Journal of Engineering Mathematics

, Volume 86, Issue 1, pp 1–7 | Cite as

Instability of stretched and twisted soap films in a cylinder

Article

Abstract

A soap film, or a flexible area-minimizing membrane without bending and torsional stiffness, that is confined in a cylinder is shown to be susceptible to a surface-tension-driven instability when it is stretched or twisted. This leads to its breakdown and places an upper limit on the aspect ratio of such structures. A simple analysis confirms the values for the critical aspect ratio of the stretched film found in both simulations and experiments on soap films, and this threshold decreases with increasing twist of the film.

Keywords

Elastic membranes Soap films Surface-tension-driven instability Surface Evolver 

References

  1. 1.
    Isenberg C (1992) The science of soap films and soap bubbles. Dover, New YorkGoogle Scholar
  2. 2.
    Cox SJ, Weaire D, Vaz MF (2002) The transition from two-dimensional to three-dimensional foam structures. Eur Phys J E 7:311–315Google Scholar
  3. 3.
    Weaire D, Vaz MF, Teixeira PIC, Fortes MA (2007) Instabilities in liquid foams. Soft Matter 3:47–57ADSCrossRefGoogle Scholar
  4. 4.
    Plateau JAF (1873) Statique expérimentale et théorique des Liquides Soumis aux Seules Forces Moléculaires. Gauthier–Villars, ParisGoogle Scholar
  5. 5.
    Taylor JE (1976) The structure of singularities in soap-bubble-like and soap-film-like minimal surfaces. Ann Math 103:489–539CrossRefMATHGoogle Scholar
  6. 6.
    Weaire D, Hutzler S (1999) The physics of foams. Clarendon Press, OxfordGoogle Scholar
  7. 7.
    Cantat I, Cohen-Addad S, Elias F, Graner F, Höhler R, Pitois O, Rouyer F, Saint-Jalmes A (2010) Les mousses—structure et dynamique. Belin, ParisGoogle Scholar
  8. 8.
    Brakke K (1992) The surface evolver. Exp Math 1:141–165CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    Brakke K (1996) The surface evolver and the stability of liquid surfaces. Phil Trans R Soc A 354:2143–2157ADSCrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Reinelt D, Boltenhagen P, Rivier N (2001) Deformed foam structure and transitions in a tube. Eur Phys J E 4:299–304CrossRefGoogle Scholar
  11. 11.
    Kern N, Weaire D (2003) Approaching the dry limit in foam. Phil Mag 83:2973–2987ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Institute of Mathematics and PhysicsAberystwyth UniversityAberystwythUK
  2. 2.Laboratoire de Physique des SolidesUniversité Paris SudOrsayFrance

Personalised recommendations