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‘Effervescent’ atomization in two dimensions

Published online by Cambridge University Press:  02 January 2013

H. Lhuissier  and
E. Villermaux
H. Lhuissier*
Affiliation:
Aix-Marseille Université, IRPHE, 13384 Marseille CEDEX 13, France
E. Villermaux
Affiliation:
Aix-Marseille Université, IRPHE, 13384 Marseille CEDEX 13, France
*
†Email address for correspondence: [email protected]
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Abstract

A planar Savart water sheet uniformly seeded with small air bubbles in a large surface concentration is studied as a model experiment of the so-called ‘effervescent’ atomization process. This two-dimensional setup allows for a quantitative observation of all the steps of the sheet’s disintegration into a collection of disjointed droplets. The bubbles are heterogeneous nucleation sites which puncture the sheet with holes. The dynamics of the opening of holes competes with the simultaneous nucleation rate of new holes in a statistically stationary fashion. The liquid constituting the sheet is then transiently concentrated in a web of ligaments of various lengths and diameters, at the junction between adjacent holes. Their breakup produces the final spray. We provide a complete description of the ligament web statistics when nucleation is synchronous, and we show that the drop size dispersion from the breakup of a single ligament is responsible for the shape of the overall spray drop size distribution.

JFM classification

Drops and Bubbles: Breakup/coalescence Drops and Bubbles: Drops and Bubbles Interfacial Flows (free surface): Interfacial Flows (free surface)
Type
Papers
Information
Journal of Fluid Mechanics , Volume 714 , 10 January 2013 , pp. 361 - 392
Copyright
©2013 Cambridge University Press

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Footnotes

‡

Also at Institut Universitaire de France.

References

Ashgriz, N. & Poo, J. Y. 1990 Coalescence and separation in binary collisions of liquid drops. J. Fluid Mech. 221, 183–204.Google Scholar
Avrami, M. 1939 Kinetics of phase change. Part 1. General theory. J. Chem. Phys. 7, 1103–1112.CrossRefGoogle Scholar
Avrami, M. 1940 Kinetics of phase change. Part 2. Transformation-time relations for random distribution of nuclei. J. Chem. Phys. 8, 212–224.CrossRefGoogle Scholar
Avrami, M. 1941 Kinetics of phase change. Part 3. Granulation, phase change, and microstructure. J. Chem. Phys. 9, 177–184.CrossRefGoogle Scholar
Beskow, K., Thorén, M. & Lundström, P.-A. 2009 World’s first high-capacity Granshot® iron granulation in operation at SSAB Oxelösund. AISTech 2009 Proceedings 1, 211–218.Google Scholar
Bohr, N. 1909 Determination of the surface-tension of water by the method of jet vibration. Phil. Trans. R. Soc. Lond. A 209, 281–317.Google 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.Google Scholar
Bremond, N. & Villermaux, E. 2006 Atomization by jet impact. J. Fluid Mech. 549, 273–306.CrossRefGoogle Scholar
Clanet, C. & Villermaux, E. 2002 Life of a smooth liquid sheet. J. Fluid Mech. 462, 307–340.Google Scholar
Clay, P. 1940 The mechanism of emulsion formation in turbulent flow. Part 1. Experimental part. Proc. R. Acad. Sci. (Amsterdam) 43, 852–865.Google Scholar
Couder, Y., Chomaz, J. & Rabaud, M. 1989 On the hydrodynamics of soap films. Physica D 37, 384–405.CrossRefGoogle Scholar
Culick, F. E. C. 1960 Comments on a ruptured soap film. J. Appl. Phys. 31, 1128.Google Scholar
Davies, J. T. & Rideal, E. K. 1963 Interfacial Phenomena, 2nd edn. Academic.Google 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
Einstein, A. 1906 Eine neue Bestimmung der Moleküldimensionen. Ann. Phys. 19 (4), 289–306.CrossRefGoogle Scholar
Hinze, J. 1949 Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes. AIChE J. 1, 289–295.CrossRefGoogle Scholar
Huang, J. C. P. 1970 The break-up of axisymmetric liquid sheets. J. Fluid Mech. 43, 305–319.Google Scholar
Johnson, W. A. & Mehl, R. F. 1939 Reaction kinetics in processes of nucleation and growth. Trans. AIME 135, 416–443.Google Scholar
Kolmogorov, A. 1941 The local structure of turbulence in incompressible viscous fluid for very large Reynolds’ numbers. Dokl. Akad. Nauk SSSR 30, 301.Google Scholar
Kolmogorov, A. 1949 On the breakage of drops in a turbulent flow. Dokl. Akad. Nauk SSSR 66, 825–828.Google Scholar
Lefebvre, A. H. 1989 Atomization and Sprays. Hemisphere.Google Scholar
Lide, D. R. (Ed.) 1999 Handbook of Chemistry and Physics, 79th edn. CRC.Google Scholar
Lord Rayleigh, 1878 On the instability of jets. Proc. R. Soc. Lond. A 10, 4–13.Google Scholar
Lord Rayleigh, 1890 On the tension of recently formed liquid surfaces. Proc. R. Soc. Lond. A 47, 281–287.Google Scholar
Marmottant, P. & Villermaux, E. 2004 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
Meijering, J. L. 1953 Interface area, edge length and number of vertices in crystal aggregates with random nucleation. Philips Res. Rep. 8, 270–290.Google Scholar
Nagata, S. 1975 Mixing, Principles and Applications. Wiley.Google Scholar
Qian, J. & Law, C. K. 1997 Regimes of coalescence and separation in droplet collision. J. Fluid Mech. 331, 59–80.Google Scholar
Reiter, G. 1992 Dewetting of thin polymer films. Phys. Rev. Lett. 68, 75–78.CrossRefGoogle ScholarPubMed
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
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
Santaló, L. 2004 Integral Geometry and Geometric Probability, 2nd edn. Cambridge University Press.Google Scholar
Savart, F. 1833a Mémoire sur le choc d’une veine liquide lancée contre un plan circulaire. Ann. Chim. 54, 56–87.Google Scholar
Savart, F. 1833b Suite du mémoire sur le choc d’une veine liquide lancée contre un plan circulaire. Ann. Chim. 54, 113–145.Google Scholar
Sovani, S., Sojka, P. & Lefebvre, A. 2001 Effervescent atomization. Prog. Energy Combust. Sci. 27, 483–521.Google Scholar
Taylor, G. I. 1932 The viscosity of a fluid containing small drops of another fluid. Proc. R. Soc. Lond. A 138, 41–48.Google Scholar
Taylor, G. I. 1959 The dynamics of thin sheets of fluid. Part 1. Water bells. Proc. R. Soc. Lond. A 253, 289–295.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
Thoroddsen, S. T., Etoh, T. G. & Takehara, K. 2006 Crown breakup by Marangoni instability. J. Fluid Mech. 557, 63–72.CrossRefGoogle Scholar
Villermaux, E. & Bossa, B. 2011 Drop fragmentation on impact. J. Fluid Mech. 668, 412–435.Google Scholar
Villermaux, E. & Clanet, C. 2002 Life of a flapping liquid sheet. J. Fluid Mech. 462, 342–363.CrossRefGoogle Scholar
Villermaux, E., Marmottant, P. & Duplat, J. 2004 Ligament-mediated spray formation. Phys. Rev. Lett. 92 (7).Google Scholar
Worthington, A. M. & Cole, R. S. 1897 Impact with a liquid surface, studied by the aid of instantaneous photography. Phil. Trans. R. Soc. Lond. A 189, 149–166.Google Scholar
Yule, A. J. & Dunkley, J. J. 1994 Atomization of Melts. Clarendon.Google Scholar