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The break-up of free films pulled out of a pure liquid bath

Published online by Cambridge University Press:  14 December 2016

Lorène Champougny ,
Emmanuelle Rio ,
Frédéric Restagno  and
Benoit Scheid
Lorène Champougny*
Affiliation:
Laboratoire de Physique des Solides, CNRS and Université Paris-Sud, Université Paris Saclay, 91405 Orsay, France
Emmanuelle Rio
Affiliation:
Laboratoire de Physique des Solides, CNRS and Université Paris-Sud, Université Paris Saclay, 91405 Orsay, France
Frédéric Restagno
Affiliation:
Laboratoire de Physique des Solides, CNRS and Université Paris-Sud, Université Paris Saclay, 91405 Orsay, France
Benoit Scheid
Affiliation:
TIPs - Fluid Physics Unit, Université Libre de Bruxelles C.P. 165/67, 1050 Brussels, Belgium
*
†Email address for correspondence: lorene.champougny@espci.fr
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Abstract

In this paper, we derive a lubrication model to describe the non-stationary free liquid film that is created when a vertical frame is pulled out of a liquid reservoir at a given velocity. We here focus on the case of a pure liquid, corresponding to a stress-free boundary condition at the liquid/air interfaces of the film, and thus employ an essentially extensional description of the flow. Taking into account van der Waals interactions between the interfaces, we observe that film rupture is well defined in time as well as in space, which allows us to compute the critical thickness and the film height at the moment of rupture. The theoretical predictions of the model turn out to be in quantitative agreement with experimental measurements of the break-up height of silicone oil films in a wide range of pulling velocities and supporting fibre diameters.

JFM classification

Drops and Bubbles: Breakup/coalescence Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 811 , 25 January 2017 , pp. 499 - 524
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Copyright
© 2016 Cambridge University Press 

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References

Bascom, W. D., Cottington, R. L. & Singleterry, C. R. 1964 Dynamic surface phenomena in the spontaneous spreading of oils on solids. In Contact Angle, Wettability and Adhesion, vol. 26, pp. 355–379. American Chemical Society.CrossRefGoogle Scholar
Benilov, E. S. & Cummins, C. P. 2013 The stability of a static liquid column pulled out of an infinite pool. Phys. Fluids 25, 112105.CrossRefGoogle Scholar
Benilov, E. S. & Oron, A. 2010 The height of a static liquid column pulled out of an infinite pool. Phys. Fluids 22, 102101.CrossRefGoogle Scholar
Breward, C. J. W.1999 The mathematics of foam. PhD thesis, Oxford University.Google Scholar
Champougny, L., Scheid, B., Restagno, F., Vermant, J. & Rio, E. 2015 Surfactant-induced rigidity of interfaces: a unified approach to free and dip-coated films. Soft Matt. 11 (14), 2758–2770.CrossRefGoogle ScholarPubMed
Chen, H., Tang, T. & Amirfazli, A. 2015 Effects of surface wettability on fast liquid transfer. Phys. Fluids 27 (11), 112102.CrossRefGoogle Scholar
Debrégeas, G., de Gennes, P.-G. & Brochard-Wyart, F. 1998 The life and death of ‘bare’ viscous bubbles. Science 279 (5357), 1704–1707.CrossRefGoogle Scholar
Derjaguin, B. V. & Kusakov, M. M. 1936 The properties of thin layers of liquids. Proc. Acad. Sci. USSR Chem. Series 5, 741–753.Google Scholar
Drummond, C. J. & Chan, D. Y. C. 1997 van der Waals interaction, surface free energies, and contact angles: dispersive polymers and liquids. Langmuir 13 (14), 3890–3895.CrossRefGoogle Scholar
Erneux, T. & Davis, S. H. 1993 Nonlinear rupture of free films. Phys. Fluids A 5, 1117–1122.CrossRefGoogle Scholar
Heller, M.2008 Numerical study of free surfaces and particle sorting in microfluidic systems. PhD thesis, Technical University of Denmark.Google Scholar
Howell, P. 1996 Models for thin viscous sheets. Eur. J. Appl. Maths 7, 321–343.CrossRefGoogle Scholar
Israelachvili, J. N. 2011 Intermolecular and Surface Forces, 3rd edn. Elsevier.Google Scholar
Ivanov, I. B. 1988 Thin Liquid Films: Fundamentals and Applications. Marcel Dekker.Google Scholar
Kappel, J., Conradt, R. & Scholze, H. 1987 Foaming behaviour on glass melts. Glastechnische Berichte 60, 189–201.Google Scholar
Kočárková, H., Rouyer, F. & Pigeonneau, F. 2013 Film drainage of viscous liquid on top of bare bubble: influence of the bond number. Phys. Fluids 25 (2), 022105.CrossRefGoogle Scholar
Landau, L. & Levich, B. 1942 Dragging of a liquid by a moving plate. Acta Physicochim. USSR 17, 42–54.Google Scholar
Manev, E. D. & Nguyen, A. V. 2005 Critical thickness of microscopic thin liquid films. Adv. Colloid Interface Sci. 114, 133–146.CrossRefGoogle ScholarPubMed
Mark, J. E. 1999 Polymer Data Handbook. Oxford University Press.Google Scholar
Marmottant, P. & Villermaux, E. 2004 Fragmentation of stretched liquid ligaments. Phys. Fluids 16 (8), 2732–2741.CrossRefGoogle Scholar
Mysels, K. J., Frankel, S. & Shinoda, K. 1959 Soap Films: Studies of their Thinning and a Bibliography. Pergamon Press.Google Scholar
van Nierop, E. A., Keupp, D. J. & Stone, H. A. 2009 Formation of free films of aqueous solutions of poly-(ethylene oxide): the influence of surfactant. Europhys. Lett. 88 (6), 66005.CrossRefGoogle Scholar
van Nierop, E. A., Scheid, B. & Stone, H. A. 2008 On the thickness of soap films: an alternative to Frankel’s law. J. Fluid Mech. 602, 119–127.CrossRefGoogle Scholar
Proussevitch, A. A., Sahagian, D. L. & Kutolin, V. A. 1993 Stability of foams in silicate melts. J. Volcanol. Geotherm. Res. 59 (1), 161–178.CrossRefGoogle Scholar
Saulnier, L., Restagno, F., Delacotte, J., Langevin, D. & Rio, E. 2011 What is the mechanism of soap film entrainment? Langmuir 27 (22), 13406–13409.CrossRefGoogle ScholarPubMed
Scheid, B., van Nierop, E. A. & Stone, H. A. 2012 Thermocapillary-assisted pulling of contact-free liquid films. Phys. Fluids 24, 032107.CrossRefGoogle Scholar
Schwartz, L. W. & Roy, R. V. 1999 Modeling draining flow in mobile and immobile soap films. J. Colloid Interface Sci. 218 (1), 309–323.CrossRefGoogle ScholarPubMed
Seiwert, J., Dollet, B. & Cantat, I. 2014 Theoretical study of the generation of soap films: role of interfacial visco-elasticity. J. Fluid Mech. 739, 124–142.CrossRefGoogle Scholar
Tabakova, S. 2010 Dynamics and stability of free thin films. AIP Conf. Proc. 1301, 531–542.CrossRefGoogle Scholar
Vaynblat, D., Lister, J. R. & Witelski, T. P. 2001 Rupture of thin viscous films by van der Waals forces: evolution and self-similarity. Phys. Fluids 13 (5), 1130–1140.CrossRefGoogle Scholar
Vincent, L., Duchemin, L. & Le Dizès, S. 2014 Forced dynamics of a short viscous liquid bridge. J. Fluid Mech. 761, 220–240.CrossRefGoogle Scholar
Vrij, A. & Overbeek, J. T. G. 1968 Rupture of thin liquid films due to spontaneous fluctuations in thickness. J. Am. Chem. Soc. 90 (12), 3074–3078.CrossRefGoogle Scholar
Weickgenannt, C., Roisman, I. V. & Tropea, C. 2015 Pinch-off of a stretching viscous filament and drop transport. New J. Phys. 17 (8), 083059.CrossRefGoogle Scholar
Yaminsky, V. V., Ohnishi, S., Vogler, E. A. & Horn, R. G. 2010 Stability of aqueous films between bubbles. Part 1. The effect of speed on bubble coalescence in purified water and simple electrolyte solutions. Langmuir 26 (11), 8061–8074.CrossRefGoogle ScholarPubMed
Zhuang, J. & Ju, Y. S. 2015 A combined experimental and numerical modeling study of the deformation and rupture of axisymmetric liquid bridges under coaxial stretching. Langmuir 31 (37), 10173–10182.CrossRefGoogle ScholarPubMed