Hostname: page-component-5b777bbd6c-xnzsz Total loading time: 0 Render date: 2025-06-24T00:14:58.081Z Has data issue: false hasContentIssue false
  • English
  • Français

Fragmentation versus Cohesion

Published online by Cambridge University Press:  25 June 2020

Emmanuel Villermaux Open the ORCID record for Emmanuel Villermaux [Opens in a new window]
Emmanuel Villermaux*
Affiliation:
Aix Marseille Université, CNRS, Centrale Marseille, IRPHE, Marseille, France Institut Universitaire de France, Paris, France
*
†Email address for correspondence: emmanuel.villermaux@univ-amu.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

Capillarity is the familiar manifestation of the cohesion of liquids. Since Laplace (Traité de mécanique céleste, vol. IV, supplément au livre X: Sur l’action capillaire, 1805, pp. 1–65), we know that intense attractive forces between the molecules bridge the small with the large as they shape liquid/vapour interfaces at the macroscopic scale through the concept of surface tension (menisci, drops, bubbles, puddles, liquid rise in tubes, etc. …). We concentrate on situations where liquids ‘disgregate’, following the neologism of Clausius (Phil. Mag., vol. 24 (159), 1862, pp. 81–97), meaning that they fragment by the action of deformation stresses whose intensity competes with that of cohesion forces. Various examples, including explosions, blow-ups, hard and soft impacts and shears applied to liquid jets, sheets and drops are reviewed. They concern applications ranging from liquid propulsion, agricultural spraying, to the formation of ocean spray, raindrops and human exhalations by violent respiratory events. In spite of their diversity, the various modes of fragment production share an ultimate common phenomenology – the ligament dynamics – suggesting that the final stable droplet size distribution can be interpreted from elementary principles.

JFM classification

Drops and Bubbles: Aerosols/atomization Drops and Bubbles: Breakup/coalescence
Type
JFM Perspectives
Information
Journal of Fluid Mechanics , Volume 898 , 10 September 2020 , P1
Copyright
© The Author(s), 2020. 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.)

Article purchase

Temporarily unavailable

References

Agbaglah, G. & Deegan, R. D. 2014 Growth and instability of the liquid rim in the crown splash regime. J. Fluid Mech. 752, 485–496.CrossRefGoogle Scholar
Agrawal, D. C. & Menon, V. J. 1992 Surface tension and evaporation: an empirical relation for water. Phys. Rev. A 46 (4), 2166–2169.CrossRefGoogle Scholar
Aljedaani, A. B., Wang, C., Jetly, A. & Thoroddsen, S. T. 2018 Experiments on the breakup of drop-impact crowns by Marangoni holes. J. Fluid Mech. 844, 162–186.CrossRefGoogle Scholar
Allen, R. F. 1975 The role of surface tension in splashing. J. Colloid Interface Sci. 51 (2), 350–351.CrossRefGoogle Scholar
Alpher, R. A., Bethe, H. & Gamow, G. 1948 The origin of the elements. Phys. Rev. E 73 (7), 803–804.CrossRefGoogle Scholar
Amarouchene, Y., Bonn, D., Meunier, J. & Kellay, H. 2001 Inhibition of the finite-time singularity during droplet fission of a polymeric fluid. Phys. Rev. Lett. 86 (16), 3558–3561.CrossRefGoogle ScholarPubMed
Anguelova, M. & Barber, R. P. 1999 Spume drops produced by the wind tearing of wave crests. J. Phys. Oceanogr. 29, 1156–1165.2.0.CO;2>CrossRefGoogle Scholar
Antkowiak, A., Bremond, N., Dizès, S. L. & Villermaux, E. 2007 Short-term dynamics of a density interface following an impact. J. Fluid Mech. 577, 241–250.CrossRefGoogle Scholar
Antonov, D. V., Piskunov, M. V. & Strizhak, P. A. 2019 Explosive disintegration of two-component drops under intense conductive, convective, and radiant heating. Appl. Therm. Engng 152, 409–419.CrossRefGoogle Scholar
Arecchi, F. T., Buah-Bassuah, P. K., Francini, F. & Residori, S. 1996 Fragmentation of a drop as it falls in a lighter miscible fluid. Phys. Rev. E 54 (1), 424–429.Google Scholar
Ashgriz, N. 2011 Handbook of Atomization and Sprays. Springer.CrossRefGoogle Scholar
Ashgriz, N. & Poo, J. Y. 1990 Coalescence and separation in binary collisions of liquid drops. J. Fluid Mech. 221, 183–204.CrossRefGoogle Scholar
Attinger, D., Moore, C., Donaldson, A., Jafari, A. & Stone, H. A. 2013 Fluid dynamics topics in bloodstain pattern analysis: comparative review and research opportunities. Forensic Sci. Intl 231 (1–3), 375–396.CrossRefGoogle ScholarPubMed
Avedisian, C. T. & Andres, R. P. 1978 Bubble nucleation in superheated liquid–liquid emulsions. J. Colloid Interface Sci. 64 (3), 438–453.CrossRefGoogle Scholar
Avila, S. R. G., Song, C. & Ohl, C. D. 2015 Fast transient microjets induced by hemispherical cavitation bubbles. J. Fluid Mech. 767, 31–51.CrossRefGoogle Scholar
Aylor, D. E. 2017 Aerial Dispersal of Pollen and Spores. American Phytopathological Society.CrossRefGoogle Scholar
Azaiez, J. & Homsy, G. M. 1994 Linear stability of free shear flow of viscoelastic liquids. J. Fluid Mech. 268, 37–69.CrossRefGoogle Scholar
Balestra, G., Kofman, N., Brun, P.-T., Scheid, B. & Gallaire, F. 2018 Three-dimensional Rayleigh–Taylor instability under a unidirectional curved substrate. J. Fluid Mech. 837, 19–47.CrossRefGoogle Scholar
Basaran, O. A., Gao, H. & Bhat, P. P. 2013 Nonstandard inkjets. Annu. Rev. Fluid Mech. 45, 85–113.CrossRefGoogle Scholar
Bayvel, L. & Orzechowski, Z. 1993 Liquid Atomization. Taylor & Francis.Google Scholar
Bazant, Z. P. & Caner, F. C. 2013 Comminution of solids caused by kinetic energy of high shear strain rate, with implications for impact, shock, and shale fracturing. Proc. Natl Acad. Sci. USA 110, 19291–19294.CrossRefGoogle ScholarPubMed
Bénard, H. 1900 Les tourbillons cellulaires dans une nappe liquide. Rev. Gen. Sci. pures et appl. 11, 1261–71, 1309–1328.Google Scholar
Bénard, H. 1901 Les tourbillons cellulaires dans une nappe liquide transportant de la chaleur par convection en régime permanent. Ann. Chim. Phys. 23, 62–144.Google Scholar
Bentley, W. A. 1904 Studies of raindrops and raindrop phenomena. Mon. Weath. Rev. 10, 450–456.Google Scholar
Berendsen, C. W. J., Zeegers, J. C. H., Kruis, G. C. F. L., Riepen, M. & Darhuber, A. A. 2012 Rupture of thin liquid films induced by impinging air-jets. Langmuir 28 (26), 9977–9985.CrossRefGoogle ScholarPubMed
Betchov, R. & Szewczyk, G. 1963 Stability of a shear layer between parallel streams. Phys. Fluids 6, 1391–1395.CrossRefGoogle Scholar
Betterton, M. D. & Brenner, M. P. 1999 Electrostatic edge instability of lipid membranes. Phys. Rev. Lett. 82 (7), 1598–1601.CrossRefGoogle Scholar
Betts, M. G., Wolf, C., Pfeifer, M., Banks-Leite, C., Arroyo-Rodríguez, V., Ribeiro, D. B., Barlow, J., Eigenbrod, F., Faria, D., Fletcher, R. J. et al. 2019 Extinction filters mediate the global effects of habitat fragmentation on animals. Science 366 (6470), 1236–1239.CrossRefGoogle ScholarPubMed
Bird, J. C., de Ruiter, R., Courbin, L. & Stone, H. A. 2010 Daughter bubble cascades produced by folding of ruptured thin films. Nature 465, 759–762.CrossRefGoogle ScholarPubMed
Birkhoff, G., MacDougall, D. P., Pugh, E. M. & Taylor, G. I. 1948 Explosives with lined cavities. J. Appl. Phys. 19, 563–582.CrossRefGoogle Scholar
Blanchard, D. C. 1963 The electrification of the atmosphere by particles from bubbles in the sea. Prog. Oceanogr. 1, 73–202.CrossRefGoogle Scholar
Blanchard, D. C. & Sysdek, L. D. 1988 Film drop production as a function of bubble size. J. Geophys. Res. 93 (C4), 3649–3654.CrossRefGoogle Scholar
Bleibel, J., Dietrich, S., Dominguez, A. & Oettel, M. 2011 Shock waves in capillary collapse of colloids: a model system for two-dimensional screened Newtonian gravity. Phys. Rev. Lett. 107, 128302.CrossRefGoogle Scholar
Bohr, N. 1939 Disintegration of heavy nuclei. Nature 143, 330.CrossRefGoogle Scholar
Boos, W. & Thess, A. 1999 Cascade of structures in long-wavelength Marangoni instability. Phys. Fluids 11 (6), 1484–1494.CrossRefGoogle Scholar
Borda, J. C.1763 Expériences sur la résistance des fluides. In Mémoires de l’Academie Royale des Sciences, pp. 356–376.Google Scholar
Born, M. 1937 Atomic Physics. Blackie & Son Limited.Google Scholar
Bouasse, H. 1923 Jets, Tubes et Canaux. Delagrave.Google Scholar
Bouasse, H. 1924 Capillarité. Delagrave.Google Scholar
Boudaoud, A., Couder, Y. & Amar, M. B. 1999 Self adaptation in vibrating soap films. Phys. Rev. Lett. 82 (19), 3047–3050.CrossRefGoogle Scholar
Bourdin, B., Francfort, G. & Marigo, J. 2008 The variational approach to fracture. J. Elast. 91 (1-3), 5–148.CrossRefGoogle Scholar
Bourouiba, L., Dehandschoewercker, E. & Bush, J. W. M. 2014 Violent expiratory events: on coughing and sneezing. J. Fluid Mech. 745, 537–563.CrossRefGoogle Scholar
Boussinesq, J. 1869a Théories des expériences de Savart, sur la forme que prend une veine liquide après s’être choquée contre un plan circulaire I. C. R. Acad. Sci. Paris 69, 45–48.Google Scholar
Boussinesq, J. 1869b Théories des expériences de Savart, sur la forme que prend une veine liquide après s’être choquée contre un plan circulaire II. C. R. Acad. Sci. Paris 69, 128–131.Google Scholar
Bowen, M. & Tilley, B. S. 2013 On self-similar thermal rupture of thin liquid sheets. Phys. Fluids 25, 102105.CrossRefGoogle Scholar
Bradley, S. G. & Stow, C. D. 1978 Collisions between liquid drops. Phil. Trans. R. Soc. Lond. A 287 (1349), 635–675.Google Scholar
Brasz, C. F., Bemy, A. & Bird, J. C. 2018 Threshold for discretely self-similar satellite drop formation from a retracting liquid cone. Phys. Rev. Fluids 3, 104002.CrossRefGoogle Scholar
Bremond, N., Clanet, C. & Villermaux, E. 2007 Atomization of undulating liquid sheets. J. Fluid Mech. 585, 421–456.CrossRefGoogle Scholar
Bremond, N. & Villermaux, E. 2005 Bursting thin liquid films. J. Fluid Mech. 524, 121–130.CrossRefGoogle Scholar
Bremond, N. & Villermaux, E. 2006 Atomization by jet impact. J. Fluid Mech. 549, 273–306.CrossRefGoogle Scholar
Brenner, M. P., Shi, X. D. & Nagel, S. R. 1994 Iterated instabilities during droplet fission. Phys. Rev. Lett. 73 (25), 3391–3394.CrossRefGoogle ScholarPubMed
Brosseau, Q. & Vlahovska, P. M. 2017 Streaming from the equator of a drop in an external electric field. Phys. Rev. Lett. 119, 034501.CrossRefGoogle Scholar
Buguin, A., Vovelle, L. & Brochard-Wyart, F. 1999 Shocks in inertial dewetting. Phys. Rev. Lett. 83 (6), 1183–1186.CrossRefGoogle Scholar
Bull, L.1904 Rupture d’un film de savon par un projectile. Institut E.-J. Marey – Chronophotographic Films, Cinémathèque Française.Google Scholar
Buller, A. H. R. 1909–1950 Researches on Fungi, vols 1–7. Longmans, Green & Co.Google Scholar
Burbidge, E. M., Burbidge, G., Fowler, W. A. & Hoyle, F. 1957 Synthesis of the elements in stars. Rev. Mod. Phys. 29 (4), 547–650.CrossRefGoogle Scholar
Burrows, A. 2000 Supernovae explosions in the universe. Nature 403, 727–733.CrossRefGoogle ScholarPubMed
Burton, J. C. & Taborek, P. 2007 Two-dimensional inviscid pinch-off: an example of self-similarity of the second kind. Phys. Fluids 19, 102109.CrossRefGoogle Scholar
Burzynski, D. A., Roisman, I. V. & Bansmer, S. E. 2020 On the splashing of high-speed drops impacting a dry surface. J. Fluid Mech. 892, A2.CrossRefGoogle Scholar
Bush, J. W. & Hasha, A. E. 2004 On the collision of laminar jets: fluid chains and fishbones. J. Fluid Mech. 511, 285–310.CrossRefGoogle Scholar
Casteletto, V., Cantat, I., Sarker, D., Bausch, R., Bonn, D. & Meunier, J. 2003 Stability of soap films: hysteresis and nucleation of black films. Phys. Rev. Lett. 90, 048302.CrossRefGoogle ScholarPubMed
Champougny, L., Miguet, J., Henaff, R., Restagno, F., Boulogne, F. & Rio, E. 2018 Influence of evaporation on soap film rupture. Langmuir 34, 3221–3227.CrossRefGoogle ScholarPubMed
Champougny, L., Rio, E., Restagno, F. & Scheid, B. 2017 The break-up of free films pulled out of a pure liquid bath. J. Fluid Mech. 811, 499–524.CrossRefGoogle Scholar
Chandra, S. & Avedisian, C. T. 1991 On the collision of a droplet with a solid surface. Proc. R. Soc. Lond. A 432, 13–41.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Dover Publication.Google Scholar
Chateau, J. & Lhuissier, H. 2019 Breakup of a particulate suspension jet. Phys. Rev. Fluids 4, 012001(R).CrossRefGoogle Scholar
Chen, Y.-J. & Steen, P. H. 1997 Dynamics of inviscid capillary breakup: collapse and pinchoff of a film bridge. J. Fluid Mech. 341, 245–267.CrossRefGoogle Scholar
Chepushtanova, S. V. & Kliakhandler, I. L. 2007 Slow rupture of viscous films between parallel needles. J. Fluid Mech. 573, 297–310.CrossRefGoogle Scholar
Clanet, C. 2007 Waterbells and liquid sheets. Annu. Rev. Fluid Mech. 39, 469–496.CrossRefGoogle Scholar
Clanet, C. & Lasheras, J. 1999 Transition from dripping to jetting. J. Fluid Mech. 383, 307–326.CrossRefGoogle Scholar
Clanet, C. & Villermaux, E. 2002 Life of a smooth liquid sheet. J. Fluid Mech. 462, 307–340.CrossRefGoogle Scholar
Clarke, N. S. 1969 The asymptotic effects of surface tension and viscosity on an axially-symmetric free jet of liquid under gravity. Q. J. Mech. Appl. Maths 22, 247–256.CrossRefGoogle Scholar
Clasen, C., Bico, J., Entov, V. & McKinley, G. H. 2009 ‘Gobbling drops’: the jetting-dripping transition in flows of polymer solutions. J. Fluid Mech. 636, 5–40.CrossRefGoogle Scholar
Clausius, R. 1862 On the application of the theorem of the equivalence of transformations to the internal work of a mass of matter. Phil. Mag. 24 (159), 81–97.CrossRefGoogle Scholar
Clay, P. 1940 The mechanism of emulsion formation in turbulent flow. I. Experimental part. Proc. R. Acad. Sci. (Amsterdam) 43, 852–865.Google Scholar
Cochran, R. E. et al. 2017 Molecular diversity of sea spray aerosol particles: impact of ocean biology on particle composition and hygroscopicity. Chem 2, 655–667.CrossRefGoogle Scholar
Cohen, I., Li, H., Hougland, J., Mrksich, M. & Nagel, S. R. 2001 Using selective withdrawal to coat microparticles. Science 292, 265.CrossRefGoogle ScholarPubMed
Cointe, R. & Armand, J.-L. 1987 Hydrodynamic impact analysis of a cylinder. J. Offshore Mech. Arctic Engng 109 (3), 237–243.CrossRefGoogle Scholar
Cole, R. H. 1948 Underwater Explosions. Princeton University Press.CrossRefGoogle Scholar
Cooker, M. J. & Peregrine, D. H. 1995 Pressure-impulse theory for liquid impact problems. J. Fluid Mech. 297, 193–214.CrossRefGoogle Scholar
Coulson, J. M., Richardson, J. F., Backhurst, J. R. & Harker, J. H. 2002 Chemical Engineering, 5th edn, vol. 2. Butterworth.Google Scholar
Courant, R., Robbins, H. & Stewart, I. 1996 What is Mathematics? Oxford University Press.Google Scholar
Courbin, L. & Stone, H. A. 2006 Impact, puncturing, and the self-healing of soap films. Phys. Fluids 18, 091105.CrossRefGoogle Scholar
Crapper, G. D., Dombrowski, N., Jepson, W. P. & Pyott, G. A. D. 1973 A note on the growth of Kelvin–Helmholtz waves on thin liquid sheets. J. Fluid Mech. 57, 671–672.CrossRefGoogle Scholar
Craster, R. V. & Matar, O. K. 2009 Dynamics and stability of thin liquid films. Rev. Mod. Phys. 81 (3), 1131–1198.CrossRefGoogle Scholar
Cu, K., Bansal, R., Mitragotri, S. & Fernadez Rivas, D. 2019 Delivery strategies for skin: comparison of nanoliter jets, needles and topical solutions. Ann. Biomed. Engng doi:10.1007/s10439-019-02383-1.Google ScholarPubMed
Culick, F. E. C. 1960 Comments on a ruptured soap film. J. Appl. Phys. 31, 1128–1129.CrossRefGoogle Scholar
Curl, R. L. 1963 Dispersed phase mixing: I. Theory and effects in simple reactors. AIChE J. 9, 175–181.CrossRefGoogle Scholar
Day, R. F., Hinch, E. J. & Lister, J. R. 1998 Self-similar capillary pinchoff of an inviscid fluid. Phys. Rev. Lett. 80 (4), 704.CrossRefGoogle Scholar
Dear, J. P., Field, J. E. & Walton, A. J. 1988 Gas compression and jet formation in cavities collapsed by a shock wave. Nature 332 (6164), 505–508.CrossRefGoogle Scholar
Debrégeas, G., de Gennes, P.-G. & Brochard-Wyart, F. 1998 The life and death of ‘bare’ viscous bubbles. Science 279, 1704–1707.Google Scholar
Debrégeas, G., Martin, P. & Brochard-Wyart, F. 1995 Viscous bursting of suspended films. Phys. Rev. Lett. 75 (21), 3886–3889.CrossRefGoogle ScholarPubMed
Decent, S. & King, A. 2008 Surface-tension-driven flow in a slender cone. IMA J. Appl. Maths 73, 37–68.CrossRefGoogle 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.CrossRefGoogle Scholar
Delaunay, C. 1841 Sur la surface de révolution dont la courbure moyenne est constante. J. Math. Pures Appl. 6, 309–314.Google Scholar
Denkov, N. D. 2004 Mechanisms of foam destruction by oil-based antifoams. Langmuir 20 (22), 9463–9505.CrossRefGoogle ScholarPubMed
Derjaguin, B. V., Churaev, N. V. & Muller, V. M. 1987 Surface Forces. Plenum.CrossRefGoogle Scholar
Dimotakis, P. E. 2000 The mixing transition in turbulent flows. J. Fluid Mech. 409, 69–98.CrossRefGoogle Scholar
DiPersio, R., Simon, J. & Martin, T. H.1960 A study of jets from scaled conical shaped charge liners. Tech. Rep. 1298. Army Ballistic Research Lab, Aberdeen Proving Ground, MD.CrossRefGoogle Scholar
Do, J. L. & Friscic, T. 2017 Mechanochemistry: a force of synthesis. ACS Central Sci. 3, 13–19.CrossRefGoogle ScholarPubMed
Dombrowski, N. & Fraser, R. P. 1954 A photographic investigation into the disintegration of liquid sheets. Phil. Trans. R. Soc. Lond. A 247, 101–130.Google Scholar
Dombrowski, N. & Johns, W. R. 1963 The aerodynamics instability and disintegration of viscous liquid sheets. Chem. Engng Sci. 18, 203–214.CrossRefGoogle Scholar
Doméjean, H., Bibette, J. & Bremond, N. 2016 Traffic collision during the breakup of an aqueous viscous compound jet. Phys. Rev. Fluids 1, 063903.CrossRefGoogle Scholar
Dressaire, E., Courbin, L., Delancy, A., Roper, M. & Stone, H. A. 2013 Study of polygonal water bells: inertia-dominated thin-film flows over microtextured surfaces. J. Fluid Mech. 721, 46–57.CrossRefGoogle Scholar
Driessen, T., Sleutel, P., Dijksman, F., Jeurissen, R. & Lohse, D. 2014 Control of jet breakup by a superposition of two Rayleigh–Plateau-unstable modes. J. Fluid Mech. 749, 275–296.CrossRefGoogle Scholar
Duchemin, L., Le Dizès, S., Vincent, L. & Villermaux, E. 2015 Self-similar impulsive capillary waves on a ligament. Phys. Fluids 27, 051704.CrossRefGoogle Scholar
Duguid, J. P. 1946 The size and the duration of air-carriage of respiratory droplets and droplet-nuclei. J. Hyg. (Lond) 6, 471–479.Google Scholar
Duplat, J. & Villermaux, E. 2015 Luminescence from collapsing centimeter bubbles expanded by chemical reaction. Phys. Rev. Lett. 115, 094501.CrossRefGoogle ScholarPubMed
Dupré, A. 1867 Théorie mécanique de la chaleur. Ann. Chim. Phys. 11, 194.Google Scholar
Dupré, A. 1869 Théorie mécanique de la chaleur. Gauthiers-Villars.Google Scholar
Edgerton, H. E. 1979 Moments of Vision: The Stroboscopic Revoltion in Photography. MIT Press.Google Scholar
Edwards, D. A., Hanes, J., Caponetti, G., Hrkach, J., Ben-Jebria, A., Eskew, M. L., Mintzes, J., Deaver, D., Lotan, N. & Langer, R. 1997 Large porous particles for pulmonary drug delivery. Science 276 (5320), 1868–1872.CrossRefGoogle ScholarPubMed
Eggers, J. 1993 Universal pinching of 3D axisymmetric free surface flow. Phys. Rev. Lett. 71 (21), 3458–3460.CrossRefGoogle ScholarPubMed
Eggers, J. 1997 Nonlinear dynamics and breakup of free-surface flows. Rev. Mod. Phys. 69, 865–929.CrossRefGoogle Scholar
Eggers, J. & Villermaux, E. 2008 Physics of liquid jets. Rep. Prog. Phys. 71, 36601.CrossRefGoogle Scholar
Eisenklam, P. 1964 On ligament formation from spinning discs and cups. AIChE J. 19 (9), 693–694.Google Scholar
Erneux, T. & Davis, S. H. 1993 Nonlinear rupture of free films. Phys. Fluids A 5 (5), 1117–1122.CrossRefGoogle Scholar
Falcon, E., Laroche, C. & Fauve, S. 2007 Observation of gravity-capillary wave turbulence. Phys. Rev. Lett. 98, 094503.Google ScholarPubMed
Fineberg, J. & Marder, M. 1999 Instability in dynamic fracture. Phys. Rep.-Rev. Section Phys. Lett. 313 (1–2), 1–108.Google Scholar
Flores-Kim, J., S., D. G., Fenton, A., Rudner, D. Z. & Bernhardt, T. G. 2019 A switch in surface polymer biogenesis triggers growth-phase-dependent and antibiotic-induced bacteriolysis. eLife 8, e44912.CrossRefGoogle ScholarPubMed
Flügge, C. 1897 Ueber luftinfection. Zeitschrft fur Hygiene und Infektionskrankheite 25, 179–224.Google Scholar
Frankel, I. & Weihs, D. 1985 Stability of a capillary jet with linearly increasing axial velocity (with application to shaped charges). J. Fluid Mech. 155, 289–307.CrossRefGoogle Scholar
Frankel, I. & Weihs, D. 1987 Influence of viscosity on the capillary instability of a stretching jet. J. Fluid Mech. 185, 361–383.CrossRefGoogle Scholar
Frankel, S. & Mysels, K. 1969 The bursting of soap films. II. Theorical considerations. J. Phys. Chem. 73 (9), 3028–3038.CrossRefGoogle Scholar
Frens, G. 1974 Aerodynamic drag on bursting bubbles. J. Phys. Chem. 78 (19), 1949–1953.CrossRefGoogle Scholar
Friedlander, S. K 2000 Smoke, Dust and Haze, 2nd edn. Oxford University Press.Google Scholar
Frost, D. L. 1988 Dynamics of explosive boiling of a droplet. Phys. Fluids 31 (9), 2554–2561.CrossRefGoogle Scholar
Frost, D. L., Ornthanalai, C., Zarei, Z., Tanguay, V. & Zhang, F. 2007 Particle momentum effects from the detonation of heterogeneous explosives. J. Appl. Phys. 101, 113529.CrossRefGoogle Scholar
Gañán-Calvo, A. M. 1997 Cone-jet analytical extension of Taylor’s electrostatic solution and the asymptotic universal scaling laws in electrospraying. Phys. Rev. Lett. 79, 217.CrossRefGoogle Scholar
Gañán-Calvo, A. M. 1998 Generation of steady liquid microthreads and micron-sized monodisperse sprays in gas streams. Phys. Rev. Lett. 80 (2), 285–288.CrossRefGoogle Scholar
Gañán-Calvo, A. M. & Gordillo, J. M. 2001 Perfectly monodisperse microbubbling by capillary flow focussing. Phys. Rev. Lett. 87 (27), 274501.CrossRefGoogle Scholar
Garrett, P. R. 1992 Defoaming: Theory and Industrial Applications, Surfactant Science Series, vol. 45. Taylor & Francis.Google Scholar
Gekle, S. & Gordillo, J. M. 2010 Generation and breakup of Worthington jets after cavity collapse. Part 1. Jet formation. J. Fluid Mech. 663, 293–330.CrossRefGoogle Scholar
Gelderblom, H., Lhuissier, H., Klein, A. L., Bouwhuis, W., Lohse, D., Villermaux, E. & Snoeijer, J. H. 2016 Drop deformation by laser-pulse impact. J. Fluid Mech. 794, 676–699.CrossRefGoogle Scholar
de Gennes, P.-G. 1985 Wetting: statics and dynamics. Rev. Mod. Phys. 57 (3), 827–863.CrossRefGoogle Scholar
de Gennes, P.-G. 1996 Mechanics of soft interfaces. Faraday Discuss. 104, 1–8.CrossRefGoogle Scholar
de Gennes, P.-G. 1998 Progression d’un agent de coalescence dans une emulsion. C. R. Acad. Sci. Paris Série IIb 326, 331–335.Google Scholar
de Gennes, P.-G., Brochard-Wyart, F. & Quere, D. 2004 Capillarity and Wetting Phenomena. Springer.CrossRefGoogle Scholar
Ghabache, E., Antkowiak, A., Josserand, C. & Séon, T. 2014a On the physics of fizziness: how bubble bursting controls droplets ejection. Phys. Fluids 26 (12), 121701.CrossRefGoogle Scholar
Ghabache, É. & Séon, T. 2016 Size of the top jet drop produced by bubble bursting. Phys. Rev. Fluids 1 (5), 051901(R).CrossRefGoogle Scholar
Ghabache, É., Seon, T. & Antkowiak, A. 2014b Liquid jet eruption from hollow relaxation. J. Fluid Mech. 761, 206–219.CrossRefGoogle Scholar
Gilet, T. & Bourouiba, L. 2015 Fluid fragmentation shapes rain-induced foliar disease transmission. J. R. Soc. Interface 12, 20141092.CrossRefGoogle ScholarPubMed
Gladden, J. R., Handzy, N. Z., Belmonte, A. & Villermaux, E. 2005 Dynamic buckling and fragmentation in brittle rods. Phys. Rev. Lett. 94, 035503.CrossRefGoogle ScholarPubMed
Glantz, S. A. & Bareham, D. W. 2018 E-cigarettes: use, effects on smoking, risks, and policy implications. Annu. Rev. Public Health 39, 215–235.CrossRefGoogle ScholarPubMed
Gonnermann, H. M. 2005 Magma fragmentation. Annu. Rev. Earth Planet. Sci. 43, 431–458.CrossRefGoogle Scholar
Goodridge, C. L., Tao Shi, W. & Lathrop, D. 1996 Threshold dynamics of singular gravity-capillary waves. Phys. Rev. Lett. 76 (11), 1824–1827.CrossRefGoogle ScholarPubMed
Gordillo, J. M., Lhuissier, H. & Villermaux, E. 2014 On the cusps bordering liquid sheets. J. Fluid Mech. 754, R1.CrossRefGoogle Scholar
Gordillo, J. M. & Pérez-Saborid, M. 2005 Aerodynamic effects in the breakup of liquid jets: on the first wind-induced breakup regime. J. Fluid Mech. 541, 1–20.CrossRefGoogle Scholar
Gordillo, J. M. & Rodríguez-Rodríguez, J. 2019 Capillary waves control the ejection of bubble bursting jets. J. Fluid Mech. 867, 556–571.CrossRefGoogle Scholar
Gordillo, L., Agbaglah, G., Duchemin, L. & Josserand, C. 2011 Asymptotic behavior of a retracting two-dimensional fluid sheet. Phys. Fluids 23, 122101.CrossRefGoogle Scholar
Grady, D. E. 1982 Local inertial effects in dynamic fragmentation. J. Appl. Phys. 53, 322–325.CrossRefGoogle Scholar
Grady, D. E. 2006 Fragmentation of Rings and Shells: the Legacy of N. F. Mott. Springer.CrossRefGoogle Scholar
Grätz, S., Beyer, D., Tkachova, V., Hellmann, S., Berger, R., Feng, X. & Borchardt, L. 2018a The mechanochemical Scholl reaction – a solvent-free and versatile graphitization tool. Chem. Commun. 54, 5307–5310.CrossRefGoogle Scholar
Grätz, S., Oltermann, M., Troschke, E., Paasch, S., Krause, S., Brunner, E. & Borchardt, L. 2018b Solvent-free synthesis of a porous thiophene polymer by mechanochemical oxidative polymerization. J. Mater. Chem. A 6, 21901–21905.CrossRefGoogle Scholar
Griffith, A. A. 1921 The phenomena of rupture and flow in solids. Phil. Trans. R. Soc. Lond. A 221, 163–198.Google Scholar
Guéna, G., Poulard, C. & Cazabat, A.-M. 2007 Evaporating drops of alkane mixtures. Colloids Surf. Physicochem. Eng. Asp. 298 (1–2), 2–11.CrossRefGoogle Scholar
Hagerty, W. W. & Shea, J. F. 1955 A study of the stability of plane fluid sheets. Trans. ASME J. Appl. Mech. 22, 509–514.Google Scholar
Han, Y., Durst, F. & Zeilmann, M. 2004 High-pressure-driven twin-jet sprays and their properties. Atomiz. Sprays 24 (5), 375–401.CrossRefGoogle Scholar
Hassett, M. O., Fischer, M. W. F., Sugawara, Z. T., Stolze-Rybczynski, J. & Money, N. P. 2013 Splash and grab: biomechanics of peridiole ejection and function of the funicular cord in bird’s nest fungi. Fungal Biol. 117, 708–714.CrossRefGoogle ScholarPubMed
Hasson, D. & Peck, R. E. 1964 Thickness distribution in a sheet formed by impinging jets. AIChE J. 10, 752–754.CrossRefGoogle Scholar
Hawksbee, F. 1709 Physico-mechanical Experiments on Various Subjects. R. Brugis.Google Scholar
von Helmholtz, H. 1847 Uber die Erhaltung der Kraft, eine physikalishe Abhandlung. G. Reimer.Google Scholar
von Helmholtz, H. 1868 On discontinuous movements of fluids. Phil. Mag. A 36, 337–346.CrossRefGoogle Scholar
Henderson, L. F. 1989 On the refraction of shock waves. J. Fluid Mech. 198, 365–386.CrossRefGoogle Scholar
Herman, J. & Mesler, R. 1987 Bubble entrainment from bursting bubbles. J. Colloid Interface Sci. 117 (2), 565–569.CrossRefGoogle Scholar
Hernández-Sánchez, J. F., Eddi, A. & Snoeijer, J. H. 2015 Marangoni spreading due to a localized alcohol supply on a thin water film. Phys. Fluids 27, 032003.CrossRefGoogle Scholar
Hewitt, A. J. 2000 Spray drift: impact of requirements to protect the environment. Crop Prot. 19, 623–627.CrossRefGoogle Scholar
Higuera, F. J., Medina, A. & Liñán, A. 2008 Capillary rise of a liquid between two vertical plates making a small angle. Phys. Fluids 20, 102102.CrossRefGoogle Scholar
Hilz, E., Vermeer, A. W. P., Cohen Stuart, M. A. & Leermakers, F. A. M. 2012 Mechanism of perforation based on spreading properties of emulsified oils. Atomiz. Sprays 22 (12), 1053–1075.CrossRefGoogle Scholar
Hinch, E. J. 1984 A note on the mechanism of the instability at the interface between two shearing fluids. J. Fluid Mech. 144, 463–465.CrossRefGoogle Scholar
Hinch, E. J. & Saint-Jean, S. 1999 The fragmentation of a line of balls by an impact. Proc. R. Soc. Lond. A 455, 3201–3220.CrossRefGoogle Scholar
Hinze, J. 1955 Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes. AIChE J. 1 (3), 289–295.CrossRefGoogle Scholar
Hirst, J. M., Stedman, O. J. & Hogg, W. H. 1967 Long-distance spore transport: methods of measurement, vertical spore profiles and the detection of immigrant spores. J. Gen. Microbiol. 48, 329–355.CrossRefGoogle ScholarPubMed
Hobbs, P. V. & Rangno, A. L. 2004 Super-large raindrops. Geophys. Res. Lett. 31, L13102.CrossRefGoogle Scholar
Hoepffner, J. & Paré, G. 2013 Recoil of a liquid filament: escape from pinch-off through creation of a vortex ring. J. Fluid Mech. 734, 183–197.CrossRefGoogle Scholar
Howard, J. L., Cao, Q. & Browne, D. L. 2018 Mechanochemistry as an emerging tool for molecular synthesis: what can it offer? Chem. Sci. 9, 3080–3094.CrossRefGoogle ScholarPubMed
Howinson, S., Ockendon, D., Olivier, J. M., Purvis, R. & Smith, F. T. 1991 Incompressible water-entry problems at small deadrise angles. J. Fluid Mech. 222, 215–230.CrossRefGoogle Scholar
Howland, C. J., Antkowiak, A., Castrejon-Pita, J. R., Howison, S. D., Oliver, J. M., Style, R. W. & Castrejon-Pita, A. A. 2016 It’s harder to splash on soft solids. Phys. Rev. Lett. 117, 184502.CrossRefGoogle ScholarPubMed
Hoyt, J. W. & Taylor, J. 1977 Waves on water jets. J. Fluid Mech. 83, 119–127.CrossRefGoogle Scholar
Huang, J. C. P. 1970 The break-up of axisymmetric liquid sheets. J. Fluid Mech. 43, 305–319.CrossRefGoogle Scholar
Huerre, P. & Rossi, M. 1998 Hydrodynamic instabilities in open flows. In Hydrodynamics and Nonlinear Instabilities (ed. Godrèche, C. & Manneville, P.), pp. 81–294. Cambridge University Press.CrossRefGoogle Scholar
Ilievski, F., Mani, M., Whitesides, G. M. & Brenner, M. P. 2011 Self-assembly of magnetically interacting cubes by a turbulent fluid flow. Phys. Rev. E 83, 017301.Google ScholarPubMed
Ilton, M., DiMaria, C. & Dalnoki-Veress, K. 2016 Direct measurement of the critical pore size in a model membrane. Phys. Rev. Lett. 117, 257801.CrossRefGoogle Scholar
Ingold, C. T. 1971 Fungal Spores: Their Liberation and Dispersal. Clarendon.Google Scholar
Inoue, C., Izato, Y., Miyake, A. & Villermaux, E. 2017 Direct self-sustained fragmentation cascade of reactive droplets. Phys. Rev. Lett. 118, 074502.CrossRefGoogle ScholarPubMed
Isenberg, C. 1978 The Science of Soap Films and Soap Bubbles, 2nd edn. Dover Publications.Google Scholar
Israelachvili, J. 1991 Intermolecular and Surface Forces, 2nd edn. Academic Press.Google Scholar
Jackson, J. D. 1998 Classical Electrodynamics, 3rd edn. Wiley.Google Scholar
Javadi, A., Eggers, J., Bonn, D., Habibi, M. & Ribe, N. M. 2013 Delayed capillary breakup of falling viscous jets. Phys. Rev. Lett. 110 (14), 144501.Google ScholarPubMed
Jensen, O. E. & Grotberg, J. B. 1992 Insoluble surfactant spreading on a thin viscous film: shock evolution and film rupture. J. Fluid Mech. 240, 259–288.CrossRefGoogle Scholar
Jensen, O. E. & Grotberg, J. B. 1993 The spreading of heat or soluble surfactant along a thin liquid film. Phys. Fluids A 5 (1), 58–68.CrossRefGoogle Scholar
Josserand, C. & Thoroddsen, S. T. 2016 Drop impact on a solid surface. Annu. Rev. Fluid Mech. 48 (1), 365–391.CrossRefGoogle Scholar
Jurin, J. 1719 An account of some experiments shown before the royal society; with an enquiry into the cause of the ascent and suspension of water in capillary tubes. Phil. Trans. R. Soc. Lond. A 30, 739–747.Google Scholar
Kabova, Y. O., Alexeev, A., Gambaryan-Roisman, T. & Stephan, P. 2006 Marangoni-induced deformation and rupture of a liquid film on a heated microstructured wall. Phys. Fluids 18, 012104.CrossRefGoogle Scholar
Kalliadasis, S., Ruyer-Quil, C., Scheid, B. & Velarde, M. G. 2012 Falling Liquid Films. Springer.CrossRefGoogle Scholar
Kamat, P. M., Wagoner, B. W., Thete, S. S. & Basaran, O. A. 2018 Role of Marangoni stress during breakup of surfactant-covered liquid threads: reduced rates of thinning and microthread cascades. Phys. Rev. Fluids 3, 043602.CrossRefGoogle Scholar
Kedrinskii, V. K. 2005 Hydrodynamics of Explosions. Springer.Google Scholar
Kedrinskii, V. K. 2009 Hydrodynamic aspects of explosive eruptions of volcanoes: simulation problems. Shock Waves 18, 451–464.CrossRefGoogle Scholar
Keiser, L., Bense, H., Colinet, P., Bico, J. & Reyssat, E. 2017 Marangoni bursting: evaporation-induced emulsification of binary mixtures on a liquid layer. Phys. Rev. Lett. 118, 074504.CrossRefGoogle ScholarPubMed
Keller, J. B., King, A. & Ting, L. 1995 Blob formation. Phys. Fluids 7 (1), 226–228.CrossRefGoogle Scholar
Keller, J. B. & Kolodner, I. 1954 Instability of liquid surfaces and the formation of drops. J. Appl. Phys. 25 (7), 918–921.CrossRefGoogle Scholar
Keller, J. B. & Miksis, M. 1983 Surface tension driven flows. J. Appl. Maths 43 (2), 268–277.Google Scholar
Kelvin, Lord 1871 Hydrokinetic solutions and observations. Phil. Mag. A 42, 362–377.CrossRefGoogle Scholar
Kendall, K. 1978 The impossibility of comminuting small particles by compression. Nature 272, 710–711.CrossRefGoogle Scholar
Keshavarz, B., Houze, E. C., Moore, J. R., Koener, M. R. & McKinley, G. H. 2020 Rotary atomization of Newtonian and viscoelastic liquids. Phys. Rev. Fluids 5, 033601.CrossRefGoogle Scholar
Keshavarz, B., Houze, E. C., Moore, J. R., Koerner, M. R. & McKinley, G. H. 2016 Ligament mediated fragmentation of viscoelastic liquids. Phys. Rev. Lett. 117, 154502.CrossRefGoogle ScholarPubMed
Kim, I. & Sirignano, W. A. 2000 Three-dimensional wave distortion and disintegration of thin planar liquid sheets. J. Fluid Mech. 410, 147–183.CrossRefGoogle Scholar
Kitavtsev, G., Fontelos, M. A. & Eggers, J. 2018 Thermal rupture of a free liquid sheet. J. Fluid Mech. 840, 555–578.CrossRefGoogle Scholar
Klein, A. L., Bouwhuis, W., Visser, C. W., Lhuissier, H., Sun, C., Snoeijer, J. H., Villermaux, E., Lohse, D. & Gelderblom, H. 2015 Drop shaping by laser-pulse impact. Phys. Rev. Appl. 3 (4), 044018.CrossRefGoogle Scholar
Klein, A. L., Kurilovich, D., Lhuissier, H., Versolato, O. O., Lohse, D., Villermaux, E. & Gelderblom, H. 2020 Drop fragmentation by laser-pulse impact. J. Fluid Mech. 893, A7.CrossRefGoogle Scholar
Knelman, F. H., Dombrowski, N. & Newitt, D. M. 1954 Mechanism of the bursting of bubbles. Nature 173, 261.CrossRefGoogle Scholar
Kolmogorov, A. N. 1941a The local structure of turbulence in incompresible viscous fluid for very large Reynolds’ numbers. Dokl. Akad. Nauk SSSR 30, 301.Google Scholar
Kolmogorov, A. N. 1941b On the logarithmic normal distribution of particles sizes under grinding. Dokl. Akad. Nauk SSSR 31, 99–101.Google Scholar
Kolmogorov, A. N. 1949 On the breakage of drops in a turbulent flow. Dokl. Akad. Nauk SSSR 66, 825–828.Google Scholar
Kooij, S., Astefanei, A., Corthals, G. L. & Bonn, D. 2019 Size distributions of droplets produced by ultrasonic nebulizers. Sci. Rep. 9, 6128.CrossRefGoogle ScholarPubMed
Kooij, S., Sijs, R., Denn, M. M., Villermaux, E. & Bonn, D. 2018 What determines the drop size in sprays? Phys. Rev. X 8, 031019.Google Scholar
Koros, R. M., Deckers, J. & Boudart, M. 1960 More experiments on liquid films. J. Appl. Phys. 31, 1129–1130.CrossRefGoogle Scholar
Kroto, H. W., Heath, J. R., O’Brien, S. C., Curl, R. F. & Smalley, R. E. 1985 C 60: buckminsterfullerene. Nature 318, 162–163.CrossRefGoogle Scholar
Kulkami, V. & Sojka, P. E. 2004 Bag breakup of low viscosity drops in the presence of a continuous air jet. Phys. Fluids 26, 072103.Google Scholar
Lafrance, P. & Ritter, R. C. 1977 Capillary breakup of a liquid jet with a random initial perturbation. Trans. ASME J. Appl. Mech. 385–388.CrossRefGoogle Scholar
Lamb, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.Google Scholar
Landau, L. & Lifshitz, E. 1987 Fluid Mechanics. Pergamon Press.Google Scholar
Landeau, M., Deguen, R. & Olson, P. 2014 Experiments on the fragmentation of a buoyant liquid volume in another liquid. J. Fluid Mech. 749, 478–518.CrossRefGoogle Scholar
Lane, W. R. & Green, H. L. 1956 The mechanics of drops and bubbles. In Survey in Mechanics (ed. Batchelor, G. K. & Davies, R. M.), pp. 162–215. Cambridge University Press.Google Scholar
Laplace, P.-S. 1805 Traité de mécanique céleste, vol. IV, supplément au livre X: Sur l’action capillaire, pp. 1–65. Courcier.Google Scholar
Lavoisier, A. L. 1789 Traîté Élémentaire de Chimie. Cuchet.Google Scholar
Lavrentiev, M. & Chabat, B. 1980 Effets Hydrodynamiques et Modèles Mathématiques. Éditions MIR, translated from the 1977 Russian edition.Google Scholar
Lawn, B. R. 1993 Fracture of Brittle Solids, 2nd edn. Cambridge University Press.CrossRefGoogle Scholar
Layes, G., Jourdan, G. & Houas, L. 2003 Distortion of a spherical gaseous interface accelerated by a plane shock wave. Phys. Rev. Lett. 91 (17), 174502.CrossRefGoogle ScholarPubMed
Le Dizès, S. 1997 Global modes in falling capillary jets. Eur. J. Mech. (B/Fluids) 16 (6), 761–778.Google Scholar
Le Dizès, S. & Villermaux, E. 2017 Capillary jet breakup by noize amplification. J. Fluid Mech. 810, 281–308.CrossRefGoogle Scholar
Leenaars, A. F. M., Huethorst, J. A. M. & Van Oekel, J. J. 1990 Marangoni drying: a new extremely clean drying process. Langmuir 6 (11), 1701–1703.CrossRefGoogle Scholar
Lefebvre, A. H. 1989 Atomization and Sprays. Hemisphere.Google Scholar
Lemenand, T., Valle, D. D., Zellouf, Y. & Peerhossaini, H. 2003 Droplets formation in turbulent mixing of two immiscible fluids in a new type of static mixer. Intl J. Multiphase Flow 29, 813–840.CrossRefGoogle Scholar
von Lenard, P. 1904 Über regen. Meteorol. Z. 06, 92–262.Google Scholar
Letcher, B. H., Nislow, K. H., Coombs, J. A., O’Donnell, M. J. & Dubreuil, T. L. 2007 Population response to habitat fragmentation in a stream-dwelling brook trout population. PLoS-ONE 11, e1139.Google Scholar
Levich, V. G. & Krylov, V. S. 1969 Surface-tension-driven phenomena. Annu. Rev. Fluid Mech. 1, 293–316.CrossRefGoogle Scholar
Lewis, D. J. 1950 The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. II. Proc. R. Soc. Lond. A 202, 81–96.Google Scholar
Leyvraz, F. 2003 Scaling theory and exactly solved models in the kinetics of irreversible aggregation. Phys. Rep. 383, 95–212.CrossRefGoogle Scholar
Lhuissier, H., Brunet, P. & Dorbolo, S. 2016 Blowing a liquid curtain. J. Fluid Mech. 795, 784–807.CrossRefGoogle Scholar
Lhuissier, H., Neel, B. & Limat, L. 2014 Viscoelasticity breaks the symmetry of impacting jets. Phys. Rev. Lett. 113, 194502.CrossRefGoogle ScholarPubMed
Lhuissier, H. & Villermaux, E. 2009a Destabilization of flapping sheets: the surprising analogue of soap films. C. R. Méc. 337, 469–480.CrossRefGoogle Scholar
Lhuissier, H. & Villermaux, E. 2009b Soap films burst like flapping flags. Phys. Rev. Lett. 103, 054501.CrossRefGoogle Scholar
Lhuissier, H. & Villermaux, E. 2011 The destabilization of an initially thick liquid sheet edge. Phys. Fluids 23 (9), 091705–091704.CrossRefGoogle Scholar
Lhuissier, H. & Villermaux, E. 2012a Bursting bubble aerosols. J. Fluid Mech. 696, 5–44.CrossRefGoogle Scholar
Lhuissier, H. & Villermaux, E. 2012b Crumpled water bells. J. Fluid Mech. 693, 508–540.CrossRefGoogle Scholar
Lhuissier, H. & Villermaux, E. 2013 ‘Effervescent’ atomization in two dimensions. J. Fluid Mech. 714, 361–392.CrossRefGoogle Scholar
Limat, L. 1993 Instabilité d’un liquide suspendu sous un surplomb solide: influence de l’épaisseur de la couche. C. R. Acad. Sci. II 317, 563–568.Google Scholar
van Limbeek, M. A. J., Lhuissier, H., Prosperetti, A., Sun, C. & Lohse, D. 2013 Explosive boiling? Phys. Fluids 25, 091102.CrossRefGoogle Scholar
Lucassen-Reynders, E. H. & Lucassen, J. 1969 Properties of capillary waves. Adv. Colloid Interface Sci. 2, 347–395.CrossRefGoogle Scholar
Lv, C., Eigenbrod, M. & Hard, S. 2018 Stability and collapse of holes in liquid layers. J. Fluid Mech. 855, 1130–1155.CrossRefGoogle Scholar
Mac Arthur, R. H. & Wilson, E. O. 1967 The Theory of Island Biogeography. Princeton University Press.Google Scholar
Mandre, S., Mani, M. & Brenner, M. P. 2009 Precursors to splashing of liquid droplets on a solid surface. Phys. Rev. Lett. 102, 134502.CrossRefGoogle ScholarPubMed
Marangoni, C. 1878 Difesa della teoria dell’elasticità superficiale dei liquidi. Plasticità superficiale. Il Nuovo Cimento Ser. 3 III (3), 193–211.CrossRefGoogle Scholar
Marangoni, C. & Stefanelli, P. 1873 Monografia delle bolle liquide. Nuovo Cimento 9 (1), 236–256.CrossRefGoogle Scholar
Marble, F. E. 1964 Spacecraft Propulsion. Space Technology Summer Institute, ST-3 (NsG-598), California Institute of Technology.Google Scholar
Marmanis, H. & Thoroddsen, S. T. 1996 Scaling of the fingering pattern of an impacting drop. Phys. Fluids 8 (6), 1344–1346.CrossRefGoogle Scholar
Marmottant, P. & Villermaux, E. 2004a Fragmentation of stretched liquid ligaments. Phys. Fluids 16, 2732–2741.CrossRefGoogle Scholar
Marmottant, P. & Villermaux, E. 2004b On spray formation. J. Fluid Mech. 498, 73–111.CrossRefGoogle Scholar
Marmottant, P., Villermaux, E. & Clanet, C. 2000 Transient surface tension of an expanding liquid sheet. J. Colloid Interface Sci. 230, 29–40.CrossRefGoogle ScholarPubMed
Marshall, J. S. & Palmer, W. McK. 1948 The distribution of raindrops with size. J. Meteorol. 5, 165–166.2.0.CO;2>CrossRefGoogle Scholar
Mason, B. J. 1971 The Physics of Clouds. Clarendon Press.Google Scholar
Matar, O. K. & Craster, R. V. 2001 Models for Marangoni drying. Phys. Fluids 13 (7), 1869–1883.CrossRefGoogle Scholar
Maxwell, J. C. 1867 On the dynamical theory of gases. Phil. Trans. R. Soc. Lond. CLVII (I), 49–88.Google Scholar
Maxwell, J. C. 1875 Capillary Action, 9th edn. Encyclopedia Britannica.Google Scholar
McEntee, W. R. & Mysels, K. 1969a The bursting of soap films. I. An experimental study. J. Phys. Chem. 73 (9), 3018–3028.CrossRefGoogle Scholar
McEntee, W. R. & Mysels, K. J. 1969b The bursting of soap films. I. An experimental study. J. Phys. Chem. 73, 3018–3028.CrossRefGoogle Scholar
Mehdizadeh, N. Z., Chandra, S. & Mostaghimi, J. 2004 Formation of fingers around the edges of a drop hitting a metal plate with high velocity. J. Fluid Mech. 510, 353–373.CrossRefGoogle Scholar
Meier, G. E. A., Klöpper, A. & Grabitz, G. 1992 The influence of kinematic waves on jet break down. Exp. Fluids 12, 173–180.CrossRefGoogle Scholar
Meshkov, E. E. 1969 Instability of the interface of two gases accelerated by a shock wave. Sov. Fluid Dyn. 4 (5), 151–157.Google Scholar
Miguet, J., Pasquet, M., Rouyer, F., Fang, Y. & Rio, E. 2020 Stability of big surface bubbles: impact of evaporation and bubbles size. Soft Matt. 16 (4), 1082–1090.CrossRefGoogle ScholarPubMed
Mora, S., Phou, T., Fromental, J. M., Pismen, L. M. & Pomeau, Y. 2010 Capillarity driven instability of a soft solid. Phys. Rev. Lett. 105, 214301.CrossRefGoogle ScholarPubMed
Morawska, L., Johnson, G. R., Ristovski, Z. D., Hargreaves, M., Mengersen, K., Corbett, S., Chao, C. Y. H., Li, Y. & Katoshevski, D. 2009 Size distribution and sites of origin of droplets expelled from the human respiratory tract during expiratory activities. Aerosol Sci. 40, 256–269.CrossRefGoogle Scholar
Mott, N. F. 1947 Fragmentation of shell cases. Proc. R. Soc. Lond. A 189, 300–308.Google ScholarPubMed
Moulinet, S. & Adda-Bedia, M. 2015 Popping balloons: a case study of dynamical fragmentation. Phys. Rev. Lett. 115, 184301.CrossRefGoogle ScholarPubMed
Mundo, C., Sommerfeld, M. & Tropea, C. 1995 Droplet-wall collisions: experimental studies of the deformation and breakup process. Intl J. Multiphase Flow 21 (2), 151–173.CrossRefGoogle Scholar
Mysels, K. & Vijayendran, B. R. 1973 Film bursting. V. The effect of various atmospheres and the anomaly of newton black films. J. Phys. Chem. 77 (13), 1692–1694.CrossRefGoogle Scholar
Néel, B., Lhuissier, H. & Villermaux, E. 2020 ‘Fines’ from the collision of liquid rims. J. Fluid Mech. 893, A16.CrossRefGoogle Scholar
Néel, B. & Villermaux, E. 2018 The spontaneous puncture of thick liquid films. J. Fluid Mech. 838, 192–221.CrossRefGoogle Scholar
Newton, I. 1687 Principia Mathematica.Google Scholar
Newton, I. 1704 Opticks.Google Scholar
Nierstrasz, V. A. & Frens, G. 1998 Marginal regeneration in thin vertical liquid films. J. Colloid Interface Sci. 207 (2), 209–217.CrossRefGoogle ScholarPubMed
Noblin, X., Yang, S. & Dumais, J. 2009 Surface tension propulsion of fungal spores. J. Expl Biol. 212, 2835–2843.CrossRefGoogle ScholarPubMed
O’Dowd, C. & de Leeuw, G. 2007 Marine aerosol production: a review of the current knowledge. Phil. Trans. R. Soc. Lond. A 365, 1753–1774.CrossRefGoogle ScholarPubMed
Oliveira, M. S. N. & McKinley, G. H. 2005 Iterated stretching and multiple beads-on-a-string phenomena in dilute solutions of high extensible flexible polymers. Phys. Fluids 17, 071704.CrossRefGoogle Scholar
Pandit, A. B. & Davidson, J. F. 1990 Hydrodynamics of the rupture of thin liquid films. J. Fluid Mech. 212, 11–24.CrossRefGoogle Scholar
Pasteur, L. 1861 Mémoire sur les corpuscules organisés qui existent dans l’atmosphère. Annales des Sciences Naturelles (Partie Zoologique) Série 4, 5–98.Google Scholar
Pearson, J. R. A. 1958 On convection cells induced by surface tension. J. Fluid Mech. 4 (5), 489–500.CrossRefGoogle Scholar
Peregrine, D. H., Shoker, G. & Symon, A. 1990 The bifurcation of liquid bridges. J. Fluid Mech. 212, 25–39.CrossRefGoogle Scholar
Philippi, J., Lagrée, P.-Y. & Antkowiak, A. 2016 Drop impact on a solid surface: short-time self-similarity. J. Fluid Mech. 795, 96–135.CrossRefGoogle Scholar
Pietsch, R. B., Grothe, H., Hanlon, R., Powers, C. W., Jung, S., Ross, S. D. & Schmale, D. G. III 2018 Wind-driven spume droplet production and the transport of pseudomonas syringae from aquatic environments. PeerJ, 1–26. doi:10.7717/peerj.5663.CrossRefGoogle ScholarPubMed
Planck, M. 1901 On the law of distribution of energy in the normal spectrum. Ann. Phys. 4 (3), 553–563.CrossRefGoogle Scholar
Plateau, J. 1849 Recherches expérimentales et théoriques sur les figures d’équilibre d’une masse liquide sans pesanteur. In Mémoires De L’académie Royale Des Sciences, Des Lettres Et Des Beaux-Arts De Belgique, vol. XXIII, pp. 5–150.Google Scholar
Plateau, J. 1873 Satique expérimentale et théorique des liquides soumis aux seules forces moléculaires. Ghauthier-Villard.Google Scholar
Pomeau, Y. & Villermaux, E. 2006 Two hundred years of capillarity research. Phys. Today 59 (3), 39–44.CrossRefGoogle Scholar
Poulain, S. & Bourouiba, L. 2018 Biosurfactants change the thinning of contaminated bubbles at bacteria–laden water interfaces. Phys. Rev. Lett. 121, 204502.CrossRefGoogle ScholarPubMed
Poulain, S., Villermaux, E. & Bourouiba, L. 2018 Ageing and burst of surface bubbles. J. Fluid Mech. 851, 636–671.CrossRefGoogle Scholar
Poulter, T. C. & Caldwell, B. M. 1957 The development of shaped charges for oil well completion. Petrol. Trans. AIME 210, 11–18.CrossRefGoogle Scholar
Pugh, E. M., Eichelberger, J. & Rostocker, N. 1952 Theory of jet formation by charges with lined conical cavities. J. Appl. Phys. 23 (5), 532–536.CrossRefGoogle Scholar
Qian, J. & Law, C. K. 1997 Regimes of coalescence and separation in droplet collision. J. Fluid Mech. 331, 59–80.CrossRefGoogle Scholar
Rallison, J. M. & Hinch, E. J. 1995 Instability of a high-speed submerged elastic jet. J. Fluid Mech. 288, 311–324.CrossRefGoogle Scholar
Ranger, A. & Nicholls, J. A. 1969 Aerodynamic shattering of liquid drops. AIAA J. 7 (2), 285–290.Google Scholar
Ranz, W. E. 1959 Some experiments on the dynamics of liquid films. J. Appl. Phys. 30, 1950–1955.CrossRefGoogle Scholar
Rao, C. K. & Basu, S. 2020 Atomization modes for levitating emulsified droplets undergoing phase change. Exp. Fluids 61, 41.CrossRefGoogle Scholar
Rao, C. K., Kamakar, S. & Basu, S. 2017 Atomization characteristics and instabilities in the combustion of multi-component fuel droplets with high volatility differential. Sci. Rep. 7, 8925.CrossRefGoogle ScholarPubMed
Raufaste, C., Celestini, F., Barzyk, A. & Frisch, T. 2015 Hole growth dynamics in a two dimensional leidenfrost droplet. Phys. Fluids 27 (3), 031704.CrossRefGoogle Scholar
Rayleigh, Lord 1878 On the instability of jets. Proc. R. Soc. Lond. A 10, 4–13.Google Scholar
Rayleigh, Lord 1879 On the capillary phenomena of jets. Proc. R. Soc. Lond. A 29, 71–97.CrossRefGoogle Scholar
Rayleigh, Lord 1880 On the stability, or instability of certain fluid motion. Proc. Lond. Math. Soc. 11, 57.Google Scholar
Rayleigh, Lord 1883 Investigation on the character of the equilibrium of an incompressible heavy fluid of variable density. Proc. R. Soc. Lond. A 14, 170–177.Google Scholar
Rayleigh, Lord 1890 On the theory of surface forces. Phil. Mag. XXX, 285–298.Google Scholar
Rayleigh, Lord 1891 Some applications of photography. Nature 44, 249–254.CrossRefGoogle Scholar
Rayleigh, Lord 1892 On the instability of a cylindre of viscous liquid under capillary forces. Phil. Mag. 34 (207), 145–155.CrossRefGoogle Scholar
Redor, I., Barthélemy, E., Michallet, H., Onorato, M. & Mordant, N. 2019 Experimental evidence of a hydrodynamic soliton gas. Phys. Rev. Lett. 122, 214502.CrossRefGoogle ScholarPubMed
Reiter, G. 1992 Dewetting of thin polymer films. Phys. Rev. Lett. 68 (1), 75–78.CrossRefGoogle ScholarPubMed
Resch, F. & Afeti, G. 1991 Film drop distribution from bubbles bursting in seawater. J. Geophys. Res. 96 (C6), 10681–10688.CrossRefGoogle Scholar
Reyssat, E. & Quere, D. 2006 Bursting of a fluid film in a viscous environment. Europhys. Lett. 76, 236–242.CrossRefGoogle Scholar
Riboux, G. & Gordillo, J. M. 2014 Experiments of drops impacting a smooth solid surface: a model of the critical impact speed for drop splashing. Phys. Rev. Lett. 113 (2), 024507.Google Scholar
Riboux, G. & Gordillo, J. M. 2015 The diameters and velocities of the droplets ejected after splashing. J. Fluid Mech. 772, 630–648.CrossRefGoogle Scholar
Richtmyer, R. D. 1960 Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Maths 13, 297–319.CrossRefGoogle Scholar
von Rittinger, P. R. 1867 Lehrbuch der Aufbereitungskunde: in ihrer neuesten Entwicklung und Ausbildung systematisch dargestellt. Ernst und Korn.Google Scholar
Robinson, N. D. & Steen, P. H. 2001 Observation of singularity formation during the capillary collapse and bubble pinch-off of a soap film bridge. J. Colloid Interface Sci. 241, 448–458.CrossRefGoogle Scholar
Roché, M., Li, Z., Griffiths, I. M., Le Roux, S., Cantat, I., Saint-Jalmes, A. & Stone, H. A. 2014 Marangoni flow of soluble amphiphiles. Phys. Rev. Lett. 112, 208302.CrossRefGoogle Scholar
Roisman, I. V. 2004 Dynamics of inertia dominated binary drop collisions. Phys. Fluids 16 (9), 3438–3449.CrossRefGoogle Scholar
Roisman, I. V., Horvat, K. & Tropea, C. 2006 Spray impact: rim transverse instability initiating fingering and splash, and description of a secondary spray. Phys. Fluids 18, 102104.CrossRefGoogle Scholar
Roisman, I. V., Riobo, R. & Tropea, C. 2002 Normal impact of a liquid drop on a dry surface: model for spreading and receding. Proc. R. Soc. Lond. A 458, 1411–1430.CrossRefGoogle Scholar
Rowlinson, J. S. 2002 Cohesion. Cambridge University Press.CrossRefGoogle Scholar
Rozhkov, A., Prunet-Foch, B. & Vignes-Adler, M. 2002 Impact of water drops on small targets. Phys. Fluids 14, 3485–3501.CrossRefGoogle Scholar
Rozhkov, A., Prunet-Foch, B. & Vignes-Adler, M. 2010 Impact of drops of surfactant solutions on small targets. Proc. R. Soc. Lond. A 466 (2122), 2897–2916.Google Scholar
Rozhkov, A., Prunet-Foch, B. & Vignes-Adler, M. 2015 Star-like breakup of polymeric drops in electrical field. J. Non Netonian Mech. 226, 46–59.CrossRefGoogle Scholar
Sallam, K. A., Aalburg, C. & Faeth, G. M. 2004 Breakup of round nonturbulent liquid jets in gaseous crossflow. AIAA J. 42 (12), 2529–2540.CrossRefGoogle Scholar
Sauter, U. S. & Buggish, H. W. 2005 Stability of initially slow viscous jets driven by gravity. J. Fluid Mech. 533, 237–257.CrossRefGoogle Scholar
Savart, F. 1833a Mémoire sur la constitution des veines liquides lancées par des orifices circulaires en mince paroi. Ann. Chim. Phys. 53, 337–386.Google Scholar
Savart, F. 1833b Mémoire sur le choc de deux veines liquides animées de mouvements directement opposés. Ann. Chim. Phys. 55, 257–310.Google Scholar
Savart, F. 1833c Mémoire sur le choc d’une veine liquide lancée contre un plan circulaire. Ann. Chim. Phys. 54, 56–87.Google Scholar
Savart, F. 1833d Suite du mémoire sur le choc d’une veine liquide lancée contre un plan circulaire. Ann. Chim. Phys. 54, 113–145.Google Scholar
Savva, N. & Bush, J. W. 2009 Viscous sheet retraction. J. Fluid Mech. 626, 211–240.CrossRefGoogle Scholar
Scharfman, B. E., Techet, A. H., Bush, J. W. M. & Bourouiba, L. 2016 Visualization of sneeze ejecta: steps of fluid fragmentation leading to respiratory droplets. Exp. Fluids 57 (24), 1–9.CrossRefGoogle ScholarPubMed
Schlichting, H. 1987 Boundary Layer Theory, 7th edn. McGraw-Hill.Google Scholar
Schulkes, R. M. S. M. 1996 The contraction of liquid filaments. J. Fluid Mech. 309, 277–300.CrossRefGoogle Scholar
Schweitzer, P. H. 1937 Mechanism of disintegration of liquid jets. J. Appl. Phys. 8, 513–521.CrossRefGoogle Scholar
Scriven, L. E. & Sternling, C. V. 1960 The Marangoni effects. Nature 187 (4733), 186–188.CrossRefGoogle Scholar
Sedov, L. I. 1946 Le mouvement d’air en cas d’une forte explosion. C. R. Acad. Sci. URSS 52, 17–20.Google Scholar
Senchenko, S. & Bohr, T. 2005 Shape and stability of a viscous thread. Phys. Rev. E 71, 056301.Google ScholarPubMed
Sharma, A. & Reiter, G. 1996 Instability of thin polymer films on coated substrates: rupture, dewetting, and drop formation. J. Colloid Interface Sci. 178 (2), 383–399.CrossRefGoogle Scholar
Sierou, A. & Lister, J. R. 2004 Self-similar recoil of inviscid drops. Phys. Fluids 16 (5), 1379–1394.CrossRefGoogle Scholar
Simmons, H. C. 1977a The correlation of drop-sizes distributions in fuel nozzles sprays. Part I. J. Engng Power 7, 309–314.CrossRefGoogle Scholar
Simmons, H. C. 1977b The correlation of drop-sizes distributions in fuel nozzles sprays. Part II. J. Engng Power 7, 315–319.CrossRefGoogle Scholar
von Smoluchowski, M. 1917 Versuch einer mathematischen theorie der koagulationskinetik kolloider lösungen. Z. Phys. Chem. 92, 129–168.Google Scholar
Sonder, I., Harp, A. G., Graettinger, A. H., Moitra, P., Valentine, G. A., Büttner, R. & Zimanowski, B. 2018 Meter-scale experiments on magma–water interaction. JGR: Solid Earth 123, 10597–10615.Google Scholar
Soundar Jerome, J. J., Vandenberghe, N. & Forterre, Y. 2016 Unifying impacts in granular matter from quicksand to cornstarch. Phys. Rev. Lett. 117, 098003.Google Scholar
Sovani, S. D., Sojka, P. E. & Lefebvre, A. H. 2001 Effervescent atomization. Prog. Energy Combust. Sci. 27, 483–521.CrossRefGoogle Scholar
Spiel, D. E. 1994 The number and size of jet drops produced by air bubbles bursting on a fresh water surface. J. Geophys. Res. 99 (C4), 10289–10296.CrossRefGoogle Scholar
Spiel, D. E. 1998 On the birth of film drops from bubbles bursting on seawater surfaces. J. Geophys. Res. 103 (C11), 24907–24918.CrossRefGoogle Scholar
Squire, H. B. 1953 Investigation of the stability of a moving liquid film. Br. J. Appl. Phys. 4, 167–169.CrossRefGoogle Scholar
Stone, H. A. & Leal, L. G. 1989 Relaxation and breakup of an initially extended drop in an otherwise quiescent fluid. J. Fluid Mech. 198, 399–427.CrossRefGoogle Scholar
Stow, C. D. & Stainer, R. D. 1977 The physical products of a splashing water drop. J. Met. Soc. Japan 55 (5), 518–531.Google Scholar
Sultanov, F. M. & Yarin, A. L. 1990 Droplet size distribution in a percolation model for explosive dispersal. J. Appl. Mech. Tech. Phys. 31 (5), 708–713.CrossRefGoogle Scholar
Swanson, J. G. & Langefeld, O. 2015 Fundamental research in water spray systems for dust control. Trans. Inst. Mining Met. A 124 (2), 78–82.Google Scholar
Tagawa, Y. et al. 2012 Highly focused supersonic microjets. Phys. Rev. X 2, 031002.Google Scholar
Takacs, L. 2013 The historical development of mechanochemistry. Chem. Soc. Rev. 42, 7649–7659.CrossRefGoogle ScholarPubMed
Taylor, A. M. K. P. 2008 Science review of internal combustion engines. Energy Policy 36, 4657–4667.CrossRefGoogle Scholar
Taylor, B. 1712 (part of a letter) concerning the ascent of water between two glass planes. Phil. Trans. R. Soc. 27, 538.Google Scholar
Taylor, G. I. 1935 Statistical theory of turbulence. Part I. Proc. R. Soc. Lond. A CLI, 421–444.CrossRefGoogle Scholar
Taylor, G. I. 1950a The formation of a blast wave by a very intense explosion. ii. the atomic explosion of 1945. Proc. R. Soc. Lond. A 201, 175–186.Google Scholar
Taylor, G. I. 1950b The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I. Proc. R. Soc. Lond. A 201 (1065), 192–196.Google Scholar
Taylor, G. I. 1959a The dynamics of thin sheets of fluid I. Water bells. Proc. R. Soc. Lond. A 253, 289–295.Google Scholar
Taylor, G. I. 1959b The dynamics of thin sheets of fluid II. Waves on fluid sheets. Proc. R. Soc. Lond. A 253, 296–312.Google Scholar
Taylor, G. I. 1959c The dynamics of thin sheets of fluid III. Desintegration of fluid sheets. Proc. R. Soc. Lond. A 253, 313–321.Google Scholar
Taylor, G. I. & Michael, D. H. 1973 On making holes in a sheet of fluid. J. Fluid Mech. 58 (4), 625–639.CrossRefGoogle Scholar
Thereulaz, G., Bonabeau, E., Sauwens, C., Deneubourg, J. L., Lioni, A., Libert, F., Passera, L. & Solé, R. 2001 Model of droplet dynamics in the argentine ant linepithema humile (mayr). Bull. Math. Biol. 63, 1079–1093.CrossRefGoogle Scholar
Thomson, J. J. & Newall, H. F. 1885 On the formation of vortex rings by drops falling into liquids, and some allied phenomena. Proc. R. Soc. Lond. 39, 417–436.Google Scholar
Thoroddsen, S. T. 2002 The ejecta sheet generated by the impact of a drop. J. Fluid Mech. 451, 373–381.CrossRefGoogle Scholar
Thoroddsen, S. T., Etoh, T. G. & Takehara, K. 2006 Crown breakup by Marangoni instability. J. Fluid Mech. 557, 63–72.CrossRefGoogle Scholar
Thoroddsen, S. T. & Takehara, K. 2000 The coalescence cascade of a drop. Phys. Fluids 12 (6), 1265–1267.CrossRefGoogle Scholar
Thoroddsen, S. T., Takehara, K. & Etoh, T. G. 2012a Microsplashing by drop impacts. J. Fluid Mech. 706, 560–570.CrossRefGoogle Scholar
Thoroddsen, S. T., Thoraval, M.-J., Takehara, K. & Etoh, T. G. 2012b Micro-bubble morphologies following drop impacts onto a pool surface. J. Fluid Mech. 708, 469–479.CrossRefGoogle Scholar
Tjahjadi, M. & Ottino, J. M. 1991 Stretching and breakup of droplets in chaotic flows. J. Fluid Mech. 232, 191–219.CrossRefGoogle Scholar
Tjahjadi, M., Stone, H. A. & Ottino, J. M. 1992 Satellite and subsatellite formation in capillary breakup. J. Fluid Mech. 243, 297–317.CrossRefGoogle Scholar
Tomotika, S. 1936 Breaking up of a drop of viscous liquid immersed in another viscous fluid which is extending at a uniform rate. Proc. R. Soc. Lond. A 153 (879), 302–318.Google Scholar
Turner, C. E., Jennison, M. W. & Edgerton, H. E. 1941 Public health applications of high-speed photography. Am. J. Public Health 31, 319–324.CrossRefGoogle ScholarPubMed
Ukiwe, C. & Kwok, D. Y. 2005 On the maximum spreading diameter of impacting droplets on well-prepared solid surfaces. Langmuir 21, 666–673.CrossRefGoogle ScholarPubMed
Utada, A. S., Lorenceau, E., Link, D. R., Kaplan, P. D., Stone, H. A. & Weitz, D. A. 2005 Monodisperse double emulsions generated from a microcapillary device. Science 308 (5721), 537–541.CrossRefGoogle ScholarPubMed
Vanhook, S. J., Schatz, M. F., Swift, J. B., McCormick, W. D. & Swinney, H. L. 1997 Long-wavelength surface-tension-driven Bénard convection: experiment and theory. J. Fluid Mech. 345, 45–78.CrossRefGoogle Scholar
Vermorel, R., Vandenberghe, N. & Villermaux, E. 2007 Rubber band recoil. Proc. R. Soc. Lond. A 463, 641–658.Google Scholar
Vernay, C., Ramos, L. & Ligoure, C. 2015a Bursting of dilute emulsion-based liquid sheets driven by a Marangoni effect. Phys. Rev. Lett. 115, 198302.CrossRefGoogle Scholar
Vernay, C., Ramos, L. & Ligoure, C. 2015b Free radially expanding liquid sheet in air: time- and space-resolved measurement of the thickness field. J. Fluid Mech. 764, 428–444.CrossRefGoogle Scholar
Veron, F. 2015 Ocean spray. Annu. Rev. Fluid Mech. 47, 507–538.CrossRefGoogle Scholar
Veron, F., Hopkins, C., Harrison, E. L. & Mueller, J. A. 2012 Sea spray spume droplet production in high wind speeds. Geophys. Res. Lett. 39, L16602.CrossRefGoogle Scholar
Vielle, P. 1900 Rôle des discontinuités dans la propagation des phénomènes explosifs. C. R. Acad. Sci. Paris CXXLI, 413–416.Google Scholar
Villermaux, E. 1994 Pulsed dynamics of fountains. Nature 371, 24–25.CrossRefGoogle Scholar
Villermaux, E. 1998a Mixing and spray formation in coaxial jets. J. Propul. Power 14, 807–817.CrossRefGoogle Scholar
Villermaux, E. 1998b On the role of viscosity in shear instability. Phys. Fluids 10 (2), 368–373.CrossRefGoogle Scholar
Villermaux, E. 2007 Fragmentation. Annu. Rev. Fluid Mech. 39, 419–446.CrossRefGoogle Scholar
Villermaux, E. 2009 Hesitant nature. J. Fluid Mech. 636, 1–4.CrossRefGoogle Scholar
Villermaux, E. 2012 The formation of filamentary structures from molten silicates: Pele’s hair, angel hair, and blown clinker. C. R. Méc. 340 (8), 555–564.CrossRefGoogle Scholar
Villermaux, E. 2019 Mixing versus stirring. Annu. Rev. Fluid Mech. 51, 245–273.CrossRefGoogle Scholar
Villermaux, E. & Almarcha, C. 2016 Node dynamics and cusps size distribution at the border of liquid sheets. Phys. Rev. Fluids 1, 041902.CrossRefGoogle 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. 2010 Size distribution of raindrops reply. Nat. Phys. 6, 232.CrossRefGoogle Scholar
Villermaux, E. & Bossa, B. 2011 Drop fragmentation on impact. J. Fluid Mech. 668, 412–435.CrossRefGoogle Scholar
Villermaux, E. & Clanet, C. 2002 Life of a flapping liquid sheet. J. Fluid Mech. 462, 342–363.CrossRefGoogle Scholar
Villermaux, E. & Duplat, J. 2003 Mixing as an aggregation process. Phys. Rev. Lett. 91 (18), 184501.CrossRefGoogle ScholarPubMed
Villermaux, E. & Eloi, F. 2011 The distribution of raindrops speeds. Geophys. Res. Lett. 38, L19805.CrossRefGoogle Scholar
Villermaux, E., Marmottant, P. & Duplat, J. 2004 Ligament-mediated spray formation. Phys. Rev. Lett. 92 (7).CrossRefGoogle ScholarPubMed
Villermaux, E., Moutte, A., Amielh, M. & Meunier, P. 2017 Fine structure of the vapor field in evaporating dense sprays. Phys. Rev. Fluids 2, 074501.CrossRefGoogle Scholar
Villermaux, E., Pistre, V. & Lhuissier, H. 2013 The viscous Savart sheet. J. Fluid Mech. 730, 607–625.CrossRefGoogle Scholar
da Vinci, L. 1508 Codex leicester. In The Notebooks of Leonardo da Vinci. George Brazillier, translated in english by MacCurdy.Google Scholar
Vledouts, A., Quinard, J., Vandenberghe, N. & Villermaux, E. 2016a Explosive fragmentation of liquid shells. J. Fluid Mech. 788, 246–273.CrossRefGoogle Scholar
Vledouts, A., Vandenberghe, N. & Villermaux, E. 2015 Fragmentation as an aggregation process. Proc. R. Soc. Lond. A 471, 20150678.Google Scholar
Vledouts, A., Vandenberghe, N. & Villermaux, E. 2016b Fragmentation as an aggregation process: the role of defects. Proc. R. Soc. Lond. A 472, 20150679.Google Scholar
Vrij, A. 1966 Possible mechanism for the spontaneous rupture of thin, free liquid films. Discuss. Faraday Soc. 42, 23–33.CrossRefGoogle Scholar
Vu, T. T. & Dumouchel, C. 2018 Analysis of ligamentary atomization of highly perturbed liquid sheets. Intl J. Multiphase Flow 107, 156–167.CrossRefGoogle Scholar
Wacheul, J. B., Le Bars, M., Monteux, J. & Aurnou, J. M. 2014 Laboratory experiments on the breakup of liquid metal diapirs. Earth Planet. Sci. Lett. 403, 236–245.CrossRefGoogle Scholar
Wagner, H. 1932 Über Stoß- und Gleitvorgänge an der Oberfläche von Flüssigkeiten. Z. Angew. Math. Mech. 12 (4), 193–215.CrossRefGoogle Scholar
Wang, Y. & Bourouiba, L. 2017 Drop impact on small surface: thickness and velocity profiles of the expanding sheet in the air. J. Fluid Mech. 814, 510–534.CrossRefGoogle Scholar
Wang, Y. & Bourouiba, L. 2018 Unsteady sheet fragmentation: droplet sizes and speeds. J. Fluid Mech. 848, 946–967.CrossRefGoogle Scholar
Wang, Y., Im, K. S. & Fezzaa, K. 2008 Similarity between the primary and secondary air-assisted liquid jet breakup mechanisms. Phys. Rev. Lett. 100, 154502.CrossRefGoogle ScholarPubMed
Watson, E. J. 1964 The radial spread of a liquid jet over a horizontal plane. J. Fluid Mech. 20, 481–499.CrossRefGoogle Scholar
Weber, C. 1931 Zum Zerfall eines Flüssigkeitsstrahles. Z. Angew. Math. U. Mech. 11 (2), 136–154.CrossRefGoogle Scholar
Wedershoven, H. M. J. M., Berendsen, C. W. J., Zeegers, J. C. H. & Darhuber, A. A. 2015 Infrared-laser-induced thermocapillary deformation and destabilization of thin liquid films on moving substrates. Phys. Rev. A 3, 024005.Google Scholar
Wells, F. W. 1955 Airborne Contagion and Air Hygiene. Harvard University Press.Google Scholar
Wijshoff, H. 2010 The dynamics of the piezo inkjet printhead operation. Phys. Rep. 491, 77–177.CrossRefGoogle Scholar
Wildeman, S., Sterl, S., Sun, C. & Lohse, D. 2017 Fast dynamics of water droplets freezing from the outside in. Phys. Rev. Lett. 118, 084101.CrossRefGoogle ScholarPubMed
Wilson, J. E., Grib, S. W., Ahmad, A. D., Renfro, M. W., Adams, S. A. & Salaimeh, A. A. 2018 Study of near-cup droplet breakup of an automotive electrostatic rotary bell (ESRB) atomizer using high-speed shadowgraph imaging. Coatings 8 (174), 1–17.CrossRefGoogle Scholar
Winslow, C.-E. A. & Robinson, E. A. 1910 An investigation of the extent of the bacterial pollution of the atmosphere by mouth spray. J. Infect. Dis. 7 (1), 17–37.CrossRefGoogle Scholar
Wodlei, F., Sebilleau, J., Magnaudet, J. & Pimienta, V. 2018 Marangoni-driven flower-like patterning of an evaporating drop spreading on a liquid substrate. Nat. Commun. 9, 820.CrossRefGoogle ScholarPubMed
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 spiralling liquid jets. Intl J. Multiphase Flow 30, 499–520.CrossRefGoogle Scholar
Woodcock, A. H., Kientzler, C. F., Arons, A. B. & Blanchard, D. C. 1953 Giant condensation nuclei from bursting bubbles. Nature 172, 1144–1145.CrossRefGoogle Scholar
Worthington, A. M. 1876 On the forms assumed by drops of liquids falling vertically on a horizontal plate. Proc. R. Soc. Lond. 25, 261–272.Google Scholar
Worthington, A. M. 1908 A Study of Splashes. Longmans, Green & Co.Google Scholar
Wu, P. K. & Faeth, G. M. 1995 Onset and end drop formation along the surface of turbulent jets in still gases. Phys. Fluids 7 (11), 2915–2917.CrossRefGoogle Scholar
Xu, L., Barcos, L. & Nagel, S. R. 2007 Splashing of liquids: interplay of surrounding gas and surface roughness. Phys. Rev. E 76, 066311.Google ScholarPubMed
Yafetto, L. et al. 2008 The fastest flights in nature: high-speed spore discharge mechanisms among fungi. PLoS-ONE 3 (9), e3237.CrossRefGoogle ScholarPubMed
Yaminsky, V. V., Ohnishi, S., Vogler, E. A. & Horn, R. G. 2010 Stability of aqueous films between bubbles. Part 1. The effect of speed on bubble coalescence in purified water and simple electrolyte solutions. Langmuir 26 (11), 8061–8074.CrossRefGoogle ScholarPubMed
Yarin, A. L., Pourdeyhimi, B. & Ramakrishna, S. 2014 Fundamentals and Applications of Micro- and Nanofibers. Cambridge University Press.CrossRefGoogle Scholar
Yarin, A. L. & Weiss, D. A. 1995 Impact of drops on solid surfaces: self-similar capillary waves, and splashing as a new type of kinematic discontinuity. J. Fluid Mech. 283, 141–173.CrossRefGoogle Scholar
York, J. L., Stubbs, H. E. & Tek, M. R. 1953 The mechanism of disintegration of liquid sheets. Trans. ASME 75, 1279–1286.Google Scholar
Young, T. 1805 An essay on the cohesion of fluids. Proc. R. Soc. Lond. 95, 65–87.Google Scholar
Yule, A. J. & Dunkley, J. J. 1994 Atomization of Melts for Powder Production and Spray Deposition. Clarendron Press.Google Scholar
Zayas, G., Chiang, M. C., Wong, E., Macdonald, F., Lange, C. F., Senthilselvan, A. & King, M. 2012 Cough aerosol in healthy participants: fundamental knowledge to optimize droplet-spread infectious respiratory disease management. BMC Pulm. Med. 12 (11), 1–11.CrossRefGoogle ScholarPubMed
Zeff, B., Kleber, B., Fineberg, J. & Lathrop, D. 2000 Singularity dynamics in curvature collapse and jet erruption on a fluid surface. Nature 403, 401–404.CrossRefGoogle Scholar
Zeldovich, Y. B. & Raizer, Y. P. 2002 Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena. Dover Publications.Google Scholar
Zhang, H. & Ravi-Chandar, K. 2007 On the dynamics of necking and fragmentation – I. Real-time and post-mortem observations in Al 6061-O. Intl J. Fract. 142 (3–4), 183–217.CrossRefGoogle Scholar
Zhang, H. & Ravi-Chandar, K. 2008 On the dynamics of necking and fragmentation – II. Effect of material properties, geometrical constraints and absolute size. Intl J. Fract. 150 (1–2), 3–36.CrossRefGoogle Scholar
Zhang, L., Brunet, P., Eggers, J. & Deegan, R. 2010 Wavelength selection in the crown splash. Phys. Fluids 22, 122105.CrossRefGoogle Scholar
Zhao, C., Sprittles, J. E. & Lockerby, D. A. 2019 Revisiting the Rayleigh–Plateau instability for the nanoscale. J. Fluid Mech. 861, R3.CrossRefGoogle Scholar
Zhao, H., Liu, H. F., Xu, J. L. & Li, W. F. 2011 Experimental study of drop size distribution in the bag breakup regime. Ind. Engng Chem. Res. 50 (16), 9767–9773.CrossRefGoogle Scholar