rev. E 72, 067301.CrossRefGoogle ScholarPubMed
Bush, J. W. M., Thurber, B. A. & Blanchette, F. 2003 Particle clouds in homogeneous and stratified environments. J. Fluid Mech. 489, 29–54.CrossRefGoogle Scholar
Camilli, R., Di Iorio, D., Bowen, A., Reddy, C. M., Techet, A. H., Yoerger, D. R., Whitcomb, L. L., Seewald, J. S., Sylva, S. P. & Fenwick, J. 2012 Acoustic measurement of the Deepwater Horizon Macondo well flow rate. Proc. Natl Acad. Sci. USA 109 (50), 20235–20239.CrossRefGoogle ScholarPubMed
Camilli, R., Reddy, C. M., Yoerger, D. R., Van Mooy, B. A. S., Jakuba, M. V., Kinsey, J. C., McIntyre, C. P., Sylva, S. P. & Maloney, J. V. 2010 Tracking hydrocarbon plume transport and biodegradation at Deepwater Horizon. Science 330 (6001), 201–204.Google Scholar
Canup, R. M. 2004 Simulations of a late lunar-forming impact. Icarus 168 (2), 433–456.CrossRefGoogle Scholar
Carazzo, G., Kaminski, E. & Tait, S. 2010 The rise and fall of turbulent fountains: a new model for improved quantitative predictions. J. Fluid Mech. 657, 265–284.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Clarendon.Google Scholar
Chung, Y. & Cramb, A. W. 2000 Dynamic and equilibrium interfacial phenomena in liquid steel-slag systems. Metall. Trans. B 31 (5), 957–971.CrossRefGoogle Scholar
Cotel, A. J. & Breidenthal, R. E. 1997 A model of stratified entrainment using vortex persistence. Appl. Sci. Res. 57 (3–4), 349–366.CrossRefGoogle Scholar
Cotel, A. J., Gjestvang, J. A., Ramkhelawan, N. N. & Breidenthal, R. E. 1997 Laboratory experiments of a jet impinging on a stratified interface. Exp. Fluids 23 (2), 155–160.Google Scholar
Dahl, T. W. & Stevenson, D. J. 2010 Turbulent mixing of metal and silicate during planet accretion – and interpretation of the Hf–W chronometer. Earth Planet. Sci. Lett. 295 (1–2), 177–186.Google Scholar
Dazin, A., Dupont, P. & Stanislas, M. 2006a Experimental characterization of the instability of the vortex ring. Part 1: linear phase. Exp. Fluids 40 (3), 383–399.CrossRefGoogle Scholar
Dazin, A., Dupont, P. & Stanislas, M. 2006b Experimental characterization of the instability of the vortex ring. Part 2: nonlinear phase. Exp. Fluids 41 (3), 401–413.Google Scholar
Deguen, R., Landeau, M. & Olson, P. 2014 Turbulent metal-silicate mixing, fragmentation, and equilibration in magma oceans. Earth Planet. Sci. Lett. 391, 274–287.Google Scholar
Deguen, R., Olson, P. & Cardin, P. 2011 Experiments on turbulent metal-silicate mixing in a magma ocean. Earth Planet. Sci. Lett. 310 (3–4), 303–313.CrossRefGoogle Scholar
Didden, N. 1979 On the formation of vortex rings: rolling-up and production of circulation. Z. Angew. Math. Phys. 30 (1), 101–116.CrossRefGoogle Scholar
Epstein, M. & Fauske, H. K. 2001 Applications of the turbulent entrainment assumption to immiscible gas–liquid and liquid–liquid systems. Chem. Engng Res. Des. 79 (A4), 453–462.CrossRefGoogle Scholar
Escudier, M. P. & Maxworthy, T. 1973 On the motion of turbulent thermals. J. Fluid Mech. 61, 541–552.CrossRefGoogle Scholar
Faeth, G. M., Hsiang, L. P. & Wu, P. K. 1995 Structure and breakup properties of sprays. Intl J. Multiphase Flow 21, 99–127.CrossRefGoogle Scholar
Fischer, H. B., List, E. J., Koh, R., Imberger, J. & Brooks, N. 1979 Mixing in Inland and Coastal Waters. Academic.Google Scholar
Friedman, P. D. & Katz, J. 1999 The flow and mixing mechanisms caused by the impingement of an immiscible interface with a vertical jet. Phys. Fluids 11 (9), 2598–2606.CrossRefGoogle Scholar
Friedman, P. D. & Katz, J. 2000 Rise height for negatively buoyant fountains and depth of penetration for negatively buoyant jets impinging an interface. Trans. ASME J. Fluids Engng 122 (4), 779–782.CrossRefGoogle Scholar
Fukumoto, Y. & Hattori, J. 2005 Curvature instability of a vortex ring. J. Fluid Mech. 526, 77–115.CrossRefGoogle Scholar
Funakoshi, K. 2010 In situ viscosity measurements of liquid Fe–S alloys at high pressures. Hi 30 (1), 60–64.Google Scholar
Gan, L., Dawson, J. R. & Nickels, T. B. 2012 On the drag of turbulent vortex rings. J. Fluid Mech. 709, 85–105.Google Scholar
Gelfand, B. E. 1996 Droplet breakup phenomena in flows with velocity lag. Prog. Energy Combust. Sci. 22 (3), 201–265.CrossRefGoogle Scholar
Gharib, M., Rambod, E. & Shariff, K. 1998 A universal time scale for vortex ring formation. J. Fluid Mech. 360, 121–140.Google Scholar
Glezer, A. & Coles, D. 1990 An experimental-study of a turbulent vortex ring. J. Fluid Mech. 211, 243–283.Google Scholar
Grace, J. R., Wairegi, T. & Brophy, J. 1978 Break-up of drops and bubbles in stagnant media. Can. J. Chem. Engng 56 (1), 3–8.Google Scholar
Guildenbecher, D. R., Lopez-Rivera, C. & Sojka, P. E. 2009 Secondary atomization. Exp. Fluids 46 (3), 371–402.Google Scholar
Han, J. & Tryggvason, G. 1999 Secondary breakup of axisymmetric liquid drops. I. Acceleration by a constant body force. Phys. Fluids 11 (12), 3650–3667.Google Scholar
Han, J. & Tryggvason, G. 2001 Secondary breakup of axisymmetric liquid drops. II. Impulsive acceleration. Phys. Fluids 13 (6), 1554–1565.CrossRefGoogle Scholar
Harper, E. Y., Grube, G. W. & Chang, I. 1972 On the breakup of accelerating liquid drops. J. Fluid Mech. 52, 565–591.Google Scholar
Hattori, Y. & Fukumoto, Y. 2003 Short-wavelength stability analysis of thin vortex rings. Phys. Fluids 15 (10), 3151–3163.Google Scholar
Hattori, Y. & Hijiya, K. 2010 Short-wavelength stability analysis of Hill’s vortex with/without swirl. Phys. Fluids 22 (7), 074104.Google Scholar
Hinze, J. O. 1955 Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes. AIChE J. 1 (3), 289–295.CrossRefGoogle Scholar
Ichikawa, H., Labrosse, S. & Kurita, K. 2010 Direct numerical simulation of an iron rain in the magma ocean. J. Geophys. Res. 115, B01404.Google Scholar
Jacobs, J. W. & Catton, I. 1988 Three-dimensional Rayleigh–Taylor instability. 1. Weakly nonlinear-theory. J. Fluid Mech. 187, 329–352.CrossRefGoogle Scholar
Joseph, D. D., Belanger, J. & Beavers, G. S. 1999 Breakup of a liquid drop suddenly exposed to a high-speed airstream. Intl J. Multiphase Flow 25 (6–7), 1263–1303.Google Scholar
Joye, S. B., MacDonald, I. R., Leifer, I. & Asper, V. 2011 Magnitude and oxidation potential of hydrocarbon gases released from the BP oil well blowout. Nature Geosci. 4 (3), 160–164.Google Scholar
Kaminski, E., Tait, S. & Carazzo, G. 2005 Turbulent entrainment in jets with arbitrary buoyancy. J. Fluid Mech. 526, 361–376.CrossRefGoogle Scholar
Karki, B. & Stixrude, L. 2010 Viscosity of $\mathrm{MgSiO}_{3}$ Liquid at Earth’s mantle conditions: implications for an Early Magma Ocean. Science 328 (5979), 740–742.CrossRefGoogle Scholar
Kojima, M., Hinch, E. J. & Acrivos, A. 1984 The formation and expansion of a toroidal drop moving in a viscous-fluid. Phys. Fluids 27 (1), 19–32.CrossRefGoogle Scholar
Lehr, B., Nristol, S. & Possolo, A.2010 Oil budget calculator – Deepwater Horizon, technical documentation: a report to the National Incident Command. Federal Interagency Solutions Group.Google Scholar
Leitch, A. M. & Baines, W. D. 1989 Liquid volume flux in a weak bubble plume. J. Fluid Mech. 205, 77–98.Google Scholar
Liebske, C., Schmickler, B., Terasaki, H., Poe, B. T., Suzuki, A., Funakoshi, K., Ando, R. & Rubie, D. C. 2005 Viscosity of peridotite liquid up to 13 GPa: implications for magma ocean viscosities. Earth Planet. Sci. Lett. 240 (3–4), 589–604.CrossRefGoogle Scholar
Linden, P. F. 1973 The interaction of a vortex ring with a sharp density interface: a model for turbulent entrainment. J. Fluid Mech. 60, 467–480.Google Scholar
Loth, E. & Faeth, G. M. 1989 Structure of underexpanded round air jets submerged in water. Intl J. Multiphase Flow 15 (4), 589–603.Google Scholar
Loth, E. & Faeth, G. M. 1990 Structure of plane underexpanded air-jets into water. AIChE J. 36 (6), 818–826.CrossRefGoogle Scholar
Lundgren, T. S., Yao, J. & Mansour, N. N. 1992 Miscroburst modelling and scaling. J. Fluid Mech. 239, 461–488.Google Scholar
Marmottant, P. H. & Villermaux, E. 2004 On spray formation. J. Fluid Mech. 498, 73–111.CrossRefGoogle Scholar
Marugan-Cruz, C., Rodriguez-Rodriguez, J. & Martinez-Bazan, C. 2009 Negatively buoyant starting jets. Phys. Fluids 21 (11), 117101.Google Scholar
Marugan-Cruz, C., Rodriguez-Rodriguez, J. & Martinez-Bazan, C. 2013 Formation regimes of vortex rings in negatively buoyant starting jets. J. Fluid Mech. 716, 470–486.Google Scholar
Maxworthy, T. 1972 Structure and stability of vortex rings. J. Fluid Mech. 51 (JAN11), 15–32.Google Scholar
Maxworthy, T. 1974 Turbulent vortex rings. J. Fluid Mech. 64, 227–240.Google Scholar
McNutt, M. K., Camilli, R., Crone, T. J., Guthrie, G. D., Hsieh, P. A., Ryerson, T. B., Savas, O. & Shaffer, F. 2012 Review of flow rate estimates of the Deepwater Horizon oil spill. Proc. Natl Acad. Sci. USA 109 (50), 20260–20267.Google Scholar
Melosh, H. J. 1990 Giant impacts and the thermal state of the early Earth. In Origin of the Earth (ed. Newsom, H. & Jones, J.), Oxford University Press.Google Scholar
Milgram, J. H. 1983 Mean flow in round bubble plumes. J. Fluid Mech. 133, 345–376.Google Scholar
Miller, G. H., Stolper, E. M. & Ahrens, T. J. 1991 The equation of state of a molten komatiite. 1. Shock-wave compression to 36 GPa. J. Geophys. Res. 96 (B7), 11831–11848.Google Scholar
Moore, D. W. 1974 Numerical study of roll-up of a finite vortex sheet. J. Fluid Mech. 63, 225–235.Google Scholar
Morard, G., Siebert, J., Andrault, D., Guignot, N., Garbarino, G., Guyot, F. & Antonangeli, D. 2013 The earth’s core composition from high pressure density measurements of liquid iron alloys. Earth Planet. Sci. Lett. 373, 169–178.Google Scholar
Morton, B. R., Taylor, G. & Turner, J. S. 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond. 234 (1196), 1–23.Google Scholar
Nitsche, M. & Krasny, R. 1994 A numerical study of vortex ring formation at the edge of a circular tube. J. Fluid Mech. 276, 139–161.Google Scholar
Ohta, M. & Sussman, M. 2012 The buoyancy-driven motion of a single skirted bubble or drop rising through a viscous liquid. Phys. Fluids 24 (11), 112101.Google Scholar
Patel, P. D. & Theofanous, T. G. 1981 Hydrodynamic fragmentation of drops. J. Fluid Mech. 103, 207–223.Google Scholar
Pierazzo, E., Vickery, A. M. & Melosh, H. J. 1997 A reevaluation of impact melt production. Icarus 127 (2), 408–423.Google Scholar
Pilch, M. & Erdman, C. A. 1987 Use of breakup time data and velocity history data to predict the maximum size of stable fragments for acceleration-induced breakup of a liquid drop. Intl J. Multiphase Flow 13 (6), 741–757.Google Scholar
Pottebaum, T. S. & Gharib, M. 2004 The pinch-off process in a starting buoyant plume. Exp. Fluids 37 (1), 87–94.Google Scholar
Priestley, C. H. B. & Ball, F. K. 1955 Continuous convection from an isolated source of heat. Q. J. R. Meteorol. Soc. 81 (348), 144–157.Google Scholar
Rahimipour, H. & Wilikinson, D.1992 Dynamic behavious of particle clouds. In 11th Australian Fluid Mech. Conference University of Tasmania, Hobart, Australia, pp. 743–746.Google Scholar
Reddy, C. M., Arey, J. S., Seewald, J. S., Sylva, S. P., Lemkau, K. L., Nelson, R. K., Carmichael, C. A., McIntyre, C. P., Fenwick, J., Ventura, G. T., Van Mooy, B. A. S. & Camilli, R. 2012 Composition and fate of gas and oil released to the water column during the Deepwater Horizon oil spill. Proc. Natl Acad. Sci. USA 109 (50), 20229–20234.Google Scholar
Ricard, Y., Sramek, O. & Dubuffet, F. 2009 A multi-phase model of runaway core-mantle segregation in planetary embryos. Earth Planet. Sci. Lett. 284 (1–2), 144–150.CrossRefGoogle Scholar
Richards, J. M. 1961 Experiments on the penetration of an interface by buoyant thermals. J. Fluid Mech. 11 (3), 369–384.CrossRefGoogle Scholar
Rubie, D. C., Melosh, H. J., Reid, J. E., Liebske, C. & Righter, K. 2003 Mechanisms of metal-silicate equilibration in the terrestrial magma ocean. Earth Planet. Sci. Lett. 205 (3–4), 239–255.Google Scholar
Ruggaber, G. J.2000 The dynamics of particle clouds related to open-water sediment disposal. PhD thesis, Department of Civil and Environmental Engineering, MIT.Google Scholar
Saffman, P. G. 1978 Number of waves on unstable vortex rings. J. Fluid Mech. 84, 625–639.Google Scholar
Saffman, P. G. 1992 Vortex Dynamics. Cambridge University Press.Google Scholar
Samuel, H. 2012 A re-evaluation of metal diapir breakup and equilibration in terrestrial magma oceans. Earth Planet. Sci. Lett. 313, 105–114.Google Scholar
Schersten, A., Elliott, T., Hawkesworth, C., Russell, S. & Masarik, J. 2006 Hf-W evidence for rapid differentiation of iron meteorite parent bodies. Earth Planet. Sci. Lett. 241 (3–4), 530–542.Google Scholar
Scorer, R. S. 1957 Experiments on convection of isolated masses of buoyant fluid. J. Fluid Mech. 2 (6), 583–594.Google Scholar
Shariff, K., Verzicco, R. & Orlandi, P. 1994 A numerical study of three-dimensional vortex ring instabilities – viscous corrections and early nonlinear stage. J. Fluid Mech. 279, 351–375.Google Scholar
Sheffield, J. S. 1977 Trajectories of an ideal vortex pair near an orifice. Phys. Fluids 20 (4), 543–545.Google Scholar
Shusser, M. & Gharib, M. 2000 A model for vortex ring formation in a starting buoyant plume. J. Fluid Mech. 416, 173–185.Google Scholar
Simpkins, P. G. & Bales, E. L. 1972 Water-drop response to sudden accelerations. J. Fluid Mech. 55, 629–639.Google Scholar
Sipp, D., Fabre, D., Michelin, S. & Jacquin, L. 2005 Stability of a vortex with a heavy core. J. Fluid Mech. 526, 67–76.Google Scholar
Socolofsky, S. A., Adams, E. E. & Sherwood, C. R. 2011 Formation dynamics of subsurface hydrocarbon intrusions following the Deepwater Horizon blowout. Geophys. Res. Lett. 38, L09602.Google Scholar
Taylor, G. I.1945 Dynamics of a hot mass rising in air. US Atomic Energy Commission, MDDC-919, LADC-276.Google Scholar
Terasaki, H., Urakawa, S., Rubie, D. C., Funakoshi, K., Sakamaki, T., Shibazaki, Y., Ozawa, S. & Ohtani, E. 2012 Interfacial tension of Fe–Si liquid at high pressure: implications for liquid Fe-alloy droplet size in magma oceans. Phys. Earth Planet. Inter. 202, 1–6.Google Scholar
Theofanous, T. G. 2011 Aerobreakup of Newtonian and Viscoelastic Liquids. Ann. Rev. Fluid Mech. 43, 661–690.CrossRefGoogle Scholar
Theofanous, T. G. & Li, G. J. 2008 On the physics of aerobreakup. Phys. Fluids 20 (5), 052103.Google Scholar
Theofanous, T. G., Li, G. J. & Dinh, T. N. 2004 Aerobreakup in rarefied supersonic gas flows. Trans. ASME J. Fluids Engng 126 (4), 516–527.Google Scholar
Theofanous, T. G., Li, G. J., Dinh, T. N. & Chang, C. H. 2007 Aerobreakup in disturbed subsonic and supersonic flow fields. J. Fluid Mech. 593, 131–170.Google Scholar
Thompson, R. S., Snyder, W. H. & Weil, J. C. 2000 Laboratory simulation of the rise of buoyant thermals created by open detonation. J. Fluid Mech. 417, 127–156.Google Scholar
Tonks, W. B. & Melosh, H. J. 1993 Magma ocean formation due to giant impacts. J. Geophys. Res. 98 (E3), 5319–5333.Google Scholar
Turner, J. S. 1957 Buoyant vortex rings. Proc. R. Soc. Lond. 239 (1216), 61–75.Google Scholar
Turner, J. S. 1964 The dynamics of spheroidal masses of buoyant fluid. J. Fluid Mech. 17, 481–490.Google Scholar
Turner, J. S. 1966 Jets and plumes with negative or reversing buoyancy. J. Fluid Mech. 26 (4), 779–792.Google Scholar
Villermaux, E. & Bossa, B. 2009 Single-drop fragmentation determines size distribution of raindrops. Nat. Phys. 5 (9), 697–702.Google Scholar
Villermaux, E. & Bossa, B. 2011 Drop fragmentation on impact. J. Fluid Mech. 668, 412–435.CrossRefGoogle Scholar
Wang, C. P. 1971 Motion of an isolated buoyant thermal. Phys. Fluids 14 (8), 1643–1647.Google Scholar
Wang, H. W. & Law, A. W. K. 2002 Second-order integral model for a round turbulent buoyant jet. J. Fluid Mech. 459, 397–428.Google Scholar
Weigand, A. & Gharib, M. 1994 On the decay of a turbulent vortex ring. Phys. Fluids 6 (12), 3806–3808.CrossRefGoogle Scholar
Weimer, J. C., Faeth, G. M. & Olson, D. R. 1973 Penetration of vapor jets submerged in subcooled liquids. AIChE J. 19 (3), 552–558.Google Scholar
Widnall, S. E., Bliss, D. B. & Tsai, C. Y. 1974 Instability of short waves on a vortex ring. J. Fluid Mech. 66, 35–47.Google Scholar
Widnall, S. E. & Sullivan, J. P. 1973 On the stability of vortex rings. Proc. R. Soc. Lond. A 332 (1590), 335–353.Google Scholar
Widnall, S. E. & Tsai, C. Y. 1977 The instability of the thin vortex ring of constant vorticity. Phil. Trans. R. Soc. Lond. A 287 (1344), 273–305.Google Scholar
de Wijs, G. A., Kresse, G., Vocadlo, L., Dobson, D., Alfe, D., Gillan, M. J. & Price, G. D. 1998 The viscosity of liquid iron at the physical conditions of the Earth’s core. Nature 392 (6678), 805–807.Google Scholar
Yang, J. W. & Yang, H. S. 1990 Liquid–liquid mixing for the breakup of accelerating drops. Korean J. Chem. Engng 7 (1), 22–30.Google Scholar
Yoshino, T., Walter, M. J. & Katsura, T. 2003 Core formation in planetesimals triggered by permeable flow. Nature 422 (6928), 154–157.Google Scholar
Zhang, Q. & Cotel, A. 2000 Entrainment due to a thermal impinging on a stratified interface with and without buoyancy reversal. J. Geophys. Res. 105 (D12), 15457–15467.Google Scholar
Zhao, H., Liu, H., Li, W. & Xu, J. 2010 Morphological classification of low viscosity drop bag breakup in a continuous air jet stream. Phys. Fluids 22 (11), 114103.Google Scholar

Landeau et al. supplementary movie

Movie of an experiment in the RT piercing fragmentation regime, We≈70, P≈0.22, Immersed configuration (24 frames per second).

Download Landeau et al. supplementary movie(Video)
Video 168.4 KB

Landeau et al. supplementary movie

Movie of an experiment in the vortex ring destabilization regime, We≈40, P≈0.22, Surface configuration (24 frames per second).

Download Landeau et al. supplementary movie(Video)
Video 715.2 KB

Landeau et al. supplementary movie

Movie of an experiment in the turbulent regime, immiscible turbulent thermal, We ≈ 1000, P ≈ 0.92, Immersed configuration (24 frames per second).

Download Landeau et al. supplementary movie(Video)
Video 873.6 KB