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‘Fines’ from the collision of liquid rims

Published online by Cambridge University Press:  22 April 2020

B. Néel Open the ORCID record for B. Néel [Opens in a new window] ,
H. Lhuissier Open the ORCID record for H. Lhuissier [Opens in a new window]  and
E. Villermaux Open the ORCID record for E. Villermaux [Opens in a new window]
B. Néel
Affiliation:
Aix-Marseille Université, CNRS, Centrale Marseille, IRPHE, Marseille, France
H. Lhuissier
Affiliation:
IUSTI, CNRS, Aix-Marseille Université, 13453Marseille, France
E. 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
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Abstract

Fines are smaller droplets produced from an auxiliary mechanism besides the formation of the standard drops in a fragmentation process. We report their formation in a controlled experiment which isolates an individual fragmentation protocol: the collision of two rims bordering growing adjacent holes on a liquid sheet. The standard drops come from the capillary breakup of the fused rims. Occasionally, the rims collision is strong enough to trigger a new, splash-like mechanism, producing an expanding lamellae perpendicular to the main sheet, which destabilizes into finer drops. We quantify the threshold condition for the onset of this mechanism first discovered by Lhuissier & Villermaux (J. Fluid Mech., vol. 714, 2013, pp. 361–392), we document the resulting lamellae dynamics and explain why it affects the mean drop size in the spray, broadening substantially the overall drop size distribution, which we determine. Possible applications of these findings are mentioned.

JFM classification

Interfacial Flows (free surface): Thin films
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 893 , 25 June 2020 , A16
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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Footnotes

The original version of this article was published with incorrect author information. A notice detailing this has been published and the error rectified in the online PDF and HTML copies.

References

Abramowitz, M. & Stegun, I. A. 1964 Handbook of Mathematical Functions. Dover Publications, Inc.Google 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.CrossRefGoogle Scholar
Antkowiak, A., Bremond, N., Dizès, S. L. & Villermaux, E. 2007 Short-term dynamics of a density interface following impact. J. Fluid Mech. 577, 241–250.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
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
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. 1953 Giant condensation nuclei from bursting bubbles. Nature 172 (4390), 1144–1145.Google Scholar
Bradley, S. G. & Stow, C. D. 1978 Collisions between liquid drops. Phil. Trans. R. Soc. Lond. A 287 (1349), 635–675.Google Scholar
Bremond, N., Clanet, C. & Villermaux, E. 2007 Atomization of undulating liquid sheets. J. Fluid Mech. 585, 421–456.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
Cointe, R. & Armand, J.-L. 1987 Hydrodynamic impact analysis of a cylinder. Trans. ASME J. Offshore Mech. Arctic Engng 109 (3), 237–243.CrossRefGoogle Scholar
Cooker, M. J. & Peregrine, D. H. 1995 Pressure-impulse theory for liquid impact problems. J. Fluid Mech. 297, 193–214.CrossRefGoogle Scholar
Culick, F. E. C. 1960 Comments on a ruptured soap film. J. Appl. Phys. 31, 1128–1129.CrossRefGoogle Scholar
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 aerodynamic instability and disintegration of viscous liquid sheets. Chem. Engng Sci. 18, 203–214.CrossRefGoogle Scholar
Eggers, J. & Villermaux, E. 2008 Physics of liquid jets. Rep. Prog. Phys. 71, 36601.Google Scholar
Eisenklam, P. 1964 On ligament formation from spinning discs and cups. AIChE J. 19 (9), 693–694.Google Scholar
Fraser, R. P., Dombrowski, N. & Routley, J. H. 1963 The filming of liquids by spinning cups. Chem. Engng Sci. 18, 323–337.CrossRefGoogle Scholar
Fraser, R. P., Eisenklam, P., Dombrowski, N. & Hasson, D. 1962 Drop formation from rapidly moving liquid sheet. AIChE J. 8, 672–680.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
Ghabache, E. & Séon, T. 2016 Size of the top jet drop produced by bubble bursting. Phys. Rev. F 1 (5), 051901(R).Google Scholar
Gordillo, J. M., Lhuissier, H. & Villermaux, E. 2014 On the cusps bordering liquid sheets. J. Fluid Mech. 754 (R1), 1–11.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
Hewitt, A. J. 2000 Spray drift: impact of requirements to protect the environment. Crop Protection 19, 623–627.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
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
Ingold, C. T. 1971 Fungal Spores: Their Liberation and Dispersal. Clarendon Press-Oxford.Google Scholar
Josserand, C. & Thoroddsen, S. T. 2016 Drop impact on a solid surface. Annu. Rev. Fluid Mech. 48 (1), 365–391.CrossRefGoogle Scholar
Kooij, S., Astefanei, A., Corthals, G. L. & Bonn, D. 2019 Size distributions of droplets produced by ultrasonic nebulizers. Sci. Rep. 9, 6128.Google 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
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
Lefebvre, A. H. 1989 Atomization and Sprays. Hemisphere.Google Scholar
Lejeune, S. & Gilet, T. 2019 Drop impact close to the edge of an inclined substrate: liquid sheet formation and breakup. Phys. Rev. F 4, 053601.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.CrossRefGoogle ScholarPubMed
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. 2013 ‘Effervescent’ atomization in two dimensions. J. Fluid Mech. 714, 361–392.CrossRefGoogle 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
Néel, B. & Villermaux, E. 2018 The spontaneous puncture of thick liquid films. J. Fluid Mech. 838, 192–221.CrossRefGoogle Scholar
Oliveira, M. & McKinley, G. 2005 Iterated stretching and multiple beads-on-a-string phenomena in dilute solutions of high extensible flexible polymers. Phys. Fluids 17, 071704.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
Planchette, C., Hinterbichler, H., Liu, M., Bothe, D. & Brenn, G. 2017 Colliding drops as coalescing and fragmenting liquid springs. J. Fluid Mech. 814, 277–300.CrossRefGoogle Scholar
Plateau, J. 1873 Satique expérimentale et théorique des liquides soumis aux seules forces moléculaires. Ghauthier-Villard.Google Scholar
Rayleigh, L. 1879 On the capillary phenomena of jets. Proc. R. Soc. Lond. 29, 71–97.Google 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
Roisman, I. V. 2004 Dynamics of inertia dominated binary drop collisions. Phys. Fluids 16 (9), 3438–3449.CrossRefGoogle Scholar
Savart, F. 1833 Mémoire sur le Choc d’une Veine liquide lancée contre un plan circulaire. Ann. Chim. Phys. 54, 55–87.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
Taylor, G. I. 1959 The dynamics of thin sheets of fluid. III. Disintegration of fluid sheets. Proc. R. Soc. Lond. A 253, 313–321.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., Takehara, K. & Etoh, T. G. 2012 Microsplashing by drop impacts. J. Fluid Mech. 706, 560–570.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
Vernay, C., Ramos, L. & Ligoure, C. 2015 Bursting of dilute emulsion-based liquid sheets driven by a marangoni effect. Phys. Rev. Lett. 115, 198302.CrossRefGoogle ScholarPubMed
Villermaux, E. & Bossa, B. 2009 Single-drop fragmentation determines size distribution of raindrops. Nat. Phys. 5 (9), 697–702.CrossRefGoogle Scholar
Villermaux, E. & Bossa, B. 2011 Drop fragmentation on impact. J. Fluid Mech. 668, 412–435.CrossRefGoogle Scholar
Villermaux, E., Pistre, V. & Lhuissier, H. 2013 The viscous Savart sheet. J. Fluid Mech. 730, 607–625.CrossRefGoogle Scholar
Vledouts, A., Quinard, J., Vandenberghe, N. & Villermaux, E. 2016 Explosive fragmentation of liquid shells. J. Fluid Mech. 788, 246–273.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. 2018 Unsteady sheet fragmentation: droplet sizes and speeds. J. Fluid Mech. 848, 946–967.CrossRefGoogle Scholar
Wells, F. W. 1955 Airborne Contagion and Air Hygiene. Harvard University Press.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 spiralling liquid jets. Intl J. Multiphase Flow 30, 499–520.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
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