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Liquid jet eruption from hollow relaxation

Published online by Cambridge University Press:  18 November 2014

Élisabeth Ghabache ,
Thomas Séon  and
Arnaud Antkowiak
Élisabeth Ghabache
Affiliation:
Sorbonne Universités, UPMC Univ Paris 06, CNRS, UMR 7190 Institut Jean Le Rond d’Alembert, F-75005 Paris, France
Thomas Séon*
Affiliation:
Sorbonne Universités, UPMC Univ Paris 06, CNRS, UMR 7190 Institut Jean Le Rond d’Alembert, F-75005 Paris, France
Arnaud Antkowiak
Affiliation:
Sorbonne Universités, UPMC Univ Paris 06, CNRS, UMR 7190 Institut Jean Le Rond d’Alembert, F-75005 Paris, France
*
†Email address for correspondence: [email protected]
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Abstract

Using a model experiment, we explore the dynamics of inertial liquid jets arising from a gravitational cavity collapse. The focus of the study is to elucidate the link between both the dynamical and kinematical properties of the jet and the initial cavity geometry, for a wide range of physical parameters. We demonstrate that the jets exhibit shape similarity and reveal a robust relationship between the jet tip velocity and the initial cavity geometry, regardless of the details of the collapse process. We argue that this relation reflects a flow focusing mechanism, and we propose a simple model capturing the key features of the erupting jet velocity scaling. Finally, the relevance of these results to other jets occurring in e.g. large bubble detachment or wave impact on walls is discussed.

JFM classification

Drops and Bubbles: Drops and Bubbles Interfacial Flows (free surface): Interfacial Flows (free surface)
Type
Papers
Information
Journal of Fluid Mechanics , Volume 761 , 25 December 2014 , pp. 206 - 219
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Copyright
© 2014 Cambridge University Press 

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References

Antkowiak, A., Bremond, N., Le Dizès, S. & Villermaux, E. 2007 Short-term dynamics of a density interface following an impact. J. Fluid Mech. 577, 241–250.Google Scholar
Banks, R. B. & Chandrasekhara, D. V. 1963 Experimental investigation of the penetration of a high-velocity gas jet through a liquid surface. J. Fluid Mech. 15, 13–34.CrossRefGoogle Scholar
Barenblatt, G. I. 2003 Scaling. Cambridge University Press.CrossRefGoogle Scholar
Barton, M. E. & Edwards, M. C. 1968 Model experiments of soil erosion by VTOL aircraft downwash impingement. J. Terramech. 5 (2), 45–51.CrossRefGoogle Scholar
Benusiglio, A., Quéré, D. & Clanet, C. 2014 Explosions at the water surface. J. Fluid Mech. 752, 123–139.CrossRefGoogle Scholar
Bisighini, A., Cossali, G. E., Tropea, C. & Roisman, I. V. 2010 Crater evolution after the impact of a drop onto a semi-infinite liquid target. Phys. Rev. E 82, 036319.CrossRefGoogle ScholarPubMed
Cheslak, F. R., Nicholls, J. A. & Sichel, M. 1969 Cavities formed on liquid surfaces by impinging gaseous jets. J. Fluid Mech. 36 (1), 55–63.CrossRefGoogle Scholar
Cooker, M. J. & Peregrine, D. H. 1990 Violent water motion at breaking-wave impact. Coastal Engineering Proceedings 1, 22.Google Scholar
Dong, H., Carr, W. W. & Morris, J. F. 2006 Visualization of drop-on-demand inkjet: drop formation and deposition. Rev. Sci. Instrum. 77 (8), 085101.CrossRefGoogle 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
Duclaux, V., Caillé, F., Duez, C., Ybert, C., Bocquet, L. & Clanet, C. 2007 Dynamics of transient cavities. J. Fluid Mech. 591, 1–19.CrossRefGoogle Scholar
Eggers, J. 1997 Nonlinear dynamics and breakup of free-surface flows. Rev. Mod. Phys. 69 (3), 865–929.CrossRefGoogle Scholar
Eggers, J. & Fontelos, M. A. 2009 The role of self-similarity in singularities of partial differential equations. Nonlinearity 22 (1), R1–R44.CrossRefGoogle Scholar
Fedorchenko, A. I. & Wang, A.-B. 2004 On some common features of drop impact on liquid surfaces. Phys. Fluids 16 (5), 1349–1365.CrossRefGoogle Scholar
Foulk, C. W. 1932 Foaming and priming of boiler water. Trans. Am. Soc. Mech. Eng. – Adv. Papers 54 (RP-54-5), 105–113.Google Scholar
Gekle, S., Gordillo, J.-M., van der Meer, D. & Lohse, D. 2009 High-speed jet formation after solid object impact. Phys. Rev. Lett. 102 (3), 034502.CrossRefGoogle ScholarPubMed
Hogrefe, J. E., Peffley, N. L., Goodridge, C. L., Shi, W. T., Hentschel, H. G. E. & Lathrop, D. P. 1998 Power-law singularities in gravity–capillary waves. Physica D 123 (1–4), 183–205.CrossRefGoogle Scholar
Lavrentiev, M. & Chabat, B. 1980 Effets Hydrodynamiques et Modèles Mathématiques. Éditions MIR.Google Scholar
Lohse, D., Bergmann, R., Mikkelsen, R., Zeilstra, C., van der Meer, D., Versluis, M., van der Weele, K., van der Hoef, M. & Kuipers, H. 2004 Impact on soft sand: void collapse and jet formation. Phys. Rev. Lett. 93, 198003.CrossRefGoogle ScholarPubMed
Longuet-Higgins, M. S. 2001 Vertical jets from standing waves. Proc. R. Soc. Lond. A 457 (2006), 495–510.CrossRefGoogle Scholar
Lorenceau, E., Quere, D., Ollitrault, J.-Y. & Clanet, C. 2002 Gravitational oscillations of a liquid column in a pipe. Phys. Fluids 14 (6), 1985–1992.CrossRefGoogle Scholar
MacIntyre, F. 1972 Flow patterns in breaking bubbles. J. Geophys. Res. 77 (27), 5211–5228.CrossRefGoogle Scholar
Peregrine, D. H. 2003 Water-wave impact on walls. Annu. Rev. Fluid Mech. 35, 23–43.CrossRefGoogle Scholar
Seon, T. & Antkowiak, A. 2012 Large bubble rupture sparks fast liquid jet. Phys. Rev. Lett. 109, 014501.CrossRefGoogle ScholarPubMed
Stuhlman, O. Jr. 1932 The mechanics of effervescence. Physics 2 (6), 457–466.CrossRefGoogle Scholar
Tagawa, Y., Oudalov, N., Visser, C.-W., Peters, I.-R., van der Meer, D., Sun, C., Prosperetti, A. & Lohse, D. 2012 Highly focused supersonic microjets. Phys. Rev. X 2, 031002.Google Scholar
Villermaux, E. 2007 Fragmentation. Annu. Rev. Fluid Mech. 39 (1), 419–446.CrossRefGoogle 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.CrossRefGoogle ScholarPubMed
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