Acta Mechanica Solida Sinica

, Volume 25, Issue 5, pp 550–556 | Cite as

Surface Instability of a Swollen Cylinder Hydrogel

  • Zhiping Xiao
  • Meie Li
  • Jinxiong Zhou


Cylinder hydrogel is simple in geometry and easy to synthesize, therefore was widely used to investigate the swelling/shrinking instability of hydrogel and many instability patterns were accumulated in the literature. The mechanism of instability pattern formation of this unique configuration, nevertheless, is far from being fully understood. We applied and extended the recently developed nonlinear theory of polymer gels into cylindrical coordinates, and performed linear perturbation analysis of swelling-induced stability of a constrained cylinder hydrogel. We derived the incremental formulations of stresses and the associated equilibrium equations. We obtained the critical conditions for the onset of instability and probed in details the effects of various parameters on the stability diagram of the hydrogel. The physical meaning of the variation of stability diagram was also interpreted.

Key words

swelling instability hydrogel cylinder perturbation 


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  1. [1]
    Calvert, P., Hydrogels for soft machines. Advanced Materials, 2009, 21: 743–756.CrossRefGoogle Scholar
  2. [2]
    Beebe, D.J., Moore, J.S., Bauer, J.M., Yu, Q., Liu, R.H., Devadoss, C. and Jo, B.H., Functional hydrogel structures for autonomous flow control inside microfluidic channels. Nature, 2000, 406: 588–590.CrossRefGoogle Scholar
  3. [3]
    Dong, L., Agarwal, A.K., Beebe, D.J. and Jiang, H., Adaptive liquid microlenses activated by stimuli-responsive hydrogels. Nature, 2006, 442: 551–554.CrossRefGoogle Scholar
  4. [4]
    Kang, Y., Walish, J.J., Gorishnyy, T. and Thomas, E., Broad-wavelength-range chemically tunable block-copolymer photonic gels. Nature, 2007, Materials 6: 957–960.CrossRefGoogle Scholar
  5. [5]
    Hikmet, R.A.M. and Kemperman, H., Electrically switchable mirrors and optical components made from liquid-crystal gels. Nature, 1998, 392: 476–479.CrossRefGoogle Scholar
  6. [6]
    Tanaka, T., Sun, S.T., Hirokawa, Y., Katayama, S., Kucera, J., Hirose, Y. and Amiya, T., Mechanical instability of gels at the phase transition. Nature, 1987, 325: 796–798.CrossRefGoogle Scholar
  7. [7]
    Eriko Sato Matsuo and Toyoichi Tanaka, Patterns in shrinking gels. Nature, 1992, 358(6): 482–485.CrossRefGoogle Scholar
  8. [8]
    Hajime Tanaka and Tomoo Sigehuzi, Surface-pattern evolution in a swelling gel under a geometrical constraint: Direct observation of fold structure and its coarsening dynamics. Physical Review E, 1994, 49(1): 39–42.CrossRefGoogle Scholar
  9. [9]
    Li, Y., Li, C.F. and Hu, Z.B., Pattern formation of constrained acrylamide/sodium acrylate copolymer gels in acetone/water mixture. Journal of Chemical Physics, 1994, 190(6): 4637–4644.CrossRefGoogle Scholar
  10. [10]
    Bai, G. and Atsushi Suzukia, Phase separation of weakly ionized polymer gels during shrinking phase transition. Journal of Chemical Physics, 1999, 111(22): 10338–10346.CrossRefGoogle Scholar
  11. [11]
    Hajime Tanaka, Hidemi Tomita, Atsunori Takasu, Takafumi Hayashi and Toshio Nishi, Morphological and kinetic evolution of surface patterns in gels during the swelling process: Evidence of dynamic pattern ordering. Physical Review Letters, 1992, 68: 2794–2797.CrossRefGoogle Scholar
  12. [12]
    Suzuki, A., Yoshikawa, S. and Bai, G., Shrinking pattern and phase transition velocity of poly. N-isopropylacrylamide gel. Journal of Chemical Physics, 1999, 111(1): 360–367.CrossRefGoogle Scholar
  13. [13]
    Masayuki Tokita, Keiich Miyamoto and Takashi Komai, Polymer network dynamics in shrinking patterns of gels. Journal of Chemical Physics. 2000, 113(4): 1647–1650.CrossRefGoogle Scholar
  14. [14]
    Eric Sultan1 and Arezki Boudaoud, The buckling of a swollen thin gel layer bound to a compliant substrate. Journal of Applied Mechanics, 2008, 75(05): 051002.CrossRefGoogle Scholar
  15. [15]
    Murat Guvendiren, Jason, A. Burdick and Shu Yang, Kinetic study of swelling-induced surface pattern formation and ordering in hydrogel films with depth-wise crosslinking gradient. Soft Matter, 2010, 6: 2044–2049.CrossRefGoogle Scholar
  16. [16]
    Jinhwan Yoon, Jungwook Kim and Ryan, C.Hayward, Nucleation, growth, and hysteresis of surface creases on swelled polymer gels. Soft Matter, 2010, 6: 5807–5816.CrossRefGoogle Scholar
  17. [17]
    Vero’nica Trujillo, Jungwook Kim and Ryan, C.Hayward, Creasing instability of surface-attached hydrogels, Soft Matter, 2008, 4: 564–569.CrossRefGoogle Scholar
  18. [18]
    Akira Onuki, Phase transition in deformed gels. Journal of the Physical Society of Japan, 1988, 57(3), 699–702.CrossRefGoogle Scholar
  19. [19]
    Akira Onuki, Theory of pattern formation in gels: Surface folding in highly compressible elastic bodies. Phsiycal Review A, 1989, 39(11): 5932–5948.CrossRefGoogle Scholar
  20. [20]
    Akira Onuki, Theory of phase transition in polymer gels. Adbances in Polymer Science, 1993, 109: 63–121.CrossRefGoogle Scholar
  21. [21]
    Hwa, T. and Kardar, M., Evolution of surface patterns on swelling gels. Physical Review Letters, 1988, 61: 106–109.CrossRefGoogle Scholar
  22. [22]
    Sekimoto, K. and Kawasaki, K. Elastic instabilities and phase coexistence of gels. Physica A, 1989, 154: 384–420.CrossRefGoogle Scholar
  23. [23]
    Jun-ichi Maskawa, Toshiki Takeuchi, Kazuo Maki, Kaoru Tsujii and Toyoichi Tanaka, Theory and numerical calculation of pattern formation in shrinking gels. Journal of Chemical Physics, 1999, 110(22), 10993–10999.CrossRefGoogle Scholar
  24. [24]
    Arezki Boudaoud and Sahraoui Chaieb, Mechanical phase diagram of shrinking cylindrical gels. Physical Review E, 2003, 68: 021801.CrossRefGoogle Scholar
  25. [25]
    Hong, W., Zhao, X.H., Zhou, J.X. and Suo, Z.G., A theory of coupled diffusion and large deformation in polymeric gels. Journal of the Mechanics and Physics of Solids. 2008, 56: 1779–1793.CrossRefGoogle Scholar
  26. [26]
    Hong, W., Zhao, X.H. and Suo, Z.G., Formation of creases on the surfaces of elastomers and gels. Applied Physic Letters, 2009. 95(11): 111901–111903.CrossRefGoogle Scholar
  27. [27]
    Hong, W., Liu, Z.S. and Suo, Z.G., Inhomogeneous swelling of a gel in equilibrium with a solvent and mechanical load. International Journal of Solids and Structures, 2009, 46: 3282–3289.CrossRefGoogle Scholar
  28. [28]
    Liu, Z.S, Hong, W., Suo, Z.G., Somsak Swaddiwudhipong and Zhang, Y.W., Modeling and simulation of buckling of polymeric membrane thin film gel. Computational Maials Science, 2010, 49: 60–64.Google Scholar
  29. [29]
    Kang, M.K. and Huang, R., Swell-induced surface instability of confined hydrogel hydrogel layers on substrates. Journal of the Mechanics and Physics of Solids, 2010, 58: 1582–1598.MathSciNetCrossRefGoogle Scholar
  30. [30]
    Zhang, J.P., Zhao, X.H., Suo, Z.G. and Jiang, H.P., A finite element method for transient analysis of concurrent large deformation and mass transport in gels. Journal of Applied Physics, 2009, 105: 093522.CrossRefGoogle Scholar
  31. [31]
    Li, B., Jia, F., Gao, Y.P., Feng, X.Q. and Gao, H., Surface wrinkling patterns on a core-shell soft sphere. Physical Review Letters, 2011, 106: 234301–234304.CrossRefGoogle Scholar
  32. [32]
    Jin, L., Cai, S. and Suo, Z. Creases in soft tissues generated by growth. Europhysics Letters, 2011, 95: 64002.CrossRefGoogle Scholar
  33. [33]
    Biot, M.A., Surface instability of rubber in compression. Applied Scientific Research, 1963, 12(2): 168–182.CrossRefGoogle Scholar
  34. [34]
    Wang, Z. and Zhao, Y., Self-instability and bending behaviors of nano-plates. Acta Mechanica Solida Sinica, 2009, 22: 630–643.MathSciNetCrossRefGoogle Scholar
  35. [35]
    Zhang, Y. and Liu, Y., Local bending of thin film on viscous layer. Acta Mechanica Solida Sinica, 2010, 23: 106–114.CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2012

Authors and Affiliations

  1. 1.State Key Laboratory for Strength and Vibration of Mechanical Structures and School of AerospaceXi’an Jiaotong UniversityXi’anChina
  2. 2.State Key Laboratory for Mechanical Behavior of Materials and School of Materials Science and EngineeringXi’an Jiaotong UniversityXi’anChina

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