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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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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