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Air trapping at impact of a rigid sphere onto a liquid

Published online by Cambridge University Press:  14 February 2012

P. D. Hicks ,
E. V. Ermanyuk ,
N. V. Gavrilov  and
R. Purvis
P. D. Hicks*
Affiliation:
School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK
E. V. Ermanyuk
Affiliation:
Lavrentyev Institute of Hydrodynamics, av. Lavrentyev 15, 630090 Novosibirsk, Russia Novosibirsk State University, str. Pirogova 2, 630090 Novosibirsk, Russia
N. V. Gavrilov
Affiliation:
Lavrentyev Institute of Hydrodynamics, av. Lavrentyev 15, 630090 Novosibirsk, Russia
R. Purvis
Affiliation:
School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK
*
†Email address for correspondence: [email protected]
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Abstract

An experimental and theoretical investigation of the air trapping by a blunt, locally spherical body impacting onto the free surface of water is conducted. In the parameter regime previously studied theoretically by Hicks & Purvis (J. Fluid Mech., vol. 649, 2010, pp. 135–163), excellent agreement between experimental data and theoretical modelling is obtained. Earlier predictions of the radius of the trapped air pocket are confirmed. A boundary element method is used to consider air cushioning of an impact of an axisymmetric body into water. Efficient computational methods are obtained by analytically integrating the boundary integral equation over the azimuthal variable. The resulting numerically computed free-surface profiles predict an annular touchdown region in excellent agreement with the experiments.

JFM classification

Drops and Bubbles: Bubble dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 695 , 25 March 2012 , pp. 310 - 320
Copyright
Copyright © Cambridge University Press 2012

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References

1. Birkhoff, G. 1960 Hydrodynamics: A Study in Logic, Fact and Similitude. Princeton University Press.Google Scholar
2. Chuang, S.-L. 1966 Experiments on flat-bottom slamming. J. Ship Res. 10, 10–17.CrossRefGoogle Scholar
3. Cook, S. S. 1928 Erosion by water-hammer. Proc. R. Soc. Lond. A 119 (783), 481–488.Google Scholar
4. Fujita, Y. 1954 On the impulsive pressure of circular plate falling upon a water-surface. J. Zosen Kiokai 94, 105–110.CrossRefGoogle Scholar
5. Gradshteyn, I. S. & Ryzhik, I. M. 2000 Table of Integrals, Series, and Products. Academic.Google Scholar
6. Herman, J. & Mesler, R. 1987 Bubble entrainment from bursting bubbles. J. Colloid Interface Sci. 117 (2), 565–569.CrossRefGoogle Scholar
7. Hicks, P. D. & Purvis, R. 2010 Air cushioning and bubble entrapment in three-dimensional droplet impacts. J. Fluid Mech. 649, 135–163.CrossRefGoogle Scholar
8. Hicks, P. D. & Purvis, R. 2011 Air cushioning in droplet impacts with liquid layers and other droplets. Phys. Fluids 23 (6), 062104.Google Scholar
9. Korobkin, A. A., Ellis, A. S. & Smith, F. T. 2008 Trapping of air in impact between a body and shallow water. J. Fluid Mech. 611, 365–394.CrossRefGoogle Scholar
10. Krechetnikov, R. 2011 A linear stability theory on time-invariant and time-dependent spatial domains with symmetry: the drop splash problem. Dyn. PDE 8 (1), 47–67.Google Scholar
11. Krechetnikov, R. & Homsy, G. M. 2009 Crown-forming instability phenomena in the drop splash problem. J. Colloid Interface Sci. 331 (2), 555–559.CrossRefGoogle ScholarPubMed
12. Lesser, M. B. & Field, J. E. 1983 The impact of compressible liquids. Annu. Rev. Fluid Mech. 15, 97–122.CrossRefGoogle Scholar
13. Mandre, S., Mani, M. & Brenner, M. P. 2009 Precursors to splashing of liquid droplets on a solid surface. Phys. Rev. Lett. 102 (13), 134502.CrossRefGoogle ScholarPubMed
14. Mani, M., Mandre, S. & Brenner, M. P. 2010 Events before droplet splashing on a solid surface. J. Fluid Mech. 647, 163–185.CrossRefGoogle Scholar
15. Purvis, R. & Smith, F. T. 2004 Air–water interactions near droplet impact. Eur. J. Appl. Maths 15, 853–871.CrossRefGoogle Scholar
16. Shelley, M. J., Tian, F.-R. & Wlodarski, K. 1997 Hele-Shaw flow and pattern formation in a time-dependent gap. Nonlinearity 10, 1471–1495.CrossRefGoogle Scholar
17. Smith, F. T., Li, L. & Wu, G. X. 2003 Air cushioning with a lubrication/inviscid balance. J. Fluid Mech. 482, 291–318.CrossRefGoogle Scholar
18. Smith, F. T., Ovenden, N. C. & Purvis, R. 2006Industrial and biomedical applications. In One Hundred Years of Boundary Layer Research (ed. G. E. A. Meier, K. R. Sreenivasan & H.-J. Heinemann), Proceedings of IUTAM Symposium, Göttingen, Germany, pp. 291–300. Springer.Google Scholar
19. Taylor, G. I. & Saffman, P. G. 1957 Effects of compressibility at low Reynolds number. J. Aeronaut. Sci. 24, 553–562.CrossRefGoogle Scholar
20. Thoroddsen, S. T., Etoh, T. G. & Takehara, K. 2003 Air entrapment under an impacting drop. J. Fluid Mech. 478, 125–134.CrossRefGoogle Scholar
21. Thoroddsen, S. T., Etoh, T. G., Takehara, K., Ootsuka, N. & Hatsuki, Y. 2005 The air bubble entrapped under a drop impacting on a solid surface. J. Fluid Mech. 545, 203–212.CrossRefGoogle Scholar
22. Verhagen, J. H. G. 1967 The impact of a flat plate on a water surface. J. Ship Res. 11, 211–223.CrossRefGoogle Scholar