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Bursting of a soap film in a viscous environment

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  • Joanny, J.-F.
  • De Gennes, P.G.

Abstract

In a dense (polyhedral) O/W emulsion the oil droplets are separated by thin films of water. If at time t = 0, one film is broken locally, it shrinks and the zone of direct contact between the two oil droplets expands, with a growing radius R(t). The analog bursting of a soap films in air was studied long ago by Mysels and coworkers. But the presence of the viscous oil should slow down the process, and suppress the shock wave aspects which are often present in air. We assume first that the surfactant is strictly insoluble in oil and we discuss two regimes: (I) The water film is at the midplane of a slab of oil, bounded by solid walls: then we expect R(t)∼t12 even if non-linearities (due to the Langmuir equation of state of the monolayers) are incorporated. (II) With a very large slab of oil (or with two large oil droplets) we are led to R(t)∼34. Regime II would be realize in dense emulsions, but regime I is probably more interesting for fundamental studies on the rheology of monolayers. Finally, when the surfactant is slightly soluble in oil, we predict R(t)∼t34 in case I, and R(t)∼t in case II.

Suggested Citation

  • Joanny, J.-F. & De Gennes, P.G., 1987. "Bursting of a soap film in a viscous environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 147(1), pages 238-255.
    • Handle: RePEc:eee:phsmap:v:147:y:1987:i:1:p:238-255
    DOI: 10.1016/0378-4371(87)90108-7
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    Cited by:

    1. Ruiz-Garcia, Jaime & Gámez-Corrales, Rogelio & Ivlev, Boris I., 1997. "Foam and cluster structure formation by latex particles at the air/water interface," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 236(1), pages 97-104.
    2. Kumar, Sanjay & Singh, Yashwant, 1996. "On the critical behaviour of a surface interacting linear polymer chain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 229(1), pages 61-71.
    3. Möhwald, H. & Kenn, R.M. & Degenhardt, D. & Kjaer, K. & Als-Nielsen, J., 1990. "Partial order in phospholipid monolayers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 168(1), pages 127-139.
    4. Chowdhury, Debashish & Stauffer, Dietrich, 1992. "Bursting of soap films," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 186(1), pages 237-249.
    5. Onuki, Akira, 1995. "Interface instability induced by an electric field in fluids," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 217(1), pages 38-52.
    6. Elezović-Hadžić, Sunčica & Knežević, Milan, 1996. "Critical exponents of surface-interacting self-avoiding walks on a family of truncated n-simplex lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 227(3), pages 213-233.
    7. Kawaguchi, Masami & Makino, Kyoko & Kato, Tadaya, 1997. "Viscous fingering patterns of silica suspensions in polymer solutions: effects of viscoelasticity and gravity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(3), pages 385-398.
    8. Aharonson, Vered & Andelman, David & Zilman, Anton & Pincus, Philip A. & Raphaël, Elie, 1994. "Polymer adsorption at liquid/air interfaces under lateral pressure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 204(1), pages 1-16.

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