Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-24T16:39:57.633Z Has data issue: false hasContentIssue false
  • English
  • Français

Soap film catastrophes

Published online by Cambridge University Press:  06 September 2021

Hamed K. Habibi  and
Rouslan Krechetnikov Open the ORCID record for Rouslan Krechetnikov [Opens in a new window]
Hamed K. Habibi
Affiliation:
Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2G1, Canada
Rouslan Krechetnikov*
Affiliation:
Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2G1, Canada
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Earlier systematic experimental studies of bursting soap films by McEntee & Mysels (J. Phys. Chem., vol. 73, 1969, pp. 3018–3028) revealed the existence of a precursor shock wave preceding the expanding hole in a punctured film, with a disturbed region of shrinking film material in between known as the ‘aureole’. In the present work we report and interpret new phenomena associated with the aureole – the formation of folds on the surface of soap films. In search of the theoretical explanation of the experimentally identified conditions under which the folds appear, we establish that they correspond to catastrophes of collapsing soap films.

JFM classification

Interfacial Flows (free surface): Thin films
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 926 , 10 November 2021 , A19
Check for updates
Copyright
© The Author(s), 2021. Published by 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.)

References

REFERENCES

Adelizzi, E.A. & Troian, S.M. 2004 Interfacial slip in entrained soap films containing associating hydrosoluble polymer. Langmuir 20, 7482–7492.CrossRefGoogle ScholarPubMed
Almgren, F.J. Jr. & Taylor, J.E. 1976 The geometry of soap films and soap bubbles. Sci. Am. 231, 82–93.CrossRefGoogle Scholar
Arnold, V.I. 2003 Catastrophe Theory. Springer.Google Scholar
Aubin, D. 2004 Forms of explanation in the catastrophe theory of René Thom: topology, morphogenesis, and the structuralism. In Growing Explanations: Historical Perspective in the Sciences of Complexity (ed. M.N. Wise), pp. 95–130. Duke University Press.CrossRefGoogle Scholar
Benjamin, T.B. & Mullin, T. 1988 Buckling instabilities in layers of viscous liquid subjected to shearing. J. Fluid Mech. 195, 523–540.CrossRefGoogle Scholar
Berg, S., Adelizzi, E.A. & Troian, S.M. 2005 Experimental study of entrainment and drainage flows in microscale soap films. Langmuir 21, 3867–3876.CrossRefGoogle ScholarPubMed
Berry, M.V. 1976 Waves and Thom's theorem. Adv. Phys. 25, 1–26.CrossRefGoogle Scholar
Birch, T. 1757 History of the Royal Society, vol. III. A. Millard.Google Scholar
Boys, C.V. 1890 Soap Bubbles and the Forces Which Mould Them. Society for Promoting Christian Knowledge.Google Scholar
Brenner, M.P. & Gueyffier, D. 1999 On the bursting of viscous sheets. Phys. Fluids 11, 737–739.CrossRefGoogle Scholar
Burkhardt, B. 2021 Soap-film and soap-bubble models. In Physical Models: Their Historical and Current Use in Civil and Building Engineering Design (ed. B. Addis), pp. 569–586. Ernst & Sohn Verlag GmbH & Co. KG.CrossRefGoogle Scholar
Carnero Ruiz, C., Diaz-Lopez, L. & Aguiar, J. 2008 Micellization of Sodium Dodecyl Sulfate in glycerol aqueous mixtures. J. Dispers. Sci. Technol. 29, 266–273.CrossRefGoogle Scholar
Chang, C.-H. & Franses, E.I. 1992 Modified Langmuir–Hinshelwood kinetics for dynamic adsorption surfactants at the air/water interface. Colloids Surf. 69, 189–201.CrossRefGoogle Scholar
Couder, Y., Chomaz, J.-M. & Rabaud, M. 1989 On the hydrodynamics of soap films. Physica D 37, 384–405.CrossRefGoogle Scholar
Courant, R. & Robbins, H. 1941 What is Mathematics? Oxford University Press.Google Scholar
Culick, F.E.C. 1960 Comments on a ruptured soap film. J. Appl. Phys. 31, 1128–1129.CrossRefGoogle Scholar
Debrégeas, G., Martin, P. & Brochard-Wyart, F. 1995 Viscous bursting of suspended films. Phys. Rev. Lett. 75, 3886–3889.CrossRefGoogle ScholarPubMed
Douglas, J. 1931 Solution of the problem of Plateau. Trans. Am. Math. Soc. 33, 263–321.CrossRefGoogle Scholar
Dupré, M.A. 1867 Sixième memoire sur la theorie méchanique de la chaleur. Ann. Chim. Phys. 4, 194–220.Google Scholar
Edwards, D.A., Brenner, H. & Wasan, D.T. 1991 Interfacial Transport Processes and Rheology. Butterworth-Heinemann.Google Scholar
Evers, L.J., Shulepov, S.Y. & Frens, G. 1996 Rupture of thin liquid films from Newtonian and viscoelastic liquids. Faraday Discuss. 104, 335–344.CrossRefGoogle Scholar
Faraday, M. 1851 Experimental researches in electricity. Twenty-fifth series. Phil. Trans. R. Soc. Lond. 141, 7–28.Google Scholar
Fernandez, J., Krechetnikov, R. & Homsy, G.M. 2005 Experimental study of a surfactant-driven fingering phenomenon in a Hele-Shaw cell. J. Fluid Mech. 527, 197–216.CrossRefGoogle Scholar
Frankel, S. & Mysels, K.J. 1969 The bursting of soap films. II. A theoretical study. J. Phys. Chem. 73, 3029–3038.CrossRefGoogle Scholar
Gharib, M. & Derango, P. 1989 A liquid film (soap film) tunnel to study two-dimensional laminar and turbulent shear flows. Physica D 37, 406–416.CrossRefGoogle Scholar
Gibbs, J.W. 1928, 1931 Collected Works, vol. I. Longmans Green.Google Scholar
Griesbauer, J., Wixforth, A. & Schneider, M.F. 2009 Wave propagation in lipid monolayers. Biophys. J. 97, 2710–2716.CrossRefGoogle ScholarPubMed
Hadamard, J. 1923 Lectures on Cauchy'S Problem in Linear Partial Differential Equations. Dover Publications.Google Scholar
Huibers, P.D.T. & Shah, D.O. 1997 Multispectral determination of soap film thickness. Langmuir 13, 5995–5998.CrossRefGoogle Scholar
Incropera, F.P. & DeWitt, D.P. 2002 Introduction to Heat Transfer. John Wiley & Sons.Google Scholar
Isenberg, C. 1992 The Science of Soap Films and Soap Bubbles. Dover.Google Scholar
Johnston, B. 1935 Torsional rigidity of structural sections. Civil Engng 5, 698–701.Google Scholar
Khan, H., Seddon, J.M., Law, R.V., Brooks, N.J., Robles, E., Cabral, J.T. & Ces, O. 2019 Effect of glycerol with sodium chloride on the Krafft point of sodium dodecyl sulfate using surface tension. J. Colloid Interface Sci. 538, 75–82.CrossRefGoogle ScholarPubMed
Khattari, Z., Langer, U., Aliaskarisohi, S., Ray, A. & Fischer, T.M. 2011 Effects of soluble surfactants on the Langmuir monolayers compressibility: a comparative study using interfacial isotherms and fluorescence microscopy. Mater. Sci. Engng C 31, 1711–1715.CrossRefGoogle Scholar
Kim, I. & Mandre, S. 2017 Marangoni elasticity of flowing soap films. Phys. Rev. Fluids 2, 082001.CrossRefGoogle Scholar
Kritikos, H.N. 1967 The eikonal equation in a moving medium. Proc. IEEE 55, 442–443.CrossRefGoogle Scholar
Landau, L.D. & Lifshitz, E.M. 1987 Fluid Mechanics. Pergamon.Google Scholar
Lyklema, J., Scholten, P.C. & Mysels, K.J. 1965 Flow in thin liquid films. J. Phys. Chem. 69, 116–123.CrossRefGoogle Scholar
Maxwell, J.C. 1878 Capillary action. In Encyclopaedia Britannica, 9th edition, vol. 5, pp. 56–71. A. & C. Black.Google Scholar
Mayer, H.C. & Krechetnikov, R. 2010 a The life of a free soap film. APS-DFD Poster no. 72.Google Scholar
Mayer, H.C. & Krechetnikov, R. 2010 b The life of a free soap film. APS-DFD Gallery of Fluid Motion no. 107.Google Scholar
Mayer, H.C. & Krechetnikov, R. 2017 Liquid film dewetting induced by impulsive Joule heating. Phys. Rev. Fluids 2, 094003.CrossRefGoogle Scholar
McEntee, W.R. & Mysels, K.J. 1969 The bursting of soap films. I. An experimental study. J. Phys. Chem. 73, 3018–3028.CrossRefGoogle Scholar
Milner, S.T., Joanny, J.-F. & Pincus, P. 1989 Buckling of Langmuir monolayers. Europhys. Lett. 9, 495–500.CrossRefGoogle Scholar
Mysels, K.J. 1964 Soap films and some problems in surface and colloid chemistry1. J. Phys. Chem. 68, 3441–3448.CrossRefGoogle Scholar
Mysels, K.J. & Cox, M.C. 1962 An experimental test of Frankel's law of film thickness. J. Colloid Sci. 17, 136–145.CrossRefGoogle Scholar
Mysels, K.J., Shinoda, K. & Frankel, S. 1959 Soap Films: Studies of their Thinning. Pergamon.Google Scholar
Newton, I. 1704 Opticks. Smith and Walford.Google Scholar
Petrovsky, I.G. 1954 Partial Differential Equations. Interscience Publishers.Google Scholar
Plateau, J. 1873 Statique expérimentale et théorique des liquides soumis aux seules forces moléculaires. Gauthier Villars.Google Scholar
Prandtl, L. 1903 Zur Torsion von prismatischen Stäben. Phys. Z. 4, 758–759.Google Scholar
Rusanov, A.I. & Krotov, V.V. 1979 Gibbs elasticity of liquid films, threads, and foams. Progr. Surf. Membrane Sci. 13, 415–524.CrossRefGoogle Scholar
Saint-Jalmes, A. & Gallet, F. 1998 Buckling in a solid Langmuir monolayer: light scattering measurements and elastic model. Eur. Phys. J. B 2, 489–494.CrossRefGoogle Scholar
Savva, N. & Bush, J.W.M. 2009 Viscous sheet retraction. J. Fluid Mech. 626, 211–240.CrossRefGoogle Scholar
Slim, A.C., Teichman, J. & Mahadevan, L. 2012 Buckling of a thin-layer Couette flow. J. Fluid Mech. 694, 5–28.CrossRefGoogle Scholar
Tajima, K., Muramatsu, M. & Sasaki, T. 1970 Radiometer studies on adsorption of surface active substance at aqueous surface. I. Accurate measurement of adsorption of tritiated Sodium Dodecylsulfate. Bull. Chem. Soc. Japan 43, 1991–1998.CrossRefGoogle Scholar
Taylor, G.I. 1959 a The dynamics of thin sheets of fluid. II. Waves on fluid sheets. Proc. R. Soc. Lond. A 253, 296–312.Google Scholar
Taylor, G.I. 1959 b The dynamics of thin sheets of fluid. III. Disintegration of fluid sheets. Proc. R. Soc. Lond. A 253, 313–321.Google Scholar
Thom, R. 1954 Quelques propriétés globales des variétés differentiables. Commentarii Math. Helvetici 28, 17–86.CrossRefGoogle Scholar
Thom, R. 1956 Un lemme sur les applications différentiables. Bol. Soc. Mat. Mexicana 2, 59–71.Google Scholar
Toro, E.F. 1999 Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer.CrossRefGoogle Scholar
Tran, T., Chakraborty, P., Gioia, G., Steers, S. & Goldburg, W. 2009 Marangoni shocks in unobstructed soap-film flows. Phys. Rev. Lett. 103, 104501.CrossRefGoogle ScholarPubMed
Wantke, K.-D., Fruhner, H. & Örtegren, J. 2003 Surface dilatational properties of mixed Sodium Dodecyl Sulfate/Dodecanol solutions. Colloids Surf. A 221, 185–195.CrossRefGoogle Scholar
Wassermann, G. 1974 Stability of unfoldings, Springer Mathematical Notes, vol. 393. Springer.CrossRefGoogle Scholar
Wen, C.Y., Chang-Jian, S.K. & Chuang, M.C. 2003 Analogy between soap film on one-dimensional motion and gas dynamics. II. Experiments of shock waves in soap films. Exp. Fluids 34, 130–180.Google Scholar
Wen, C.Y. & Lai, J.Y. 2003 Analogy between soap film and gas dynamics. I. Equations and shock jump conditions. Exp. Fluids 34, 107–114.CrossRefGoogle Scholar
Wiggins, S. 2003 Introduction to Applied Nonlinear Dynamical Systems and Chaos. Springer.Google Scholar
Zauderer, E. 2006 Partial Differential Equations of Applied Mathematics. Wiley-Interscience.CrossRefGoogle Scholar