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On the scaling of jetting from bubble collapse at a liquid surface

Published online by Cambridge University Press:  08 June 2017

Sangeeth Krishnan ,
E. J. Hopfinger  and
Baburaj A. Puthenveettil Open the ORCID record for Baburaj A. Puthenveettil [Opens in a new window]
Sangeeth Krishnan
Affiliation:
Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai - 600 036, India
E. J. Hopfinger
Affiliation:
LEGI-CNRS, BP 53, 38041 Grenoble CEDEX 9, France
Baburaj A. Puthenveettil*
Affiliation:
Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai - 600 036, India
*
†Email address for correspondence: [email protected]
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Abstract

We present scaling laws for the jet velocity resulting from bubble collapse at a liquid surface which bring out the effects of gravity and viscosity. The present experiments conducted in the range of Bond numbers $0.004<Bo<2.5$ and Ohnesorge numbers $0.001<Oh<0.1$ were motivated by the discrepancy between previous experimental results and numerical simulations. We show here that the actual dependence of $We$ on $Bo$ is determined by the gravity dependency of the bubble immersion (cavity) depth which has no power-law variation. The power-law variation of the jet Weber number, $We\sim 1/\sqrt{Bo}$, suggested by Ghabache et al. (Phys. Fluids, vol. 26 (12), 2014, 121701) is only a good approximation in a limited range of $Bo$ values ($0.1<Bo<1$). Viscosity enters the jet velocity scaling in two ways: (i) through damping of precursor capillary waves which merge at the bubble base and weaken the pressure impulse, and (ii) through direct viscous damping of the jet formation and dynamics. These damping processes are expressed by a dependence of the jet velocity on Ohnesorge number from which critical values of $Oh$ are obtained for capillary wave damping, the onset of jet weakening, the absence of jetting and the absence of jet breakup into droplets.

JFM classification

Drops and Bubbles: Breakup/coalescence Drops and Bubbles: Drops and Bubbles Wakes/Jets: Jets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 822 , 10 July 2017 , pp. 791 - 812
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Copyright
© 2017 Cambridge University Press 

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References

Blanchard, D. C. 1963 The electrification of the atmosphere by particles from bubbles in the sea. Prog. Oceanogr. 1, 73IN7113–112202.Google Scholar
Boulton-Stone, J. M. & Blake, J. R. 1993 Gas bubbles bursting at a free surface. J. Fluid Mech. 254, 437–466.CrossRefGoogle Scholar
Clanet, C. & Lasheras, J. C. 1999 Transition from dripping to jetting. J. Fluid Mech. 383, 307–326.Google Scholar
Das, S. P. & Hopfinger, E. J. 2008 Parametrically forced gravity waves in a circular cylinder and finite-time singularity. J. Fluid Mech. 599, 205–228.Google Scholar
Doshi, P., Cohen, I., Zhang, W. W., Siegel, M., Howell, P., Basaran, O. A. & Nagel, S. R. 2003 Persistence of memory in drop breakup: the breakdown of universality. Science 302 (5648), 1185–1188.Google Scholar
Duchemin, L., Popinet, S., Josserand, C. & Zaleski, S. 2002 Jet formation in bubbles bursting at a free surface. Phys. Fluids 14 (9), 3000–3008.CrossRefGoogle Scholar
Feng, J., Roché, M., Vigolo, D., Arnaudov, L. N., Stoyanov, S. D., Gurkov, T. D., Tsutsumanova, G. G. & Stone, H. A. 2014 Nanoemulsions obtained via bubble-bursting at a compound interface. Nat. Phys. 10 (8), 606–612.CrossRefGoogle Scholar
Ghabache, E., Antkowiak, A., Josserand, C. & Séon, T. 2014 On the physics of fizziness: How bubble bursting controls droplets ejection. Phys. Fluids 26 (12), 121701.CrossRefGoogle Scholar
Joung, Y. S. & Buie, C. R. 2015 Aerosol generation by raindrop impact on soil. Nat. Commun. 6, 6083.CrossRefGoogle ScholarPubMed
Kientzler, C. F., Arons, A. B., Blanchard, D. C. & Woodcock, A. H. 1954 Photographic investigation of the projection of droplets by bubbles bursting at a water surface 1. Tellus 6 (1), 1–7.Google Scholar
Krishnan, S. & Puthenveettil, B. A. 2015 Dynamics of collapse of free surface bubbles. Proc. IUTAM 15, 207–214.Google Scholar
Krishnan, S., Puthenveettil, B. A. & Hopfinger, E. J. 2012 Jet formation from bubble collapse at a free surface. In Proceedings of the 23rd International Congress of Theoretical and Applied Mechanics, Beijing (ed. Bai, Y., Wang, J. & Fang, D.), p. 171.Google Scholar
Lhuissier, H. & Villermaux, E. 2012 Bursting bubble aerosols. J. Fluid Mech. 696, 5–44.CrossRefGoogle Scholar
Liger-Belair, G., Seon, T. & Antkowiak, A. 2012 Collection of collapsing bubble driven phenomena found in champagne glasses. Bubble Sci. Engng Technol. 4 (1), 21–34.CrossRefGoogle Scholar
MacIntyre, F. 1972 Flow patterns in breaking bubbles. J. Geophys. Res. 77 (27), 5211–5228.Google Scholar
Oguz, H. N. & Prosperetti, A. 1993 Dynamics of bubble growth and detachment from a needle. J. Fluid Mech. 257, 111–145.Google Scholar
Perlin, M., Lin, H. & Ting, C.-L. 1993 On parasitic capillary waves generated by steep gravity waves: an experimental investigation with spatial and temporal measurements. J. Fluid Mech. 255, 597–620.CrossRefGoogle Scholar
San Lee, J., Weon, B. M., Park, S. J., Je, J. H., Fezzaa, K. & Lee, W.-K. 2011 Size limits the formation of liquid jets during bubble bursting. Nat. Commun. 2, 367.Google Scholar
Shakhova, N., Semiletov, I., Leifer, I., Sergienko, V., Salyuk, A., Kosmach, D., Chernykh, D., Stubbs, C., Nicolsky, D., Tumskoy, V. et al. 2014 Ebullition and storm-induced methane release from the east siberian arctic shelf. Nat. Geosci. 7 (1), 64–70.Google Scholar
Spiel, D. E. 1995 On the births of jet drops from bubbles bursting on water surfaces. J. Geophys. Res. 100 (C3), 4995–5006.Google Scholar
Walls, P. L. L., Henaux, L. & Bird, J. C. 2015 Jet drops from bursting bubbles: How gravity and viscosity couple to inhibit droplet production. Phys. Rev. E 92, 021002.Google ScholarPubMed
Woodcock, A. H., Kientzler, C. F., Arons, A. B. & Blanchard, D. C. 1953 Giant condensation nuclei from bursting bubbles. Nature 172, 1144–1145.Google Scholar
Zeff, B. W., Kleber, B., Fineberg, J. & Lathrop, D. P. 2000 Singularity dynamics in curvature collapse and jet eruption on a fluid surface. Nature 403 (6768), 401–404.Google Scholar
Zhang, F. H., Thoraval, M.-J., Thoroddsen, S. T. & Taborek, P. 2015 Partial coalescence from bubbles to drops. J. Fluid Mech. 782, 209–239.CrossRefGoogle Scholar
Zhang, F. H. & Thoroddsen, S. T. 2008 Satellite generation during bubble coalescence. Phys. Fluids 20 (2), 022104.CrossRefGoogle Scholar

Krishnan et al. supplementary movie

Bursting of a bubble of radius R=2.15 mm at the free surface of water resulting in vertical jet. Images are captured at 4000 fps. The movie is playing at 3 fps.

Download Krishnan et al. supplementary movie(Video)
Video 2.3 MB