11–13 May 2016, Grenoble, France
On the scaling of jetting from bubble collapse at a liquid surface
Sangeeth Krishnan  1@  , Emil Hopfinger  2@  , Baburaj Puthenveettil  1, *@  
1 : Indian Institute of Technology Madras  (IIT Madras)  -  Website
Fluid Mechanics Laboratory, Dept of Applied Mechanics, IIT Madras, Chennai -  India
2 : Laboratoire des écoulements géophysiques et industriels  (LEGI)  -  Website
Université Grenoble Alpes, CNRS : UMR5519
1209–1211 Rue de la piscine - BP 53 38041 GRENOBLE CEDEX 9 -  France
* : Corresponding author

We present a scaling law for the jet velocity from bubble collapse at a liquid surface which brings out the effects of gravity and viscosity. The present experiments in the range of Bond numbers $0.02 < \mathit{Bo} < 2.5$ and Ohnesorge numbers $0.001 < \mathit{Oh} < 0.1$ were motivated by the discrepancy between previous experimental results and numerical simulations. We show here that power law variation of the jet Weber number, $\mathit{We} \sim 1/\sqrt{Bo}$ suggested by Ghabache et al.\ (2014) is only a good approximation in a limited range of $\mathit{Bo}$ values; there is no power law dependency of the jet velocity on $\mathit{Bo}$. The actual dependence of $\mathit{We}$ on $\mathit{Bo}$ is here shown to be identical to that of the square of the dimensionless cavity depth on $\mathit{Bo}$. Viscosity enters the jet velocity scaling in two ways: (a)~through damping of the parasitic capillary waves which merge at the bubble base and weaken the pressure impulse, and (b)~through direct viscous damping of the jet formation and the bubble collapse. These damping processes are expressed by a dependence of the jet velocity on $\mathit{Oh}$, from which critical values of $\mathit{Oh}$ are given for the onset of jet weakening, the absence of jetting and the absence of jet breakup into droplets.



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