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Bursting bubble aerosols

Published online by Cambridge University Press:  18 November 2011

H. Lhuissier
Affiliation:
Aix-Marseille Université, IRPHE, 13384 Marseille CEDEX 13, France
E. Villermaux*
Affiliation:
Aix-Marseille Université, IRPHE, 13384 Marseille CEDEX 13, France Institut Universitaire de France, 75005 Paris, France
*
Email address for correspondence: [email protected]

Abstract

We depict and analyse the complete evolution of an air bubble formed in a water bulk, from the time it emerges at the liquid surface, up to its fragmentation into dispersed drops. To this end, experiments describing the drainage of the bubble cap film, its puncture and the resulting bursting dynamics determining the aerosol formation are conducted on tapwater bubbles. We discover that the mechanism of marginal pinching at the bubble foot and associated convection motions in the bubble cap, known as marginal regeneration, both drive the bubble cap drainage rate, and are responsible for its puncture. The resulting original film thickness evolution law in time, supplemented with considerations about the nucleation of holes piercing the film together culminate in a determination of the cap film thickness at bursting , where is the bubble cap radius of curvature, and a length which we determine. Subsequent to a hole nucleation event, the cap bursting dynamics conditions the resulting spray. The latter depends both on the bubble shape prescribed by , where is the capillary length based on gravity, and on . The mean drop size , the number of drops generated per bubble and the drop size distribution are derived, comparing well with measurements. Combined with known bubble production rates over the ocean, our findings offer an adjustable parameter-free prediction for the aerosol flux and spray structure caused by bubble bursting in this precise context.

Type
Papers
Copyright
Copyright © Cambridge University Press 2011

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References

1. Aitken, J. 1881 Dust, fog, and clouds. Nature 23, 384385.CrossRefGoogle Scholar
2. Amarouchene, Y. & Kellay, H. 2004 Batchelor scaling in fast-flowing soap films. Phys. Rev. Lett. 93 (21), 214504.CrossRefGoogle ScholarPubMed
3. Andreas, E. L., Edson, J. B., Monahan, E. C., Rouault, M. P. & Smith, S. D. 1995 The spray contribution to net evaporation from the sea: a review of recent progress. Boundary-Layer Meteorol. 72, 352.CrossRefGoogle Scholar
4. Aradian, A., Raphaël, E. & de Gennes, P. G. 2001 Marginal pinching in soap films. Europhys. Lett. 55 (6), 834840.CrossRefGoogle Scholar
5. Barger, W. R., Daniel, W. H. & Garrett, W. D. 1974 Surface chemical properties of banded sea slicks. Deep-Sea Res. (I) 21, 8389.Google Scholar
6. Bird, J. C., de Ruiter, R., Courbin, L. & Stone, H. A. 2010 Daughter bubble cascade produced by folding of ruptured thin films. Nature 465, 759762.CrossRefGoogle ScholarPubMed
7. Blanchard, D. 1963 The electrification of the atmosphere by particles from bubbles in the sea. PhD thesis, Woods Hole Oceanographic Institution.CrossRefGoogle Scholar
8. Blanchard, D. C., Bilofsky, H. S. & Bridgman, W. B. 1972 The effervescence of ocean surf. J. Chem. Educ. 49 (1), 2930.Google Scholar
9. Blanchard, D. C. & Sysdek, L. D. 1988 Film drop production as a function of bubble size. J. Geophys. Res. 93 (C4), 36493654.CrossRefGoogle Scholar
10. Bouchiat, M. & Meunier, J. 1971 Spectre des fluctuations thermiques de la surface libre d’un liquide simple. J. Phys. 32, 561571.CrossRefGoogle Scholar
11. Breward, C. J. & Howell, P. D. 2002 The drainage of a foam lamella. J. Fluid Mech. 458, 379406.Google Scholar
12. Bruinsma, R. 1995 Theory of hydrodynamic convection in soap films. Physica A 213, 5976.CrossRefGoogle Scholar
13. Bull, L. 1904 Rupture d’un film de savon par un projectile. Environ 1500 images/seconde. Stereoscopic Movie – Institut E.-J. Marey.Google Scholar
14. 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 (4).CrossRefGoogle ScholarPubMed
15. Coantic, M. 1980 Mass transfert across the ocean–air interface: small scale hydrodynamic and aerodynamic mechanisms. Physico-Chem. Hydrodyn. 1, 249279.Google Scholar
16. Couder, Y., Fort, E., Gautier, C. H. & Boudaoud, A. 2005 From bouncing to floating: noncoalescence of drops on a fluid bath. Phys. Rev. Lett. 94 (4), 177801.CrossRefGoogle ScholarPubMed
17. Culick, F. E. C. 1960 Comments on a ruptured soap film. J. Appl. Phys. 31, 1128.CrossRefGoogle Scholar
18. Deane, G. B. & Stokes, D. 2002 Scale dependence of bubble creation mechanisms in breaking waves. Nature 418, 839844.CrossRefGoogle ScholarPubMed
19. Debrégeas, G., de Gennes, P. G. & Brochard-Wyart, F. 1998 The life and death of ‘bare’ viscous bubbles. Science 279, 17041707.CrossRefGoogle Scholar
20. Dupré, A. 1869 Théorie Mécanique de la Chaleur. Gauthiers-Villars.Google Scholar
21. Eggers, J. & Villermaux, E. 2008 Physics of liquid jets. Rep. Prog. Phys. 71, 36601.CrossRefGoogle Scholar
22. Faraday, M. 1861 A Course of Six Lectures on the Chemical History of a Candle. Royal Society (Copyright 1988 Chicago Review Press).Google Scholar
23. de Gennes, P. G. 2001 Young soap films. Langmuir 17, 24162419.CrossRefGoogle Scholar
24. Hagen, G. 1846 Über die oberfläche der flüssigkeiten. Ann. Poggendorff 67 (1), 152.Google Scholar
25. Howell, P. D. 1999 The draining of a two dimensional bubble. J. Engng Maths 35, 251272.CrossRefGoogle Scholar
26. Jacobs, W. C. 1937 Preliminary reports on the study of atmospheric chlorides. Mon. Weath. Rev. 65, 147151.2.0.CO;2>CrossRefGoogle Scholar
27. Jarvis, N. L., Garrett, W. D., Scheiman, M. A. & Timmons, C. O. 1967 Surface chemical characterization of surface-active material in seawater. Limnol. Oceanogr. 12, 8896.CrossRefGoogle Scholar
28. Kellay, H., Wu, X. L. & Goldburg, W. I. 1995 Experiments with turbulent soap films. Phys. Rev. Lett. 74 (20), 3975 4.CrossRefGoogle ScholarPubMed
29. Knelman, F. H., Dombrowski, N. & Newitt, D. M. 1954 Mechanism of the bursting of bubbles. Nature 173, 261.CrossRefGoogle Scholar
30. Kraichnan, R. 1967 Inertial ranges in two-dimensional turbulence. Phys. Fluids 10, 14171423.CrossRefGoogle Scholar
31. Latham, J. & Smith, M. H. 1990 Effect on global warming of wind-dependent aerosol generation at the ocean surface. Nature 347, 372373.CrossRefGoogle Scholar
32. Lhuissier, H. & Villermaux, E. 2009 Bursting bubbles. Phys. Fluids 21, 091111.CrossRefGoogle Scholar
33. Lide, D. R.  (Ed.) 1999 Handbook of Chemistry and Physics, 79th edn CRC.Google Scholar
34. Marangoni, C. & Stefanelli, P. 1872 Monografia sulle bolle liquide. Nuovo Cimento 7-8 (1), 301–356.Google Scholar
35. Maris, H. J. 2006 Introduction to the physics of nucleation. C. R. Phys. 7, 946958.CrossRefGoogle Scholar
36. Meunier, P. & Leweke, T. 2003 Analysis and minimization of errors due to high gradients in particle image velocimetry. Exp. Fluids 35, 408421.CrossRefGoogle Scholar
37. Monahan, E. C. & Dam, H. G. 2001 Bubbles: an estimate of their role in the global oceanic flux. J. Geophys. Res. 106, 93779383.CrossRefGoogle Scholar
38. Mysels, K. J., Shinoda, K. & Frankel, S. 1959 Soap Films, Studies of their Thinning and a Bibliography. Pergamon.Google Scholar
39. Newitt, D. M., Dombrowski, N. & Knelman, F. H. 1954 Liquid entrainment. 1. The mechanism of drop formation from gas or vapour bubbles. Trans. Inst. Chem. Engrs 32, 244261.Google Scholar
40. Nierstrasz, V. A. & Frens, G. 1998 Marginal regeneration in thin vertical liquid films. J. Colloid Interface Sci. 207, 209217.CrossRefGoogle ScholarPubMed
41. O’Dowd, C. & de Leeuw, G. 2007 Marine aerosol production: a review of the current knowledge. Phil. Trans. R. Soc. Lond. A 365, 17531774.Google ScholarPubMed
42. Plateau, J. 1873 Satique expérimentale et théorique des liquides soumis aux seules forces moléculaires. Ghauthier-Villard.Google Scholar
43. Preobrazhenskii, L. 1973 Estimate of the content of spray-drops in the near-water layer of the atmosphere. Fluid Mech. -Sov. Res. 2, 95100.Google Scholar
44. Resch, F. & Afeti, G. 1991 Film drop distribution from bubbles bursting in seawater. J. Geophys. Res. 96 (C6), 1068110688.CrossRefGoogle Scholar
45. Schwartz, L. W. & Roy, R. V. 1999 Modelling draining flow in mobile and immobile soap films. J. Colloid Interface Sci. 218, 309323.Google Scholar
46. Spiel, D. E. 1998 On the birth of film drops from bubbles bursting on seawater surfaces. J. Geophys. Res. 103 (C11), 2490724918.CrossRefGoogle Scholar
47. Taylor, G. I. 1959 The dynamics of thin sheets of fluid III. desintegration of fluid sheets. Proc. R. Soc. Lond. A 253, 313321.Google Scholar
48. Toba, Y. 1959 Drop production by bursting of air bubbles on the sea surface. ii theoretical study on the shape of floating bubbles. J. Oceanogr. Soc. Japan 15, 121130.CrossRefGoogle Scholar
49. Van Kampen, N. G. 1981 Stochastic Processes in Chemistry and Physics. North-Holland.Google Scholar
50. Villermaux, E. 2007 Fragmentation. Annu. Rev. Fluid Mech. 39, 419446.CrossRefGoogle Scholar
51. Villermaux, E., Marmottant, P. & Duplat, J. 2004 Ligament-mediated spray formation. Phys. Rev. Lett. 92 (7).CrossRefGoogle ScholarPubMed
52. Worthington, A. M. & Cole, R. S. 1897 Impact with a liquid surface, studied by the aid of instantaneaous photography. Phil. Trans. R. Soc. Lond. A 189, 149166.Google Scholar
53. Wu, J., Murray, J. & Lai, R. 1984 Production and distributions of sea spray. J. Geophys. Res. 89 (C5), 81638169.Google Scholar
54. Xia, H., Shats, M. & Falkovich, G. 2009 Spectrally condensed turbulence in thin layers. Phys. Fluids 21, 125101.CrossRefGoogle Scholar
55. Zheng, Q. A., Klemas, V. & Hsu, Y.-H. L. 1983 Laboratory measurements of water surface bubble life time. J. Geophys. Res. 88, 701706.Google Scholar