Abstract
The wrinkling law of annular sheet which is induced by capillary force with inner liquid film is analyzed in this paper. The results show that the inner liquid film can wrinkle the annular sheet when the surface tension of the liquid film reaches a critical value, and the critical value can be dramatically altered by changing the geometry and properties of the annular sheet. The results obtained in this article may hold potential applications in generating three-dimensional structures through capillary effects.
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De Gennes P G, Brochard F, Quere D. Capillarity and wetting Phenomena: Drops, Bubbles, Pearls, Waves. New York: Springer, 2003
Zheng Y M, Bai H, Huang Z B, et al. Directional water collection on wetted spider silk. Nature, 2010, 463: 640–643
Kim H Y, Mahadevan L. Capillary rise between elastic sheets. J Fluid Mech, 2006, 548: 141–150
Hu D L, Bush J W M. Meniscus-climbing insects. Nature, 2005, 437: 733–736
Heil M, Hazel A L, Smith J A. The mechanics of airway closure. Respir Physiol Neurbiol, 2008, 163: 214–221
Liu J L, Feng X Q. On elastocapillarity: a review. Acta Mech Sin, 2012, 28(4): 928–940
Roman B, Bico J. Elasto-capillarity: deforming an elastic structure with a liquid droplet. J Phys-Condensed Matter, 2010, 22(49): 493101
Liu J L, Feng X Q, Xia R, et al. Hierarchical capillary adhesion of micro-cantilevers or hairs. J Phys D-Appl Phys, 2007, 40: 5564–5570
Li H, Guo X, Nuzzo R G, et al. Capillary induced self assembly of thin foils into 3D structures. J Mech Phys Solids, 2010, 58: 2033–2042
Yuan Q Z, Zhao Y P. Precursor film in dynamic wetting, electrowetting and electro-elasto-capillarity. Phys Rev Lett, 2010, 104: 246101
Py C, Reverdy P, Doppler L, et al. Capillary origami: spontaneous wrapping of a droplet with an elastic sheet. Phys Rev Lett, 2007, 98: 156103
Chakrapani N, Wei B, Carrillo A, et al. Capillarity-driven assembly of two-dimensional cellular carbon nanotube foams. P Natl Acad Sci USA, 2004, 101: 4009–4012
Wang Z, Wang F C, Zhao Y P. Tap dance of a water droplet. Proc R Soc London Ser A, 2012, 8: 2485–2495
Gao X F, Jiang L. Water-repellent legs of water striders. Nature, 2004, 432: 36
Pokroy B, Kang S H, Mahadevan L, et al. Selforganization of a mesoscale bristle into ordered, hierarchical helical assemblies. Science, 2009, 323: 237–240
Duprat C, Protière S, Beebe A Y, et al. Wetting of flexile fiber arrays. Nature, 2012, 482: 510–513
Bico J, Roman B, Moulin L, et al. Adhesion: elastocapillary coalescence in wet hair. Nature, 2004, 432: 690
Tawfick S, Volder M D, Hart A J. Structurally programmed capillary folding of vertical carbon nanotube assemblies. Langmuir, 2011, 27: 6389–6394
Li B, Cao Y P, Feng X Q, Gao H. Mechanics of morphological instabilities and surface wrinkling in soft materials: A review. Soft Matter, 2012, 8: 5728–5745
King H, Schroll R D, Davidovitch B, et al. Elastic sheet on a liquid drop reveals wrinkling and crumpling as distinct symmetry-breaking instabilities. P Natl Acad Sci USA, 2012, 109: 9716–9720
Yang Y, Gao Y F, Sun DY, et al. Capillary force induced structural deformation in liquid infiltrated elastic circular tubes. Phys Rev B, 2010, 81: 241407
Huang J, Juszkiewicz M, de Jeu W H, et al. Capillary wrinkling of floating thin polymer films. Science, 2007, 317: 650–653
Vella D, Adda-Bedia M, Cerda E. Capillary wrinkling of elastic membranes. Soft Matter, 2010, 6: 5778–5782
Davidovitch B, Schroll R, Vella D, et al. Prototypical model for tensional wrinkling in thin sheets. P Natl Acad Sci USA, 2011, 108: 18227–18232
Davidovitch B, Schroll R, Cerda E. Nonperturbative model for wrinkling in highly bendable sheets. Phys Rev E, 2012, 85: 066115
Schroll R, Adda-Bedia M, Cerda E, et al. Capillary deformations of bendable films. Phys Rev Lett, 2013, 111: 014301
Cerda E. Mechanics of scars. J Biomech Eng, 2005, 38: 1598–1603
Géminard J, Bernal R, Melo F. Wrinkle formations in axi-symme-trically stretched membranes. Eur Phys J E, 2004, 15: 117–126
Pineirua M, Tanaka N, Roman B, et al. Capillary buckling of a floating annulus. Soft Matter, 2013, 9: 10985–10992
Coman C, Haughton D M. On some approximate methods for the tensile instabilities of thin annular plates. J Eng Math, 2006, 56(1): 79–99
Coman C, Haughton D. Localized wrinkling instabilities in radially stretched annular thin films. Acta Mech, 2006, 185: 179–200
Coman C. On the applicability of tension field theory to a wrinkling instability problem. Acta Mech, 2007, 190: 57–72
Cox S, Jones S. Instability of stretched and twisted soap films in a cylinder. J Eng Math, 2013, 0022: 0833
Mansfield E H. The Bending and Stretching of Plates. Cambridge: Cambridge University Press, 1989
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Zhang, B., Li, K. & Zhao, J. Regularity analysis of wrinkles under the action of capillary force in an annular thin film. Sci. China Phys. Mech. Astron. 57, 1574–1580 (2014). https://doi.org/10.1007/s11433-014-5473-6
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DOI: https://doi.org/10.1007/s11433-014-5473-6