Hostname: page-component-758b78586c-t6tmf Total loading time: 0 Render date: 2023-11-29T00:37:46.280Z Has data issue: false Feature Flags: { "corePageComponentGetUserInfoFromSharedSession": true, "coreDisableEcommerce": false, "useRatesEcommerce": true } hasContentIssue false

Liquid jet eruption from hollow relaxation

Published online by Cambridge University Press:  18 November 2014

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


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.

© 2014 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)


Antkowiak, A., Bremond, N., Le Dizès, S. & Villermaux, E. 2007 Short-term dynamics of a density interface following an impact. J. Fluid Mech. 577, 241250.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, 1334.Google Scholar
Barenblatt, G. I. 2003 Scaling. Cambridge University Press.Google Scholar
Barton, M. E. & Edwards, M. C. 1968 Model experiments of soil erosion by VTOL aircraft downwash impingement. J. Terramech. 5 (2), 4551.Google Scholar
Benusiglio, A., Quéré, D. & Clanet, C. 2014 Explosions at the water surface. J. Fluid Mech. 752, 123139.Google 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.Google Scholar
Cheslak, F. R., Nicholls, J. A. & Sichel, M. 1969 Cavities formed on liquid surfaces by impinging gaseous jets. J. Fluid Mech. 36 (1), 5563.Google 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.Google Scholar
Duchemin, L., Popinet, S., Josserand, C. & Zaleski, S. 2002 Jet formation in bubbles bursting at a free surface. Phys. Fluids 14 (9), 30003008.Google Scholar
Duclaux, V., Caillé, F., Duez, C., Ybert, C., Bocquet, L. & Clanet, C. 2007 Dynamics of transient cavities. J. Fluid Mech. 591, 119.Google Scholar
Eggers, J. 1997 Nonlinear dynamics and breakup of free-surface flows. Rev. Mod. Phys. 69 (3), 865929.Google Scholar
Eggers, J. & Fontelos, M. A. 2009 The role of self-similarity in singularities of partial differential equations. Nonlinearity 22 (1), R1R44.Google Scholar
Fedorchenko, A. I. & Wang, A.-B. 2004 On some common features of drop impact on liquid surfaces. Phys. Fluids 16 (5), 13491365.Google Scholar
Foulk, C. W. 1932 Foaming and priming of boiler water. Trans. Am. Soc. Mech. Eng. – Adv. Papers 54 (RP-54-5), 105113.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.Google Scholar
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), 183205.Google 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.Google Scholar
Longuet-Higgins, M. S. 2001 Vertical jets from standing waves. Proc. R. Soc. Lond. A 457 (2006), 495510.Google Scholar
Lorenceau, E., Quere, D., Ollitrault, J.-Y. & Clanet, C. 2002 Gravitational oscillations of a liquid column in a pipe. Phys. Fluids 14 (6), 19851992.Google Scholar
MacIntyre, F. 1972 Flow patterns in breaking bubbles. J. Geophys. Res. 77 (27), 52115228.Google Scholar
Peregrine, D. H. 2003 Water-wave impact on walls. Annu. Rev. Fluid Mech. 35, 2343.Google Scholar
Seon, T. & Antkowiak, A. 2012 Large bubble rupture sparks fast liquid jet. Phys. Rev. Lett. 109, 014501.Google Scholar
Stuhlman, O. Jr. 1932 The mechanics of effervescence. Physics 2 (6), 457466.Google 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), 419446.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), 401404.Google Scholar
Supplementary material: PDF

Ghabache et al. supplementary material

Supplementary material

Download Ghabache et al. supplementary material(PDF)