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The European Physical Journal E

, Volume 20, Issue 2, pp 119–124 | Cite as

Buckling of swelling gels

  • T. Mora
  • A. Boudaoud
Regular Article

Abstract.

The patterns arising from the differential swelling of gels are investigated experimentally and theoretically as a model for the differential growth of living tissues. Two geometries are considered: a thin strip of soft gel clamped to a stiff gel, and a thin corona of soft gel clamped to a disk of stiff gel. When the structure is immersed in water, the soft gel swells and bends out of plane leading to a wavy periodic pattern whose wavelength is measured. The linear stability of the flat state is studied in the framework of linear elasticity using the equations for thin plates. The flat state is shown to become unstable to oscillations above a critical swelling rate and the computed wavelengths are in quantitative agreement with the experiment.

PACS.

46.32.+x Static buckling and instability 61.41.+e Polymers, elastomers, and plastics 87.18.La Morphogenesis 68.35.Gy Mechanical properties; surface strains 

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References

  1. 1.
    C.R. Steele, J. Appl. Mech. 67, 237 (2000).CrossRefGoogle Scholar
  2. 2.
    P. Shipman, A. Newell, Phys. Rev. Lett. 92, 168102 (2004).CrossRefADSGoogle Scholar
  3. 3.
    E. Sharon, B. Roman, M. Marder, G.S. Shin, H.L. Swinney, Nature 419, 579 (2002).CrossRefADSGoogle Scholar
  4. 4.
    B. Audoly, A. Boudaoud, Phys. Rev. Lett. 91, 086105 (2003).CrossRefADSGoogle Scholar
  5. 5.
    A. Boudaoud, Phys. Rev. Lett. 91, 018104 (2003).CrossRefADSGoogle Scholar
  6. 6.
    E. Brouzès, E. Farge, Curr. Opin. Gen. Dev. 14, 367 (2004).CrossRefGoogle Scholar
  7. 7.
    M. Ben Amar, A. Goriely, J. Mech. Phys. Solids 53, 2284 (2005).MathSciNetCrossRefGoogle Scholar
  8. 8.
    T. Tanaka, Phys. Rev. A 17, 763 (1978).MathSciNetCrossRefADSGoogle Scholar
  9. 9.
    T. Tanaka, D. Fillmore, S.-T. Sun, I. Nishio, G. Swislow, A. Shah, Phys. Rev. Lett. 45, 1636 (1980).CrossRefADSGoogle Scholar
  10. 10.
    T. Tanaka, I. Nishio, S.-T. Sun, S. Ueno-Nishio, Science 218, 467 (1982).ADSGoogle Scholar
  11. 11.
    S. Juodkazis, N. Mukai, R. Wakaki, A. Yamaguchi, S. Matsuo, H. Misawa, Nature 408, 178 (2000).CrossRefADSGoogle Scholar
  12. 12.
    A. Boudaoud, S. Cha\"ıeb, Phys. Rev. E 68, 021801 (2003).CrossRefADSGoogle Scholar
  13. 13.
    T. Tanaka, S.-T. Sun, Y. Hirokawa, S. Katayama, J. Kucera, Y. Hirose, T. Amiya, Nature 325, 796 (1987).CrossRefADSGoogle Scholar
  14. 14.
    T. Hwa, M. Kardar, Phys. Rev. Lett. 61, 106 (1988).CrossRefADSGoogle Scholar
  15. 15.
    A. Onuki, Phys. Rev. A 39, 5932 (1989).CrossRefADSGoogle Scholar
  16. 16.
    N. Suematsu, K. Sekimoto, K. Kawasaki, Phys. Rev. A 41, 5751 (1990).CrossRefADSGoogle Scholar
  17. 17.
    H. Tanaka, H. Tomita, A. Takatsu, T. Hayashi, T. Nishi, Phys. Rev. Lett. 68, 2794 (1992).CrossRefADSGoogle Scholar
  18. 18.
    N. Bowden, S. Brittain, A.G. Evans, J.W. Hutchinson, G.M. Whitesides, Nature 393, 146 (1998).CrossRefADSGoogle Scholar
  19. 19.
    N. Bowden, W.T.S. Huck, K.E. Paul, G.M. Whitesides, Appl. Phys. Lett. 75, 2557 (1999).CrossRefADSGoogle Scholar
  20. 20.
    J.S. Sharp, R.A.L. Jones, Phys. Rev. E 68, 011801 (2002).MathSciNetCrossRefADSGoogle Scholar
  21. 21.
    S. Joon Kwon, Jae-Gwan Park, J. Chem. Phys. 122, 031101 (2005).CrossRefGoogle Scholar
  22. 22.
    P.J. Yoo, K.Y. Suh, H. Kang, H.H. Lee, Phys. Rev. Lett. 93, 034301 (2005).CrossRefADSGoogle Scholar
  23. 23.
    T. Ohzono, M. Shimomura, Phys. Rev. E. 72, 023203(R) (2005).CrossRefGoogle Scholar
  24. 24.
    Y. Li, C. Li, Z. Hu, J. Chem. Phys. 100, 4637 (1994).CrossRefADSGoogle Scholar
  25. 25.
    L. Landau, E. Lifchitz, Théorie de l'élasticité (Mir, Moscou, 1990).Google Scholar
  26. 26.
    P. Manneville, Dissipative Structures and Weak Turbulence (Academic Press, New York, 1990).Google Scholar

Copyright information

© EDP Sciences, Società Italiana di Fisica and Springer-Verlag 2006

Authors and Affiliations

  • T. Mora
    • 1
  • A. Boudaoud
    • 1
  1. 1.Laboratoire de Physique Statistique de l'École Normale SupérieureParis Cedex 05France

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