液气界面张力垂直分量引起的基底弹性变形

余迎松

doi:10.3879/j.issn.1000-0887.2012.09.001

液气界面张力垂直分量引起的基底弹性变形

doi: 10.3879/j.issn.1000-0887.2012.09.001

余迎松

湖北工业大学土木工程与建筑学院,武汉 430068

基金项目: 国家自然科学基金资助项目(11002051)

详细信息

通讯作者:
余迎松(1979—),男,湖北黄冈人,博士(E-mail: wetting.yu@gmail.com).

中图分类号: O343.2
计量
- 文章访问数: 2280
- HTML全文浏览量: 138
- PDF下载量: 1836
- 被引次数: 0
出版历程
- 收稿日期: 2012-05-08
- 修回日期: 2012-05-23
- 刊出日期: 2012-09-15

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

YU Ying-song

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

摘要

摘要: Young方程是毛细理论和润湿的重要方程之一．但是，该方程只描述了3个界面张力的水平分量之间的平衡与接触角的关系，而对液气界面张力垂直分量未作任何描述．现在，随着软材料的广泛应用，该垂直分量将引起基底的表面变形，并在微流体系统的制造过程中起到重要作用，这已是该研究领域的共识．综述了关于表面变形这一问题在理论分析，实验研究和数值模拟等方面取得的进展．而且，还讨论了由垂直分量引起的表面变形对液滴润湿和铺展行为、微悬臂梁的弯曲、弹性毛细现象、电弹性毛细现象等的影响．不仅对该问题的历史发展和目前的研究进展进行了简单的综述，并且也针对后续的研究提出了几点建议．
- 表面变形 /
- 液气界面张力垂直分量 /
- 软基底 /
- 接触角 /
- 润湿
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

HTML全文

参考文献(48)

[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