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Theoretical study of the generation of soap films: role of interfacial visco-elasticity

Published online by Cambridge University Press:  17 December 2013

Jacopo Seiwert
Affiliation:
Institut de Physique de Rennes, UMR 6251 CNRS/Université de Rennes 1, Campus Beaulieu, Bâtiment 11A, 35042 Rennes CEDEX, France
Benjamin Dollet
Affiliation:
Institut de Physique de Rennes, UMR 6251 CNRS/Université de Rennes 1, Campus Beaulieu, Bâtiment 11A, 35042 Rennes CEDEX, France
Isabelle Cantat*
Affiliation:
Institut de Physique de Rennes, UMR 6251 CNRS/Université de Rennes 1, Campus Beaulieu, Bâtiment 11A, 35042 Rennes CEDEX, France
*
Email address for correspondence: [email protected]

Abstract

In this work, we study theoretically the thickness of a liquid film (typically made of a surfactant solution) pulled out of a bath at constant speed in the absence of gravity, when it features a viscous or an elastic interfacial rheology. We show that a purely viscous rheology does not lead to the extraction of a steady state film of constant thickness. In contrast, the thickness of the film is well defined in the elastic case, which allows us to compute it. This thickness depends on the capillary number of the experiment, and on the elasticity of the interface. It is always lower than or equal to that obtained for an incompressible interface predicted by Frankel (Mysels, Shinoda and Frankel, Soap Films: Studies of their Thinning and a Bibliography, 1959), which is recovered in the limit of an arbitrary large elasticity.

Type
Papers
Copyright
©2013 Cambridge University Press 

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References

Alvarez, N. J., Walker, L. M. & Anna, S. L. 2012 A criterion to assess the impact of confined volumes on surfactant transport to liquid–fluid interfaces. Soft Matt. 8, 89178925.CrossRefGoogle Scholar
Berg, S., Adelizzi, E. A. & Troian, S. M. 2005 Experimental study of entrainment and drainage flows in microscale soap films. Langmuir 21 (9), 38673876.Google Scholar
Biance, A.-L., Delbos, A. & Pitois, O. 2011 How topological rearrangements and liquid fraction control liquid foam stability. Phys. Rev. Lett. 106, 068301.Google Scholar
Breward, C. J. W 1999 The mathematics of foam. PhD thesis, Oxford University.Google Scholar
Breward, C. J. W. & Howell, P. D. 2002 The drainage of a foam lamella. J. Fluid Mech. 458, 379406.Google Scholar
Bruinsma, R., di Meglio, J.-M., Quéré, D. & Cohen-Addad, S. 1992 Formation of soap films from polymer solutions. Langmuir 8, 31613167.Google Scholar
Cantat, I. 2013 Liquid meniscus friction on a wet wall: bubbles, lamellae and foams. Phys. Fluids 25, 031303.CrossRefGoogle Scholar
Cohen-Addad, S. & di Meglio, J.-M. 1994 Stabilization of aqueous foam by hydrosoluble polymers. Part 2. Role of polymer/surfactant interactions. Langmuir 10 (3), 773778.Google Scholar
Couder, Y., Chomaz, J.-M. & Rabaud, M. 1989 On the hydrodynamics of soap films. Physica D 37, 384405.Google Scholar
Derjaguin, B. V. 1943 Thickness of liquid layer adhering to walls of vessels on their emptying. Acta Physicochim. USSR 20, 349.Google Scholar
Gaudet, S., McKinley, G. H. & Stone, H. A. 1996 Extensional deformation of Newtonian liquid bridges. Phys. Fluids 8, 25682580.Google Scholar
de Gennes, P. G. 2001 Young soap films. Langmuir 17 (8), 24162419.Google Scholar
Howell, P. D. & Stone, H. A. 2005 On the absence of marginal pinching in thin free films. Eur. J. Appl. Maths 16, 569582.CrossRefGoogle Scholar
Lal, J. & di Meglio, J.-M. 1994 Formation of soap films from insoluble surfactants. J. Colloid Interface Sci. 164 (2), 506509.Google Scholar
Landau, L. & Levich, B. 1942 Dragging of a liquid by a moving plate. Acta Physicochim. USSR 17, 42.Google Scholar
Levich, V. G. 1962 Physicochemical Hydrodynamics. Prentice Hall.Google Scholar
Mysels, K. J., Shinoda, K. & Frankel, S. 1959 Soap Films: Studies of their Thinning and a Bibliography. Pergamon.Google 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, 119127 and Corrigendum 630, 443 (2009).Google Scholar
Park, C. W. 1991 Effects of insoluble surfactants on dip coating. J. Colloid Interface Sci. 146 (2), 382394.Google Scholar
Quéré, D. 1999 Fluid coating on a fibre. Annu. Rev. Fluid. Mech. 31 (1), 347384.Google Scholar
Reynolds, O. 1886 On the theory of lubrication and its application to Mr. Beauchamp Tower’s experiment, including an experimental determination of the viscosity of olive oil. Proc. R. Soc. Lond. 177, 157.Google Scholar
Sagis, L. M. C. 2011 Dynamic properties of interfaces in soft matter: experiments and theory. Rev. Mod. Phys 83, 13671403.Google Scholar
Saulnier, L., Restagno, F., Delacotte, J., Langevin, D. & Rio, E. 2011 What is the mechanism of soap film entrainment? Langmuir 27 (22), 1340613409.Google Scholar
Scheid, B., Delacotte, J., Dollet, B., Rio, E., Restagno, F., van Nierop, E. A., Cantat, I., Langevin, D. & Stone, H. A. 2010 The role of surface force rheology in liquid film formation. Eur. Phys. Lett. 90, 24002.Google Scholar
Schwartz, L. W & Roy, R. V 1999 Modelling draining flow in mobile and immobile soap films. J. Colloid Interface Sci. 218 (1), 309323.Google Scholar
Seiwert, J., Monloubou, M., Dollet, B. & Cantat, I. 2013 Extension of a suspended soap film: a homogeneous dilatation followed by new film extraction. Phys. Rev. Lett. 111, 094501.Google Scholar
Tambe, D. E. & Sharma, M. M. 1991 Hydrodynamics of thin liquid films bounded by viscoelastic interfaces. J. Colloid Interface Sci. 147 (1), 137151.Google Scholar
Wilson, S. D. R. 1988 The slow dripping of a viscous fluid. J. Fluid Mech. 190, 561570.CrossRefGoogle Scholar