Hostname: page-component-76c49bb84f-zv2rg Total loading time: 0 Render date: 2025-07-07T03:01:53.181Z Has data issue: false hasContentIssue false
  • English
  • Français

Recoil of a liquid filament: escape from pinch-off through creation of a vortex ring

Published online by Cambridge University Press:  08 October 2013

Jérôme Hoepffner  and
Gounséti Paré
Jérôme Hoepffner*
Affiliation:
UPMC Univ Paris 06 & CNRS, UMR 7190, Institut Jean Le Rond d’Alembert, F-75005 Paris, France
Gounséti Paré
Affiliation:
UPMC Univ Paris 06 & CNRS, UMR 7190, Institut Jean Le Rond d’Alembert, F-75005 Paris, France
*
†Email address for correspondence: jerome.hoepffner@upmc.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

A liquid filament recoils because of its surface tension. It may recoil to one sphere, the geometrical shape with lowest surface, or otherwise segment to several pieces which individually will recoil to spheres. This experiment is classical and its exploration is fundamental to the understanding of how liquid volumes relax. In this paper, we uncover a mechanism involving the creation of a vortex ring which plays a central role in escaping segmentation. The retracting blob is connected to the untouched filament by a neck. The radius of the neck decreases in time such that we may expect pinch-off. There is a flow through the neck because of the retraction. This flow may detach into a jet downstream of the neck when fluid viscosity exceeds a threshold. This sudden detachment creates a vortex ring which strongly modifies the flow pressure: fluid is expelled back into the neck which in turn reopens.

JFM classification

Drops and Bubbles: Drops and Bubbles Interfacial Flows (free surface): Interfacial Flows (free surface) Vortex Flows: Vortex shedding

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 734 , 10 November 2013 , pp. 183 - 197
Copyright
©2013 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.)

Article purchase

Temporarily unavailable

References

Antkowiak, A., Bremond, N. & le Dizès, S. 2007 Short-term dynamics of a density interface following an impact. J. Fluid Mech. 577, 241–250.CrossRefGoogle Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Brenner, M., Eggers, J., Joseph, K., Nagel, S. R. & Shi, X. D. 1997 Breakdown of scaling in droplet fission at high Reynolds number. Phys. Fluids 9, 1573–1590.CrossRefGoogle Scholar
Castrejón-Pita, A. A., Castrejón-Pita, J. R. & Hutchings, I. M. 2012 Breakup of liquid filaments. Phys. Rev. Lett. 108, 074506.CrossRefGoogle ScholarPubMed
Culick, F. E. C. 1960 Comments on a ruptured soap film. J. Appl. Phys. 31, 1128–1129.CrossRefGoogle Scholar
De Gennes, P.-G., Quéré, D. & Brochard-Wyart, F. 2004 Capillary and Wetting Phenomena: Drops, Bubble, Pearls, Waves. Springer.CrossRefGoogle Scholar
Driessen, T., Jeurissen, R., Wijshoff, H., Toschi, F. & Lohse, D. 2013 Stability of viscous long liquid filaments. Phys. Fluids 25 (6), 062709.CrossRefGoogle Scholar
Eggers, J. 1997 Nonlinear dynamics and breakup of a free-surface flow. Rev. Mod. Phys. 69 (3), 865–929.CrossRefGoogle Scholar
Eggers, J. & Dupont, T. F. 1994 Drop formation in a one-dimensional approximation of the Navier–Stokes equation. J. Fluid Mech. 262, 205–221.CrossRefGoogle Scholar
Eggers, J. & Villermaux, E. 2008 Physics of liquid jets. Rep. Prog. Phys. 71, 036601.CrossRefGoogle Scholar
Gier, S. & Wagner, C. 2012 Visualization of the flow profile inside a thinning filament during capillary breakup of a polymer solution via particle image velocimetry and particle tracking velocimetry. Phys. Fluids 24, 053102.CrossRefGoogle Scholar
Gordillo, L., Agbaglah, G., Duchemin, L. & Josserand, C. 2011 Asymptotic behaviour of a retracting two-dimensional fluid sheet. Phys. Fluids 23, 122101.CrossRefGoogle Scholar
Javadi, A., Eggers, J., Bonn, D., Habibi, M. & Ribe, N. M. 2013 Delayed capillary breakup of falling viscous jets. Phys. Rev. Lett. 110 (14), 144501.CrossRefGoogle ScholarPubMed
Keller, J. B. 1983 Breaking of liquid films and threads. Phys. Fluids 26, 3451–3453.CrossRefGoogle Scholar
Keller, J. B., King, A. & Ting, L. 1995 Blob formation. Phys. Fluids 7, 226–228.CrossRefGoogle Scholar
Keller, J. B. & Miksis, M. J. 1983 Surface tension driven flow. SIAM J. Appl. Maths 43 (2), 268–277.CrossRefGoogle Scholar
Laplace, P.-S. 1805 Traité de mécanique céleste. Supplément au livre X, Courcier.Google Scholar
Marmottant, P. & Villermaux, E. 2004 Fragmentation of stretched liquid ligaments. Phys. Fluids 16 (8), 2732–2741.CrossRefGoogle Scholar
Notz, P. K. & Basaran, O. A. 2004 Dynamics and breakup of a contracting liquid filament. J. Fluid Mech. 512, 223–256.CrossRefGoogle Scholar
Plateau, J. 1873 Statique expérimentale et théorique des liquides soumis aux seules forces moléculaires. Gauthier-Villars.Google Scholar
Popinet, S. 2009 An accurate adaptive solver for surface-tension-driven interfacial flows. J. Comput. Phys. 228, 5838–5866.CrossRefGoogle Scholar
Rayleigh, 1879 On the instability of jets. Proc. Lond. Math. Soc. 10, 4–13.Google Scholar
Schulkes, R. M. S. M. 1996 The contraction of liquid filaments. J. Fluid Mech. 309, 277–300.CrossRefGoogle Scholar
Senchenko, S. & Bohr, T. 2005 Shape and stability of a viscous thread. Phys. Rev. E 71 (056301).CrossRefGoogle ScholarPubMed
Sierou, A. & Lister, J. R. 2004 Self-similar recoil of inviscid drops. Phys. Fluids 16 (5), 1379–1394.CrossRefGoogle Scholar
Stone, H. A., Bentley, B. J. & Leal, L. G. 1986 An experimental study of transient effects in the breakup of viscous drops. J. Fluid Mech. 173, 131–158.CrossRefGoogle Scholar
Stone, H. A. & Leal, L. G. 1989 Relaxation and breakup of an initially extended drop in an otherwise quiescent fluid. J. Fluid Mech. 198, 399–427.CrossRefGoogle Scholar
Taylor, G. I. 1959 The dynamics of thin sheets of fluids, III Disintegration of fluid sheets. Proc. R. Soc. Lond. A 253, 313.Google Scholar
Weber, C. 1931 Zum Zerfall eines Flüssigkeitsstrahles. Z. Angew. Math. Mech. 11 (2), 136–154.CrossRefGoogle Scholar

Hoepffner and Paré supplementary movie

Here are the movies for the paper, combined into one single video sequence.

Download Hoepffner and Paré supplementary movie(Video)
Video 2.5 MB
Supplementary material: PDF

Hoepffner and Paré supplementary material

Supplementary material

Download Hoepffner and Paré supplementary material(PDF)
PDF 34 KB