Hostname: page-component-745bb68f8f-5r2nc Total loading time: 0 Render date: 2025-02-01T03:59:16.385Z Has data issue: false hasContentIssue false
  • English
  • Français

Splash behaviour and oily marine aerosol production by raindrops impacting oil slicks

Published online by Cambridge University Press:  07 September 2015

David W. Murphy ,
Cheng Li ,
Vincent d’Albignac ,
David Morra  and
Joseph Katz
David W. Murphy
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
Cheng Li
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
Vincent d’Albignac
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
David Morra
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
Joseph Katz*
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The high-speed impact of a droplet on a bulk fluid at high Weber number (We) is not well understood but is relevant to the production of marine aerosol by raindrop impact on the sea surface. These splashes produce a subsurface cavity and a crown which closes into a bubble canopy, but a floating layer of immiscible oil, such as a crude oil slick, alters the splash dynamics. The effects of oil layer fluid properties and thickness, droplet size and impact speed are examined by high-speed visualization. Oil layer rupture and crown behaviour are classified by dimensional scaling. The subsurface cavity volume for impact on thick layers is shown to depend on the Reynolds number (Re), although canopy formation at high Re introduces a competing We effect since rapid canopy closure is found to retard cavity expansion. Time-resolved kinematic measurements show that thin crude oil slicks similarly alter crown closure and cavity growth. The size and spatial distributions of airborne droplets are examined using high-speed holographic microscopy. The droplets have a bimodal distribution with peaks at 50 and $225~{\rm\mu}\text{m}$ and are clustered by size at different elevation angles. Small droplets ($50~{\rm\mu}\text{m}$) are ejected primarily at shallow angles, indicating production by splashing within the first $100~{\rm\mu}\text{s}$ and by breakup of microligaments. Larger droplets ($225~{\rm\mu}\text{m}$) are found at steeper elevation angles, indicating later production by capillary instability acting on large ligaments protruding upward from the crown. Intermittent droplet release while the ligaments grow and sweep upward is thought to contribute to the size-dependent spatial ordering. Greater numbers of small droplets are produced at high elevation angles when a crude oil layer is present, indicating satellite droplet formation from ligament breakup. A crude oil layer also increases the target fluid Ohnesorge number, leading to creation of an intact ejecta sheet, which then ruptures to form aerosolized oil droplets.

JFM classification

Drops and Bubbles: Aerosols/atomization Geophysical and Geological Flows: Air/sea interactions Drops and Bubbles: Drops and Bubbles
Type
Papers
Information
Journal of Fluid Mechanics , Volume 780 , 10 October 2015 , pp. 536 - 577
Check for updates
Copyright
© 2015 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

Aeppli, C., Nelson, R. K., Radović, J. R., Carmichael, C. A., Valentine, D. L. & Reddy, C. M. 2014 Recalcitrance and degradation of petroleum biomarkers upon abiotic and biotic natural weathering of Deepwater Horizon oil. Environ. Sci. Technol. 48, 6726–6734.Google Scholar
Afeti, G. M. & Resch, F. J. 1990 Distribution of the liquid aerosol produced from bursting bubbles in sea and distilled water. Tellus 42 B, 378–384.CrossRefGoogle Scholar
Agbaglah, G. & Deegan, R. D. 2014 Growth and instability of the liquid rim in the crown splash regime. J. Fluid Mech. 752, 485–496.Google Scholar
Agbaglah, G., Thoraval, M. J., Thoroddsen, S. T., Zhang, L. V., Fezzaa, K. & Deegan, R. D. 2015 Drop impact into a deep pool: vortex shedding and jet formation. J. Fluid Mech. 764, R1.Google Scholar
Aguilera, F., Méndez, J., Pásaro, E. & Laffon, B. 2010 Review on the effects of exposure to spilled oils on human health. J. Appl. Toxicol 30, 291–301.CrossRefGoogle ScholarPubMed
Alm, S. R., Reichard, D. L. & Hall, F. R. 1987 Effects of spray drop size and distribution of drops containing bifenthrin on Tetranychus urticae (Acari: Tetranychidae). J. Econ. Entomol. 80, 517–520.Google Scholar
Amador, G. J., Yamada, Y., McCurley, M. & Hu, D. L. 2013 Splash-cup plants accelerate raindrops to disperse seeds. J. R. Soc. Interface 10, 1–12.Google Scholar
Bauget, F., Langevin, D. & Lenormand, R. 2001 Dynamic surface properties of asphaltenes and resins at the oil–air interface. J. Colloid Interface Sci. 239, 501–508.Google Scholar
Bernardin, J. D., Stebbins, C. J. & Mudawar, I. 1997 Mapping of impact and heat transfer regimes of water drops impinging on a polished surface. Intl J. Heat Mass Transfer 40 (2), 247–267.Google Scholar
Bisighini, A., Cossali, G. E., Tropea, C. & Roisman, I. V. 2010 Crater evolution after the impact of a drop onto a semi-infinite liquid target. Phys. Rev. E 82, 036319.Google Scholar
Blanchard, D. C. 1989 The ejection of drops from the sea and their enrichment with bacteria and other materials: a review. Estuaries 12 (3), 127–137.Google Scholar
Blanchard, D. C. & Woodcock, A. H. 1957 Bubble formation and modification in the sea and its meteorological significance. Tellus 9 (2), 145–158.Google Scholar
Bremond, N. & Villermaux, E. 2006 Atomization by jet impact. J. Fluid Mech. 549, 273–306.Google Scholar
Cai, Y. K. 1989 Phenomena of a liquid drop falling to a liquid surface. Exp. Fluids 7, 388–394.Google Scholar
Chapman, D. S. & Critchlow, P. R. 1967 Formation of vortex rings from falling drops. J. Fluid Mech. 29, 177–185.Google Scholar
Cheng, Y. S., Zhou, Y., Irvin, C. M., Pierce, R. H., Naar, J., Backer, L. C., Fleming, L. E., Kirkpatrick, B. & Baden, D. G. 2005 Characterization of marine aerosol for assessment of human exposure to brevetoxins. Environ. Health Perspect. 113 (5), 638–643.Google Scholar
Clanet, C. 2007 Waterbells and liquid sheets. Annu. Rev. Fluid Mech. 39, 469–496.CrossRefGoogle Scholar
Cossali, G. E., Coghe, A. & Marengo, M. 1997 The impact of a single drop on a wetted solid surface. Exp. Fluids 22, 463–472.Google Scholar
Csanady, G. T. 2001 Air–Sea Interaction: Laws and Mechanisms. Cambridge University Press.Google Scholar
Deegan, R. D., Brunet, P. & Eggers, J. 2008 Complexities of splashing. Nonlinearity 21, C1–C11.Google Scholar
Delvigne, G. A. L. & Sweeney, C. E. 1988 Natural dispersion of oil. Oil Chem. Pollut. 4, 281–310.CrossRefGoogle Scholar
Deng, Q., Anilkumar, A. V. & Wang, T. G. 2007 The role of viscosity and surface tension in bubble entrapment during drop impact onto a deep liquid pool. J. Fluid Mech. 578, 119–138.Google Scholar
Donnelly, R. J. & Glaberson, W. 1966 Experiments on the capillary instability of a liquid jet. Proc. R. Soc. Lond. A 290 (1423), 547–556.Google Scholar
Eggers, J. & Villermaux, E. 2008 Physics of liquid jets. Rep. Prog. Phys. 71, 036601.Google Scholar
Ehrenhauser, F. S., Avij, P., Shu, X., Dugas, V., Woodson, I., Liyana-Arachchi, T., Zhang, Z., Hung, F. R. & Valsaraj, K. T. 2014 Bubble bursting as an aerosol generation mechanism during an oil spill in the deep-sea environment: laboratory experimental demonstration of the transport pathway. R. Soc. Chem. 16, 65–73.Google ScholarPubMed
Ellison, W. D. 1944 Studies of raindrop erosion. Agr. Engng 25, 131–136.Google Scholar
Elmore, P. A., Chahine, G. L. & Oguz, H. N. 2001 Cavity and flow measurements of reproducible bubble entrainment following drop impacts. Exp. Fluids 31, 664–673.Google Scholar
Engel, O. G. 1966 Crater depth in fluid impacts. J. Appl. Phys. 37 (4), 1798–1808.Google Scholar
Engel, O. G. 1967 Initial pressure, initial flow velocity, and the time dependence of crater depth in fluid impacts. J. Appl. Phys. 38 (10), 3935–3940.Google Scholar
Esmailizadeh, L. & Mesler, R. 1986 Bubble entrainment with drops. J. Colloid Interface Sci. 110 (2), 561–574.Google Scholar
Farooq, U., Simon, S., Tweheyo, M. E., Øye, G. & Sjöblom, J. 2013 Interfacial tension measurements between oil fractions of a crude oil and aqueous solutions with different ionic composition and pH. J. Disper. Sci. Technol. 34, 701–708.Google Scholar
Fedorchenko, A. I. & Wang, A. 2004 On some common features of drop impact on liquid surfaces. Phys. Fluids 16 (5), 1349–1365.Google Scholar
Fingas, M. 2013 The Basics of Oil Spill Cleanup. Taylor & Francis.Google Scholar
Fitt, B. D. L., McCartney, H. A. & Walklate, P. J. 1989 The role of rain in dispersal of pathogen inoculum. Annu. Rev. Phytopathol. 27, 241–271.Google Scholar
Franklin, B., Brownrigg, W. & Farish 1774 Of the stilling of waves by means of oil. Extracted from Sundry Letters between Benjamin Franklin, LL. D. F. R. S., William Brownrigg, M. D. F. R. S. and the Reverend Mr Farish. Phil. Trans. 64, 445–460.Google Scholar
Franz, G. J. 1959 Splashes as sources of sound in liquids. J. Acoust. Soc. Am. 31 (8), 1080–1096.Google Scholar
Freer, E. M. & Radke, C. J. 2004 Relaxation of asphaltenes at the toluene/water interface: diffusion exchange and surface rearrangement. J. Adhes. 80, 481–496.Google Scholar
Fujimatsu, T., Fujita, H., Hirota, M. & Okada, O. 2003 Interfacial deformation between an impacting water drop and a silicone-oil surface. J. Colloid Interface Sci. 264, 212–220.Google Scholar
Gopalan, B. & Katz, J. 2010 Turbulent shearing of crude oil mixed with dispersants generates long microthreads and microdroplets. Phys. Rev. Lett. 104, 054501.Google Scholar
Grimaldi, C. S. L., Coviello, I., Lacava, N., Pergola, N. & Tramutoli, V. 2011 A new RST-based approach for continuous oil spill detection in TIR range: the case of the Deepwater Horizon platform in the Gulf of Mexico. In Monitoring and Modeling the Deepwater Horizon Oil Spill: A Record-Breaking Enterprise (ed. Ji, Z. G., Liu, Y., MacFayden, A. & Wesiberg, R. H.), pp. 51–61. American Geophysical Union.Google Scholar
Guildenbecher, D. R., Engvall, L., Gao, J., Grasser, T. W., Reu, P. L. & Chen, J. 2014 Digital in-line holography to quantify secondary droplets from the impact of a single drop on a thin film. Exp. Fluids 55, 1670.Google Scholar
Guillot, P., Colin, A., Utada, A. S. & Ajdari, A. 2007 Stability of a jet in a confined pressure-driven biphasic flow at low Reynolds numbers. Phys. Rev. Lett. 99, 104502.Google Scholar
Gunn, R. & Kinzer, G. D. 1949 The terminal velocity of fall for water droplets in stagnant air. J. Meteorol. 6, 243–248.Google Scholar
Hallet, J. & Christensen, L. 1984 Splash and penetration of drops in water. J. Rech. Atmosph. 18 (4), 225–242.Google Scholar
Hardy, J. T. 1982 The sea surface microlayer: biology, chemistry and anthropogenic enrichment. Prog. Oceanogr. 11, 307–328.Google Scholar
Harvey, E. 1925 The surface tension of crude oils. Ind. Engng Chem. 17 (1), 85–85.CrossRefGoogle Scholar
Hines, R. L. 1966 Electrostatic atomization and spray painting. J. Appl. Phys. 37 (7), 2730–2735.Google Scholar
Hobbs, P. V. & Osheroff, T. 1967 Splashing of drops on shallow liquids. Science 158, 1184–1186.Google Scholar
Hsiao, M., Lichter, S. & Quintero, L. G. 1988 The critical Weber number for vortex and jet formation for drops impinging on a liquid pool. Phys. Fluids 31 (12), 3560–3562.Google Scholar
Hu, Y. T., Pine, D. J. & Leal, G. 2000 Drop deformation, breakup, and coalescence with compatibilizer. Phys. Fluids 12 (3), 484–489.Google Scholar
Javadi, A., Eggers, J., Bonn, D., Habibi, M. & Ribe, N. M. 2013 Delayed capillary breakup of falling viscous jets. Phys. Rev. Lett. 11, 144501.Google Scholar
Katz, J. & Sheng, J. 2010 Applications of holography in fluid mechanics and particle dynamics. Annu. Rev. Fluid Mech. 42, 531–555.Google Scholar
Khaleeq-ur-Rahman, M. & Saunders, C. P. R. 1988 Corona from splashing water drops. J. Atmos. Terr. Phys. 50 (6), 545–555.Google Scholar
Kientzler, C. F., Arons, A. B., Blanchard, D. C. & Woodcock, A. H. 1954 Photographic investigation of the projection of droplets by bubbles bursting at a water surface. Tellus 6 (1), 305658.Google Scholar
Kowalewski, T. A. 1996 On the separation of droplets from a liquid jet. Fluid Dyn. Res. 17, 121–145.Google Scholar
Krechetnikov, R. & Homsy, G. M. 2009 Crown-forming instability phenomena in the drop splash problem. J. Colloid Interface Sci. 331, 555–559.Google Scholar
Leng, L. J. 2001 Splash formation by spherical drops. J. Fluid Mech. 427, 73–105.Google Scholar
Levin, Z. & Hobbs, P. V. 1971 Splashing of water drops on solid and wetted surfaces: hydrodynamics and charge separation. Phil. Trans. R. Soc. Lond. A 269, 555–585.Google Scholar
Lewis, E. R. & Schwartz, S. E. 2004 Sea Salt Aerosol Production: Mechanisms, Methods, Measurements and Models – A Critical Review. American Geophysical Union.Google Scholar
Lhuissier, H., Sun, C., Prosperetti, A. & Lohse, D. 2013 Drop fragmentation at impact onto a bath of an immiscible liquid. Phys. Rev. Lett. 110, 264503.Google Scholar
Lhuissier, H. & Villermaux, E. 2012 Bursting bubble aerosols. J. Fluid Mech. 696, 5–44.Google Scholar
Li, M. & Garrett, C. 1998 The relationship between oil droplet size and upper ocean turbulence. Mar. Pollut. Bull. 36 (12), 961–970.Google Scholar
Li, Z., Lee, K., King, T., Boufadel, M. C. & Venosa, A. D. 2008 Assessment of chemical dispersant effectiveness in a wave tank under regular non-breaking and breaking wave conditions. Mar. Pollut. Bull. 56, 903–912.Google Scholar
Liow, J. L. & Cole, D. E. 2007 Bubble entrapment mechanisms during the impact of a water drop. In 16th Australasian Fluid Mechanics Conference, Gold Coast, Queensland, 3–7 December, 2007 (ed. Jacobs, P., McIntyre, T., Cleary, M., Buttsworth, D., Mee, D., Clements, R., Morgan, R. & Lemckert, C.), pp. 866–869. School of Engineering, The University of Queensland.Google Scholar
Liow, J. L. & Cole, D. E. 2009 High framing rate PIV studies of an impinging water drop. In 28th International Congress on High-Speed Imaging and Photonics, International Society for Optics and Photonics.Google Scholar
Macklin, W. C. & Hobbs, P. V. 1969 Subsurface phenomena and the splashing of drops on shallow liquids. Science 166, 107–108.Google Scholar
Macklin, W. C. & Metaxas, G. J. 1976 Splashing of drops on liquid layers. J. Appl. Phys. 47 (9), 3963–3970.CrossRefGoogle Scholar
Malkiel, E., Sheng, J., Katz, J. & Strickler, R. 2003 The three-dimensional flow field generated by a feeding calanoid copepod measured using digital holography. J. Expl Biol. 206, 3657–3666.Google Scholar
Marmottant, P., Villermaux, E. & Clanet, C. 2000 Transient surface tension of an expanding liquid sheet. J. Colloid Interface Sci. 230, 29–40.Google Scholar
Medwin, H., Nystuen, J. A., Jacobus, P. W., Ostwald, L. H. & Snyder, D. E. 1992 The anatomy of underwater rain noise. J. Acoust. Soc. Am. 92 (3), 1613–1623.Google Scholar
Morton, D., Rudman, M. & Leng, J. L. 2000 An investigation of the flow regimes resulting from splashing drops. Phys. Fluids 12 (4), 747–763.Google Scholar
Oguz, H. N. & Propseretti, A. 1990 Bubble entrainment by the impacts of drops on liquid surfaces. J. Fluid Mech. 219, 143–179.Google Scholar
Okawa, T., Shiraishi, T. & Mori, T. 2006 Production of secondary drops during the single water drop impact onto a plane surface. Exp. Fluids 41, 965–974.Google Scholar
Pelz, O., Brown, J., Huddleston, M., Rand, G., Gardinali, P., Stubblefield, W., BenKinney, M. T. & Ahnell, A.2011 Selection of a surrogate MC252 oil as a reference material for future aquatic toxicity tests and other studies. In SETAC 2011 Meeting, Boston, MA.Google Scholar
Prather, K. A., Bertram, T. H., Grassian, V. H., Deane, G. B., Stokes, M. D., DeMott, P. J., Aluwihare, L. I., Palenik, B. P., Azam, F., Seinfeld, J. H., Moffet, R. C., Molina, M. J., Cappa, C. D., Geiger, F. M., Roberts, G. C., Russell, L. M., Ault, A. P., Baltrusaitis, J., Collins, D. B., Corrigan, C. E., Cuadra-Rodriguez, L. A., Ebben, C. J., Forestieri, S. D., Guasco, T. L., Hersey, S. P., Kim, M. J., Lambert, W. F., Modini, R. L., Mui, W., Pedler, B. E., Ruppel, M. J., Ryder, O. S., Schoepp, N. G., Sullivan, R. C. & Zhao, D. 2013 Bringing the complexity of the ocean into the laboratory to probe the chemical complexity of sea spray aerosol. Proc. Natl Acad. Sci. USA 110, 7550–7555.Google Scholar
Pumphrey, H. C. & Elmore, P. A. 1990 The entrainment of bubbles by drop impacts. J. Fluid Mech. 220, 539–567.Google Scholar
Reichert, M. D. & Walker, L. M. 2013 Interfacial tension dynamics, interfacial mechanics, and response to rapid dilution of bulk surfactant of a model oil–water–dispersant system. Langmuir 29, 1857–1867.Google Scholar
Rein, M. 1993 Phenomena of liquid drop impact on solid and liquid surfaces. Fluid Dyn. Res. 12, 61–93.Google Scholar
Rein, M. 1996 The transitional regime between coalescing and splashing drops. J. Fluid Mech. 306, 145–165.Google Scholar
Resch, F. J. & Afeti, G. M. 1991 Film drop distributions from bubbles bursting in seawater. J. Geophys. Res. 96 (C6), 10681–10688.Google Scholar
Resch, F. J., Darrozes, J. S. & Afeti, G. M. 1986 Marine liquid aerosol production from bursting of air bubbles. J. Geophys. Res. 91 (C1), 1019–1029.Google Scholar
Riehm, D. A. & McCormick, A. V. 2014 The role of dispersants’ dynamic interfacial tension in effective crude oil spill dispersion. Mar. Pollut. Bull. 84, 155–163.Google Scholar
Rioboo, R., Bauthier, C., Conti, J., Voué, M. & De Coninck, J. 2003 Experimental investigation of splash and crown formation during single drop impact on wetted surfaces. Exp. Fluids 35, 648–652.Google Scholar
Rotenberg, Y., Boruvka, L. & Neumann, A. W. 1983 Determination of surface tension and contact angle from the shapes of axisymmetric fluid interfaces. J. Colloid Interface Sci. 93 (1), 169–183.Google Scholar
van de Sande, E., Smith, J. M. & van Oord, J. J. J. 1974 Energy transfer and cavity formation in liquid-drop collisions. J. Appl. Phys. 45 (2), 748–753.Google Scholar
Schneider, C. A., Rasband, W. S. & Eliceiri, K. W. 2012 NIH image to imageJ: 25 years of image analysis. Nat. Meth. 9 (7), 671–675.Google Scholar
Sheng, J., Malkiel, E. & Katz, J. 2006 Digital holographic microscope for measuring three-dimensional particle distributions and motions. Appl. Opt. 45 (16), 3893–3901.Google Scholar
Shetabivash, H., Ommi, F. & Heidarinejad, G. 2014 Numerical analysis of droplet impact onto liquid film. Phys. Fluids 26, 012102.Google Scholar
Sigler, J. & Mesler, R. 1989 The behavior of a gas film formed upon drop impact with a liquid surface. J. Colloid Interface Sci. 134 (2), 459–474.Google Scholar
Snyder, D. E.1990 Characteristics of sound radiation from large raindrops. PhD thesis, Naval Postgraduate School.Google Scholar
Song, B. & Springer, J. 1996 Determination of interfacial tension from the profile of a pendant drop using computer-aided image processing. 1. Theoretical. J. Colloid Interface Sci. 184, 64–76.Google Scholar
Stone, H. 1994 Dynamics of drop deformation and breakup in viscous fluids. Annu. Rev. Fluid Mech. 26, 65–102.Google Scholar
Stow, C. D. & Stainer, R. D. 1977 The physical products of a splashing water drop. J. Met. Soc. Japan 55 (5), 518–532.Google Scholar
Talapatra, S., Hong, J., McFarland, M., Nayak, A., Zhang, C., Katz, J., Sullivan, J., Twardowski, M., Rines, J. & Donaghay, P. 2013 Characterization of biophysical interactions in the water column using in situ digital holography. Mar. Ecol. Prog. Ser. 473, 29–51.Google Scholar
Talapatra, S. & Katz, J. 2013 Three-dimensional velocity measurements in a roughness sublayer using microscopic digital in-line holography and optical index matching. Meas. Sci. Technol. 24, 024004.Google Scholar
Taylor, G. I. 1934 The formation of emulsions in definable fields of flow. Proc. R. Soc. Lond. A 146, 501–523.Google Scholar
Teal, J. M. & Howarth, R. W. 1984 Oil spill studies: a review of ecological effects. Environ. Manage. 8 (1), 27–44.Google Scholar
Tervahattu, H., Hartonen, K., Kerminen, V., Kupiainen, K., Aarnio, P., Koskentalo, T., Tuck, A. & Vaida, V. 2002 New evidence of an organic layer on marine aerosols. J. Geophys. Res. 107 (D7), 4053.Google Scholar
Thoraval, M. J., Takehara, K., Etoh, T. G., Popinet, S., Ray, P., Josserand, C. & Thoroddsen, S. T. 2012 von Kármán vortex street within an impacting drop. Phys. Rev. Lett. 108, 264506.Google Scholar
Thoraval, M. J., Takehara, K., Etoh, T. G. & Thoroddsen, S. T. 2013 Drop impact entrapment of bubble rings. J. Fluid Mech. 724, 235–258.Google Scholar
Thoroddsen, S. T. 2002 The ejecta sheet generated by the impact of a drop. J. Fluid Mech. 451, 373–381.Google Scholar
Thoroddsen, S. T., Thoraval, M.-J., Takehara, K. & Etoh, T. G. 2011 Droplet splashing by a slingshot mechanism. Phys. Rev. Lett. 106, 034501.Google Scholar
Thoroddsen, S. T., Thoraval, M. J., Takehara, K. & Etoh, T. G. 2012 Micro-bubble morphologies following drop impacts onto a pool surface. J. Fluid Mech. 708, 469–479.Google Scholar
Thorpe, S. A. 1995 Vertical dispersion of oil droplets in strong winds: the Braer oil spill. Mar. Pollut. Bull. 30 (11), 756–758.Google Scholar
Tomita, Y., Saito, T. & Ganbara, S. 2007 Surface breakup and air bubble formation by drop impact in the irregular entrainment region. J. Fluid Mech. 588, 131–152.Google Scholar
Tran, T., de Maleprade, H., Sun, C. & Lohse, D. 2013 Air entrainment during impact of droplets on liquid surfaces. J. Fluid Mech. 726, R3.Google Scholar
Tsimplis, M. & Thorpe, S. A. 1989 Wave damping by rain. Nature 342, 893–895.Google Scholar
Vassallo, P. & Ashgriz, N. 1991 Satellite formation and merging in liquid jet breakup. Proc. R. Soc. Lond. A 433, 269–286.Google Scholar
Villermaux, E. 2007 Fragmentation. Annu. Rev. Fluid Mech. 39, 419–446.Google Scholar
Villermaux, E. & Bossa, B. 2009 Single-drop fragmentation determines size distribution of raindrops. Nat. Phys. 5, 697–702.CrossRefGoogle Scholar
Villermaux, E. & Bossa, B. 2011 Drop fragmentation on impact. J. Fluid Mech. 668, 412–435.Google Scholar
Villermaux, E., Marmottant, Ph. & Duplat, J. 2004 Ligament-mediated spray formation. Phys. Rev. Lett. 92, 074501.Google Scholar
Villermaux, E., Pistre, V. & Lhuissier, H. 2013 The viscous Savart sheet. J. Fluid Mech. 730, 607–625.Google Scholar
Wacheul, J.-B., Le Bars, M., Monteux, J. & Aurnou, J. 2014 Laboratory experiments on the breakup of liquid metal diapirs. Earth Planet. Sci. Lett. 403, 236–245.Google Scholar
Wang, A. & Chen, C. 2000 Splashing impact of a single drop onto very thin liquid films. Phys. Fluids 12 (9), 2155–2158.Google Scholar
Weiss, D. A. & Yarin, A. L. 1999 Single drop impact onto liquid films: neck distortion, jetting, tiny bubble entrainment, and crown formation. J. Fluid Mech. 385, 229–254.Google Scholar
Wong, D. C. Y., Simmons, M. J. H., Decent, S. P., Parau, E. I. & King, A. C. 2004 Break-up dynamics and drop size distributions created from spiraling liquid jets. Intl J. Multiphase Flow 30, 499–520.Google Scholar
Worthington, A. M. 1876 On the forms assumed by drops of liquids falling vertically on a horizontal plate. Proc. R. Soc. Lond. 25, 261–282.Google Scholar
Worthington, A. M. 1882 On impact with a liquid surface. Proc. R. Soc. Lond. 25, 217–230.Google Scholar
Worthington, A. M. 1908 A Study of Splashes. Longmans Green.Google Scholar
Worthington, A. M. & Cole, R. S. 1896 Impact with a liquid surface studied by the aid of instantaneous photography. Proc. R. Soc. Lond. 25, 137–148.Google Scholar
Xu, L., Barcos, L. & Nagel, S. R. 2007 Splashing of liquids: interplay of surface roughness with surrounding gas. Phys. Rev. E 76, 066311.Google Scholar
Zhang, D. F. & Stone, H. A. 2007 Drop formation in viscous flows at a vertical capillary tube. Phys. Fluids 8, 2234–2242.Google Scholar
Zhang, L. V., Brunet, P., Eggers, J. & Deegan, R. D. 2010 Wavelength selection in the crown splash. Phys. Fluids 22, 122105.Google Scholar
Zhang, L. V., Toole, J., Fezzaa, K. & Deegan, R. D. 2011 Evolution of the ejecta sheet from the impact of a drop with a deep pool. J. Fluid Mech. 690, 5–15.Google Scholar