Substrate Elastic Deformation Due to Vertical Component of Liquid-Vapor Interfacial Tension

YU Ying-song

doi:10.3879/j.issn.1000-0887.2012.09.001

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YU Ying-song. Substrate Elastic Deformation Due to Vertical Component of Liquid-Vapor Interfacial Tension[J]. Applied Mathematics and Mechanics, 2012, 33(9): 1025-1042. doi: 10.3879/j.issn.1000-0887.2012.09.001

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Substrate Elastic Deformation Due to Vertical Component of Liquid-Vapor Interfacial Tension

doi: 10.3879/j.issn.1000-0887.2012.09.001

YU Ying-song

Department of Engineering Mechanics, School of Civil Engineering and Architecture, Hubei University of Technology, Wuhan 430068, P.R.China

Received Date: 2012-05-08
Rev Recd Date: 2012-05-23
Publish Date: 2012-09-15

Abstract

Abstract

Young’s equation is one of the fundamental equations in capillarity and wetting. However, it just reflected the balance of the horizontal components of the three interfacial tensions with contact angle while there was no description of the vertical component of liquidvapor interfacial tension (VCLVIT). Nowadays, there is a clear consensus that the VCLVIT induces an elastic deformation of the solid substrate, which plays a significant influence on the fabrications of the microfluidic devices because of the wide use of the soft materials. The theoretical, experimental and numerical aspects of the investigations on this problem were reviewed. Moreover, the effects of the VCLVIT-induced surface deformation on wetting and spreading, the deflection of the microcantilever as well as elasto-capillarity and electroelasto-capillarity, were discussed. It seeks to offer not only a brief review of the historical and current advances, but also some suggestions on this problem for further investigations.
- surface deformation,
- vertical component of the liquid-vapor interfacial tension,
- soft substrate,
- contact angle,
- wetting

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References(48)

References

[1]	Bonn D, Eggers J, Indekeu J, Meunier J, Rolley E. Wetting and spreading[J]. Reviews of Modern Physics, 2009, 81(2): 739-805.
[2]	De Gennes P G. Wetting: statics and dynamics[J]. Reviews of Modern Physics, 1985, 57(3): 827-863.
[3]	Adamson A W, Gast A P. Physical Chemistry of Surfaces[M]. 6th Edition. New York: A Wiley-Interscience Publication, 1997.
[4]	Leger L, Joanny J F. Liquid spreading[J]. Reports on Progress in Physics, 1992, 55(4): 431-486.
[5]	Finn R. Equilibrium Capillary Surfaces[M]. New York: Springer, 2005.
[6]	Young T. An essay on the cohesion of fluids[J]. Philosophical Transactions of the Royal Society of London, 1805, 95: 65-87.
[7]	Hondros E D Dr. Thomas Young—natural philosopher[J]. Journal of Materials Science, 2005, 40(9/10): 2119-2123.
[8]	Finn R. The contact angle in capillarity[J]. Physics of Fluids, 2006, 18(4): 047102.
[9]	Maxwell J C. Capillary Action[M]. 9th ed. Encyclopedia Britannica, Inc, 1875: 566.
[10]	De Gennes P G, Brochard-Wyart F, Quéré D. Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves[M]. Berlin: Springer, 2004: 18.
[11]	胡文瑞, 徐硕昌. 微重力流体力学[M]. 北京: 科学出版社, 1999. (HU Wen-rui, XU Shuo-chang. Micro-Gravity Fluid Mechanics[M]. Beijing: Science Press, 1999. (in Chinese))
[12]	Lester G R. Contact angles of liquids at deformable solid surfaces[J]. Journal of Colloid Science, 1961, 16(4): 315-326.
[13]	Rusanov A I. Theory of wetting of elastically deformed bodies—1: deformation with a finite contact-angle[J]. Colloid Journal of the USSR, 1975, 37(4): 614-622. (in Russian)
[14]	Fortes M A. Deformation of solid surfaces due to capillary forces[J]. Journal of Colloid and Interface Science, 1984, 100(1): 17-26.
[15]	Yu Y S, Zhao Y P. Elastic deformation of soft membrane with finite thickness induced by a sessile liquid droplet[J]. Journal of Colloid and Interface Science, 2009, 339(2): 489-494.
[16]	Liu J L, Nie Z X, Jiang W G. Deformation field of the soft substrate induced by capillary force[J]. Physica B, 2009, 404(8/11): 1195-1199.
[17]	Shanahan M E R, De Gennes P G. Equilibrium of the triple line solid/liquid/fluid of a sessile drop[C]Allen K W. Adhesion. London: Elsevier Applied Science, 1987: 71-81.
[18]	Shanahan M E R, Carré A. Spreading and dynamics of liquid drops involving nanometric deformations on soft substrates[J]. Colloids and Surfaces A, 2002, 206(1/3): 115-123.
[19]	Shanahan M E R, Carré A. Nanometric solid deformation of soft materials in capillary phenomena[C]Rosoff M. Nano-Surface Chemistry. New York: Marcel Dekker Inc, 2002.
[20]	White L R. The contact angle on the elastic substrate—1: the role of disjoining pressure in the surface mechanics[J]. Journal of Colloid and Interface Science, 2003, 258(1): 82-96.
[21]	Das S, Marchand A, Andreotti B, Snoeijer J H. Elastic deformation due to tangential capillary forces[J]. Physics of Fluids, 2011, 23(7): 072006.
[22]	Kern R, Müller P. Deformation of an elastic thin solid induced by a liquid droplet [J]. Surface Science, 1992, 264(3): 467-494.
[23]	Treloar L R G. The Physics of Rubber Elasticity[M]. Oxford: Clarendon, 1949: 66.
[24]	Shanahan M E R. The influence of solid micro-deformation on contact angle equilibrium[J]. Journal of Physics D: Applied Physics, 1987, 20(7): 945-950.
[25]	Shanahan M E R. Statics and dynamics of wetting on thin solids[J]. Revue de Physique Appliquée, 1988, 23(6): 1031-1037.
[26]	Shanahan M E R. The spreading dynamics of a liquid drop on a viscoelastic solid [J]. Journal of Physics D: Applied Physics, 1988, 21(6): 981-985.
[27]	Carré A, Shanahan M E R. Direct evidence for viscosity-independent spreading on a soft solid[J]. Langmuir, 1995, 11(1): 24-26.
[28]	Shanahan M E R, Carré A. Viscoelastic dissipation in wetting and adhesion phenomena[J]. Langmuir, 1995, 11(4): 1396-1402.
[29]	Carré A, Gastel J C, Shanahan M E R. Viscoelastic effects in the spreading of liquids[J]. Nature, 1996, 379(6564): 432-434.
[30]	Carré A, Shanahan M E R. Effect of cross-linking on the dewetting of an elastomeric surface[J]. Journal of Colloid and Interface Science, 1997, 191(1): 141-145.
[31]	Long D, Ajdari A, Leibler L. Static and dynamic wetting properties of thin rubber films[J]. Langmuir, 1996, 12(21): 5221-5230.
[32]	Andrade J D, King R N, Gregonis D E, Coleman D L. Surface characterization of poly(hydroxyethyl methacrylate) and related polymers—Ⅰ: contact angle methods in water[J]. Journal of Polymer Science: Polymer Symposium, 1979, 66(1): 313-336.
[33]	Métois J J. Elastic straining of a thin graphite layer by a liquid droplet or a non-epitaxed Pb crystallite[J]. Surface Science, 1991, 241(3): 279-288.
[34]	Extrand C W, Kumagai Y. Contact angle and hysteresis on soft surfaces[J]. Journal of Colloid and Interface Science, 1996, 184(1): 191-200.
[35]	Saiz E, Tomsia A P, Cannon R M. Ridging effects on wetting and spreading of liquids on solids[J]. Acta Materialia, 1998, 46(7): 2349-2361.
[36]	Pu G, Guo J H, Gwin L E, Severtson S J. Mechanical pinning of liquids through inelastic wetting ridge formation on thermally stripped acrylic polymers[J]. Langmuir, 2007, 23(24): 12142-12146.
[37]	Pericet-Cmara R, Auernhammer G K, Koynov K, Lorenzoni S, Raiteri R, Bonaccurso E. Solid-supported thin elastomer films deformed by microdrops[J]. Soft Matter, 2009, 5(19): 3611-3617.
[38]	Pericet-Cámara R, Best A, Butt H J, Bonaccurso E. Effect of capillary pressure and surface tension on the deformation of elastic surfaces by sessile liquid microdrops: an experimental investigation[J]. Langmuir, 2008, 24(19): 10565-10568.
[39]	Jerison E R, Xu Y, Wilen L A, Dufresne E R. Deformation of an elastic substrate by a three-phase contact line[J]. Physical Review Letters, 2011, 106(18): 186103.
[40]	Saiz E, Cannon R M, Tomsia A P. Reactive spreading: adsorption, ridging and compound formation[J]. Acta Materialia, 2000, 48(18/19): 4449-4462.
[41]	Madasu S, Cairncross R A. Static wetting on flexible substrates: a finite element formulation[J]. International Journal for Numerical Methods in Fluids, 2004, 45(3): 301-319.
[42]	Yu Y S, Yang Z Y, Zhao Y P. Role of vertical component of surface tension of the droplet on the elastic deformation of PDMS membrane[J]. Journal of Adhesion Science and Technology, 2008, 22(7): 687-698.
[43]	Yu Y S, Zhao Y P. Deformation of PDMS membrane and microcantilever by a water droplet: comparison between Mooney-Rivlin and linear elastic constitutive models[J]. Journal of Colloid and Interface Science, 2009, 332(2): 467-476.
[44]	王奉超. 纳尺度固液界面力学中的边界滑移与接触角滞后[D]. 北京：中国科学院力学研究所博士学位论文, 2012.(WANG Feng-chao. Boundary slip and contact angle hysteresis in the nanoscale liquid-interfacial mechanics[D]. Ph D Dissertation. Beijing: Graduate University of Chinese Academy of Sciences, 2012.(in Chinese))
[45]	Rugar D, Hansma P. Atomic force microscopy[J]. Physics Today, 1990, 43(10): 23-30.
[46]	Dimitriadis E K, Horkay F, Maresca J, Kachar B, Chadwick R S. Determination of elastic moduli of thin layers of soft material using the atomic force microscopy [J]. Biophysical Journal, 2002, 82(5): 2798-2810.
[47]	Magonov S N, Reneker D H. Characterization of polymer surfaces with atomic force microscopy[J]. Annual Review of Materials Science, 1997, 27: 175-222.
[48]	Zhao L M, Schaefer D, Marten M R. Assessment of elasticity a