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.
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References
C.R. Steele, J. Appl. Mech. 67, 237 (2000).
P. Shipman, A. Newell, Phys. Rev. Lett. 92, 168102 (2004).
E. Sharon, B. Roman, M. Marder, G.S. Shin, H.L. Swinney, Nature 419, 579 (2002).
B. Audoly, A. Boudaoud, Phys. Rev. Lett. 91, 086105 (2003).
A. Boudaoud, Phys. Rev. Lett. 91, 018104 (2003).
E. Brouzès, E. Farge, Curr. Opin. Gen. Dev. 14, 367 (2004).
M. Ben Amar, A. Goriely, J. Mech. Phys. Solids 53, 2284 (2005).
T. Tanaka, Phys. Rev. A 17, 763 (1978).
T. Tanaka, D. Fillmore, S.-T. Sun, I. Nishio, G. Swislow, A. Shah, Phys. Rev. Lett. 45, 1636 (1980).
T. Tanaka, I. Nishio, S.-T. Sun, S. Ueno-Nishio, Science 218, 467 (1982).
S. Juodkazis, N. Mukai, R. Wakaki, A. Yamaguchi, S. Matsuo, H. Misawa, Nature 408, 178 (2000).
A. Boudaoud, S. Cha\"ıeb, Phys. Rev. E 68, 021801 (2003).
T. Tanaka, S.-T. Sun, Y. Hirokawa, S. Katayama, J. Kucera, Y. Hirose, T. Amiya, Nature 325, 796 (1987).
T. Hwa, M. Kardar, Phys. Rev. Lett. 61, 106 (1988).
A. Onuki, Phys. Rev. A 39, 5932 (1989).
N. Suematsu, K. Sekimoto, K. Kawasaki, Phys. Rev. A 41, 5751 (1990).
H. Tanaka, H. Tomita, A. Takatsu, T. Hayashi, T. Nishi, Phys. Rev. Lett. 68, 2794 (1992).
N. Bowden, S. Brittain, A.G. Evans, J.W. Hutchinson, G.M. Whitesides, Nature 393, 146 (1998).
N. Bowden, W.T.S. Huck, K.E. Paul, G.M. Whitesides, Appl. Phys. Lett. 75, 2557 (1999).
J.S. Sharp, R.A.L. Jones, Phys. Rev. E 68, 011801 (2002).
S. Joon Kwon, Jae-Gwan Park, J. Chem. Phys. 122, 031101 (2005).
P.J. Yoo, K.Y. Suh, H. Kang, H.H. Lee, Phys. Rev. Lett. 93, 034301 (2005).
T. Ohzono, M. Shimomura, Phys. Rev. E. 72, 023203(R) (2005).
Y. Li, C. Li, Z. Hu, J. Chem. Phys. 100, 4637 (1994).
L. Landau, E. Lifchitz, Théorie de l'élasticité (Mir, Moscou, 1990).
P. Manneville, Dissipative Structures and Weak Turbulence (Academic Press, New York, 1990).
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Mora, T., Boudaoud, A. Buckling of swelling gels. Eur. Phys. J. E 20, 119–124 (2006). https://doi.org/10.1140/epje/i2005-10124-5
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DOI: https://doi.org/10.1140/epje/i2005-10124-5