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The viscous Savart sheet

Published online by Cambridge University Press:  02 August 2013

E. Villermaux ,
V. Pistre  and
H. Lhuissier
E. Villermaux*
Affiliation:
Aix Marseille Université, CNRS, Centrale Marseille, IRPHE UMR 7342, F-13384, Marseille, France
V. Pistre
Affiliation:
TECHNI-PROCESS, ZI La Muscatelle, 13790 Châteauneuf-Le-Rouge, France
H. Lhuissier
Affiliation:
Aix Marseille Université, CNRS, Centrale Marseille, IRPHE UMR 7342, F-13384, Marseille, France
*
†Also at: Institut Universitaire de France. Email address for correspondence: villermaux@irphe.univ-mrs.fr
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Abstract

We study the viscous version of the planar Savart sheet problem, using an impacting liquid jet up to 300 times more viscous than water. Two surprising observations are made, contrasting with the traditional case introduced by Savart where viscosity plays no role. First, if the radius of a viscous sheet is typically reduced compared to the case of water for a given jet radius and impacting velocity, the smooth–flapping transition is delayed, allowing for smooth sheet radii substantially bigger than those permitted with water at large impacting Weber number. Second, the drop size distribution is bimodal, with a substantial fraction of the drops having a very small, well-defined diameter. We understand these two facts in terms of an additional model experiment, and simple physical arguments.

JFM classification

Drops and Bubbles: Aerosols/atomization Drops and Bubbles: Breakup/coalescence Drops and Bubbles: Drops and Bubbles
Type
Papers
Information
Journal of Fluid Mechanics , Volume 730 , 10 September 2013 , pp. 607 - 625
Copyright
©2013 Cambridge University Press 

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References

Basaran, O. A., Gao, H. & Bhat, P. P. 2013 Nonstandard inkjets. Annu. Rev. Fluid Mech. 45, 85–113.Google Scholar
Bouasse, H. 1924 Capillarité. Delagrave.Google Scholar
Boucher, E. A. & Evans, J. B. 1975 Pendent drop profiles and related capillary phenomena. Proc. R. Soc. Lond. A 346, 349–374.Google Scholar
Bremond, N., Clanet, C. & Villermaux, E. 2007 Atomization of undulated liquid sheets. J. Fluid Mech. 585, 421–456.Google Scholar
Bremond, N. & Villermaux, E. 2006 Atomization by jet impact. J. Fluid Mech. 549, 273–306.CrossRefGoogle Scholar
Brenner, M. P., Shi, X. D. & Nagel, S. R. 1994 Iterated instabilities during droplet fission. Phys. Rev. Lett. 73 (25), 3391–3394.Google Scholar
Castrejon-Pita, A. A., Castrejon-Pita, J. R. & Hutchings, I. M. 2012 Breakup of liquid ligaments. Phys. Rev. Lett. 108, 074506.CrossRefGoogle Scholar
Christianti, Y. & Walker, L. M. 2000 Surface tension driven jet break up of strain-hardening polymer solutions. J. Non-Newtonian Fluid Mech. 100, 9–26.Google Scholar
Clanet, C. & Villermaux, E. 2002 Life of a smooth liquid sheet. J. Fluid Mech. 462, 307–340.Google Scholar
Culick, F. E. C. 1960 Comments on a ruptured soap film. J. Appl. Phys. 31, 1128–1129.Google Scholar
Dokic, P., Jakovljevic, J. & Dokic-Baucal, L. 1998 Molecular characteristics of maltodextrins and rheological behaviour of diluted and concentrated solutions. Colloids Surf. A 141, 435–440.Google Scholar
Eggers, J. & Fontelos, M. A. 2005 Isolated inertialess drops cannot break up. J. Fluid Mech. 530, 177–180.CrossRefGoogle Scholar
Eggers, J. & Villermaux, E. 2008 Physics of liquid jets. Rep. Prog. Phys. 71, 036601.Google Scholar
Entov, V. M. & Hinch, E. J. 1997 Effect of a spectrum of relaxation times on the capillary thinning of a filament of elastic liquid. J. Non-Newtonian Fluid Mech. 72, 31–53.Google 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.Google Scholar
Harkins, W. D. & Brown, F. E. 1919 The determination of surface tension (free surface energy), and the weight of falling drops: the surface tension of water and benzene by the capillary height method. J. Am. Chem. Soc. 41, 499–524.Google Scholar
Henderson, D., Segur, H., Smolka, L. B. & Wadati, M. 2000 The motion of a falling liquid filament. Phys. Fluids 12 (3), 550–565.CrossRefGoogle Scholar
Hoath, S. D., Jung, S. & Hutchings, I. M. 2013 A simple criterion for filament break-up in drop-on-demand inkjet printing. Phys. Fluids 25, 021701.CrossRefGoogle Scholar
Howell, P. D., Scheid, B. & Stone, H. A. 2010 Newtonian pizza: spinning a viscous sheet. J. Fluid Mech. 659, 1–23.Google Scholar
Huang, J. C. P. 1970 The break-up of axisymmetric liquid sheets. J. Fluid Mech. 43, 305–319.CrossRefGoogle Scholar
Lafrance, P. & Ritter, R. C. 1977 Capillary breakup of a liquid jet with a random initial perturbation. J. Appl. Mech. 385–388.Google Scholar
Landau, L. & Lifshitz, E. 1987 Fluid Mechanics. Pergamon.Google Scholar
Lefebvre, A. H. 1989 Atomization and Sprays. Hemisphere.Google Scholar
Lhuissier, H. & Villermaux, E. 2009 Soap films burst like flapping flags. Phys. Rev. Lett. 103, 054501–(4).Google Scholar
Lhuissier, H. & Villermaux, E. 2012 Crumpled water bells. J. Fluid Mech. 693, 508–540.CrossRefGoogle Scholar
Mastin, L. G. 2007 Generation of fine hydromagmatic ash by growth and disintegration of glassy rinds. J. Geophys. Res. 112, B02203.Google Scholar
Notz, P. K. & Basaran, O. A. 2004 Dynamics and breakup of a contracting liquid filament. J. Fluid Mech. 512, 223–256.Google Scholar
Oliveira, M. & McKinley, G. 2005 Iterated stretching and multiple beads-on-a-string phenomena in dilute solutions of high extensible flexible polymers. Phys. Fluids 17, 071704.Google Scholar
Plateau, J. 1873 Statique Expérimentale et Théorique des Liquides Soumis aux Seules Forces Moléculaires. Gauthiers-Villars.Google Scholar
Rayleigh, Lord 1899 Investigations in capillarity. Phil. Mag. 48, 321–337.Google Scholar
Savart, F. 1833a Mémoire sur le choc d’une veine liquide lancée sur un plan circulaire. Ann. Chim. 54, 56–87.Google Scholar
Savart, F. 1833b Suite du mémoire sur le choc d’une veine liquide lancée sur un plan circulaire. Ann. Chim. 54, 113–145.Google Scholar
Savva, N. & Bush, J. W. M. 2009 Viscous sheet retraction. J. Fluid Mech. 626, 211–240.CrossRefGoogle Scholar
Schlichting, H. 1987 Boundary Layer Theory, 7th edn. McGraw-Hill.Google Scholar
Semenova, M. G., Belyakova, L. E., Antipova, A. S., Polikarpov, Y. N., Klouda, L., Markovic, A. & Il’in, M. M. 2003 Effect of maltodextrins on the surface activity of small-molecule surfactants. Colloids Surf. B 31, 47–54.CrossRefGoogle Scholar
Squire, H. B. 1953 Investigation of the stability of a moving liquid film. British J. Appl. Phys. 4, 167–169.Google Scholar
Stone, H. A. 1994 Dynamics of drop deformation and breakup in viscous fluids. Annu. Rev. Fluid Mech. 26, 65–102.CrossRefGoogle Scholar
Taylor, G. I. 1959a The dynamics of thin sheets of fluid. Part 2. Waves on fluid sheets. Proc. R. Soc. Lond. A 253, 296–312.Google Scholar
Taylor, G. I. 1959b The dynamics of thin sheets of fluid. Part 3. Disintegration of fluid sheets. Proc. R. Soc. Lond. A 253, 313–321.Google Scholar
Tjahjadi, M., Stone, H. A. & Ottino, J. M. 1992 Satellite and subsatellite formation in capillary breakup. J. Fluid Mech. 243, 297–317.Google Scholar
Tomotika, S. 1936 Breaking up of a drop of viscous liquid immersed in another fluid which is extending at uniform rate. Proc. R. Soc Lond. A 153, 302–318.Google Scholar
Villermaux, E. 2007 Fragmentation. Annu. Rev. Fluid Mech. 39, 419–446.Google Scholar
Villermaux, E. 2012 The formation of filamentary structures from molten silicates: Pele’s hair, angel hair, and blown clinker. C. R. Mécanique 340, 555–564.CrossRefGoogle Scholar
Villermaux, E. & Clanet, C. 2002 Life of a flapping liquid sheet. J. Fluid Mech. 462, 341–363.Google Scholar
Watson, E. J. 1964 The radial spread of a liquid jet over a horizontal plane. J. Fluid Mech. 20, 481–499.CrossRefGoogle Scholar
Wong, D. C. Y., Simmons, M. J. H., Decent, S. P., Parau, E. I. & King, A. C. 2004 Break-up dynamics and drop size distributions created from spiralling liquid jets. Intl J. Multiphase Flow 30, 499–520.Google Scholar
Yule, A. J. & Dunkey, J. J. 1994 Atomization of Melts. Clarendon.Google Scholar