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Drop fragmentation on impact

Published online by Cambridge University Press:  26 January 2011

E. VILLERMAUX  and
B. BOSSA
E. VILLERMAUX*
Affiliation:
IRPHE, Aix-Marseille Université, 13384 Marseille CEDEX 13, France
B. BOSSA
Affiliation:
IRPHE, Aix-Marseille Université, 13384 Marseille CEDEX 13, France
*
†Also at Institut Universitaire de France, 75005 Paris, France. Email address for correspondence: villermaux@irphe.univ-mrs.fr
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Abstract

We address the sequence of events accompanying the transition from an initially compact volume of liquid – a drop – into dispersed fragments when it impacts a solid surface. We describe the change of topology of the drop to a radially expanding sheet and discuss the reasons of its rim destabilization, responsible for the emergence of radial ligaments which ultimately fragment into smaller drops. The dynamics ruling the radius of the sheet, its stability and the resulting fragment drop size distribution are documented experimentally. The radius dynamics results from a simple balance between inertia of the initial drop and capillary restoring forces at the rim, with damping due to the continuous transfer of momentum from the sheet to the rim. The ligaments expelled from the rim originate from a Rayleigh–Taylor mechanism localized at the rim. The final drop size distribution in the spray is shown to be a linear superposition of gamma distributions characteristic of ligament breakup, leading generically to Bessel functions.

JFM classification

Drops and Bubbles: Aerosols/atomization Instability: Instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 668 , 10 February 2011 , pp. 412 - 435
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

Abramowitz, M. & Stegun, I. A. 1964 Handbook of Mathematical Functions. Dover.Google Scholar
Allen, R. F. 1975 The role of surface tension in splashing. J. Colloid. Interface Sci. 51 (2), 350–351.CrossRefGoogle Scholar
Ashgriz, N. & Poo, Y. L. 1990 Coalescence and separation in binary collisions of liquid drops. J. Fluid Mech. 221, 183–204.CrossRefGoogle Scholar
Bartolo, D., Josserand, C. & Bonn, D. 2005 Retraction dynamics of aqueous drops upon impact on non-wetting surfaces. J. Fluid Mech. 545, 329–338.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Borda, J. C. 1763 Experiences sur la Résistance des Fluides. Mémoires de l'Academie Royale des Sciences, Paris, pp. 356–376.Google Scholar
Bremond, N., Clanet, C. & Villermaux, E. 2007 Atomization of undulated liquid sheets. J. Fluid Mech. 585, 421–456.Google 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
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
Clanet, C. & Villermaux, E. 2002 Life of a smooth liquid sheet. J. Fluid Mech. 462, 307–340.Google 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
Culick, F. E. C. 1960 Comments on a ruptured soap film. J. Appl. Phys. 31, 1128–1129.Google Scholar
Dupré, A. 1867 Théorie mécanique de la chaleur. Ann. Chim. Phys. 11, 194–216.Google Scholar
Eggers, J. & Villermaux, E. 2008 Physics of liquid jets. Rep. Prog. Phys. 71, 036601.Google Scholar
de Gennes, P. G. 1996 Mechanics of soft interfaces. Faraday Discuss. 104, 1–8.CrossRefGoogle Scholar
Kim, H. Y., Feng, Z. C. & Chun, J. H. 2000 Instability of a liquid jet emerging from a droplet collision with a solid surface. Phys. Fluids 12 (3), 531–541.Google Scholar
Krechetnikov, R. 2010 Stability of liquid sheet edges. Phys. Fluids 22, 092101.CrossRefGoogle Scholar
Lord, Rayleigh 1891 Some applications of photography. Nature XLIV, 249–254.Google Scholar
Marmanis, H. & Thoroddsen, S. T. 1996 Scaling of the fingering pattern of an impacting drop. Phys. Fluids 8 (6), 1344–1346.Google Scholar
Marmottant, P. & Villermaux, E. 2004 On spray formation. J. Fluid Mech. 498, 73–112.Google 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.Google Scholar
Mundo, C., Sommerfeld, M. & Tropea, C. 1995 Droplet–wall collisions: experimental studies of the deformation and breakup process. Intl J. Multiph. Flow 21 (2), 151–173.Google Scholar
Pepper, R. E., Courbin, L. & Stone, H. A. 2008 Splashing on elastic membranes: the importance of early-time dynamics. Phys. Fluids 20 (8), 082103.CrossRefGoogle Scholar
Qian, J. & Law, C. 1997 Regimes of coalescence and separation in droplet collision. J. Fluid Mech. 331, 59–80.Google Scholar
Richard, D., Clanet, C. & Quéré, D. 2002 Contact time of a bouncing drop. Nature 417, 811.Google 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.Google Scholar
Roisman, I. V., Riobo, R. & Tropea, C. 2002 Normal impact of a liquid drop on a dry surface: model for spreading and recedind. Proc. R. Soc. Lond. A 458, 1411–1430.Google Scholar
Rozhkov, A., Prunet-Foch, B. & Vignes-Adler, M. 2002 Impact of water drops on small targets. Phys. Fluids 14 (10), 3485–3501.Google Scholar
Rozhkov, A., Prunet-Foch, B. & Vignes-Adler, M. 2003 Impact of drops of polymer solutions on small targets. Phys. Fluids 15 (7), 2006–2019.CrossRefGoogle Scholar
Rozhkov, A., Prunet-Foch, B. & Vignes-Adler, M. 2004 Dynamics of a liquid lamella resulting from the impact of a water drop on a small target. Proc. R. Soc. Lond. A 460, 2681–2704.Google Scholar
Savart, F. 1833 Mémoire sur le choc d'une veine liquide lancée sur un plan circulaire. Ann. Chim. 54, 56–87.Google Scholar
Savva, N. & Bush, J. W. M. 2009 Viscous sheet retraction. J. Fluid Mech. 626, 211–240.Google Scholar
Simpkins, P. G. & Bales, E. L. 1972 Water drop response to sudden accelerations. J. Fluid Mech. 55 (4), 629–639.CrossRefGoogle Scholar
Squire, H. B. 1953 Investigation of the stability of a moving liquid film. Br. J. Appl. Phys. 4, 167–169.CrossRefGoogle Scholar
Stern, S. A., Weaver, H. A., Steffl, A. J., Mutchler, M. J., Merline, W. J., Buie, M. W., Young, E. F., Young, L. A. & Spencer, J. R. 2006 A giant impact origin for Pluto's small moons and satellite multiplicity in the Kuiper belt. Nature 439, 946–948.Google Scholar
Stow, C. D. & Stainer, R. 1977 The physical products of a splashing water drop. J. Met. Soc. Japan 55 (5), 518–531.Google Scholar
Taylor, G. I. 1959 The dynamics of thin sheets of fluid. Part III. Disintegration of fluid sheets. Proc. R. Soc. Lond. 253, 313–321.Google Scholar
Taylor, G. I. 1961 A study of the behavior of a thin sheet of a moving liquid. J. Fluid Mech. 10, 305.Google Scholar
Thoroddsen, S., Etoh, T. & Takehara, K. 2006 Crown-breakup by Marangoni instability. J. Fluid Mech. 557, 63–72.CrossRefGoogle Scholar
Thoroddsen, S. & Sakakibara, J. 1998 Evolution of the fingering pattern of an impacting drop. Phys. Fluids 10 (6), 1359–1374.Google Scholar
Tomotika, S. 1936 Breaking up of drop of viscous liquid immersed in another fluid which is extending at uniform rate. Proc. R. Soc Lond. A 153, 302–318.Google Scholar
Trouton, F. T. 1906 On the coefficient of viscous traction and its relation to that of viscosity. Proc. R. Soc. Lond. 77, 426–440.Google Scholar
Tsiolkovsky, K. E. 1903 The exploration of cosmic space by means of reaction devices. Rev. Sci. Phil. Lit. 5, 1–23.Google Scholar
Ukiwe, C. & Kwok, D. Y. 2005 On the maximum spreading diameter of impacting droplets on well-prepared solid surfaces. Langmuir 21, 666–673.Google Scholar
Villermaux, E. 2007 Fragmentation. Annu. Rev. Fluid Mech. 39, 419–446.CrossRefGoogle Scholar
Villermaux, E. & Bossa, B. 2009 Single drop fragmentation determines size distribution of raindrops. Nature Phys. 5, 697–702.Google Scholar
Villermaux, E. & Clanet, C. 2002 Life of a flapping liquid sheet. J. Fluid Mech. 462, 341–363.Google Scholar
d AVinci, L. 1508 Codex Leicester. In The Notebooks of Leonardo da Vinci (ed. and trans. MacCurdy, E.). George Brazillier.Google Scholar
Watchers, L. H. J. & Westerling, N. A. J. 1966 The heat transfer from a hot wall to impinging water drops in the spheroidal sate. Chem. Engng Sci. 21, 1047–1056.Google Scholar
Worthington, A. M. 1908 A Study of Splashes. Longmans, Green.Google Scholar
Xu, L., Barcos, L. & Nagel, S. R. 2007 Splashing of liquids: interplay of surrounding gas and surface roughness. Phys. Rev. E 76, 066311.CrossRefGoogle ScholarPubMed
Yarin, A. L. 2006 Drop impact dynamics: splashing, spreading, receding, bouncing . . .. Annu. Rev. Fluid Mech. 38, 159–192.Google 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