LÜ Cun-jing, YIN Ya-jun, ZHENG Quan-shui. Nonlinear Effects of Line Tension in Adhesion of Small Droplets[J]. Applied Mathematics and Mechanics, 2008, 29(10): 1135-1146.
Citation: LÜ Cun-jing, YIN Ya-jun, ZHENG Quan-shui. Nonlinear Effects of Line Tension in Adhesion of Small Droplets[J]. Applied Mathematics and Mechanics, 2008, 29(10): 1135-1146.

Nonlinear Effects of Line Tension in Adhesion of Small Droplets

  • Received Date: 2008-09-02
  • Rev Recd Date: 2008-09-16
  • Publish Date: 2008-10-15
  • Three-phase line tensions may become crucial in the adhesion of micro-nano or small droplets on solid planes.For the first time the nonlinear effects in adhesion spanned the full physically possible parameter ranges of surface tensions,line tensions,and droplet sizes are studied.It is shown that the nonlinear adhesion solution spaces can be characterized into four districts.Within each district the adhesion behaves essentially the same.Especially,inside the characteristic districts with violent nonlinearities,the co-existence of multiple adhesion states for given materials is disclosed.Besides, two common fixed points in the solution space are revealed.The above new results are consistent with numerical analysis and experimental observations in the literatures.
  • loading
  • [1]
    Boal D.Mechanics of the Cell[M].Cambridge:Cambridge University Press,2002.
    Seifert U.Configurations of fluid membranes and vesicles[J].Adv Phys,1997,46(1):13-137. doi: 10.1080/00018739700101488
    Lipowsky R,Lenz P,Swain P S.Wetting and dewetting of structured and imprinted surfaces[J].Colloids Surf,A,2000,161(1):3-22. doi: 10.1016/S0927-7757(99)00321-0
    de Gennes P G.Wetting:statics and dynamics[J].Rev Mod Phys,1985,57(3):827-863. doi: 10.1103/RevModPhys.57.827
    Sackmann E.Supported membranes[J].Scientific and Practical Applications Science,1996,271(5245):43-48.
    Nealey P F,Black A J,Wilbur J L,et al.Molecular Electronics[M].Oxford:Blackwell Science,1997.
    Liu X H,Ross F M,Schwarz K W.Dislocated epitaxial islands[J].Phys Rev Lett,2000,85(19):4088-4091. doi: 10.1103/PhysRevLett.85.4088
    Mendez-Villuendas E,Bowles R K.Surface nucleation in the freezing of gold nanoparticles[J].Phys Rev Lett,2007,98(18):185503. doi: 10.1103/PhysRevLett.98.185503
    Peters R,Yang X,Kim T,et al.Using self-assembled monolayers exposed to X-rays to control the wetting behavior of thin films of diblock copolymers[J].Langmuir,2000,16(10):4625-4631. doi: 10.1021/la991500c
    Lopes W,Jaeger H.Lopes-hierarchical self-assembly of metal nanostructures on diblock copolymer scaffolds[J].Nature,2001,414(6865):735-738. doi: 10.1038/414735a
    Whitesides G,Stroock A.Flexible methods for microfluidics[J].Phys Today,2001,54(6):42-48.
    Zheng Q S,Yu Y,Zhao Z H.Effects of hydraulic pressure on the stability and transition of wetting modes of superhydrophobic surfaces[J].Langmuir,2005,21(26):12207-12212. doi: 10.1021/la052054y
    Gibbs J W.The Scientific Papers[M].New York:Dover,1961.
    Yutaka S,Nobuyuki M,Tsutomu H,et al.Self-running droplet:emergence of regular motion from nonequilibrium noise[J].Phys Rev Lett,2005,94(6):068301. doi: 10.1103/PhysRevLett.94.068301
    Drelich J.The significance and magnitude of the line tension in three-phase (solid-liquid-fluid) systems[J].Colloids Surf,A,1996,116(1/2):43-54. doi: 10.1016/0927-7757(96)03651-5
    Li D.Drop size dependence of contact angles and line tensions of solid-liquid systems[J].Colloids Surf,A,1996,116(1/2):1-23. doi: 10.1016/0927-7757(96)03582-0
    Li D,Steigmann D J.Positive line tension as a requirement of stable equilibrium[J].Colloids Surf,A,1996,116(1/2):25-30. doi: 10.1016/0927-7757(96)03583-2
    Amirfazli A,Neumann A W.Status of the three-phase line tension:a review[J].Advance in Colloid and Interface Science,2004,110(3):121-141. doi: 10.1016/j.cis.2004.05.001
    Widom B.Line tension and the shape of a sessile drop[J].J Phys Chem,1995,99(9):2803-2806. doi: 10.1021/j100009a041
    Rosso R,Virga E G.Local stability for a general wetting functional[J].J Phys A:Math Gen,2004,37(13):3989-4015. doi: 10.1088/0305-4470/37/13/006
    Guzzardi L,Rosso R.Sessile droplets on a curved substrate:effects of line tension[J].J Phys A:Math Theor,2007,40(1):19-46. doi: 10.1088/1751-8113/40/1/002
    Rosso R,Virga E G.General stability criterion for wetting[J].Phys Rev E,2003,68(1):012601. doi: 10.1103/PhysRevE.68.012601
    Guzzardi L,Rosso R,Virga E G.Residual stability of sessile droplets with negative line tension[J].Phys Rev E,2006,73(2):021602. doi: 10.1103/PhysRevE.73.021602
    Rosso R,Virga E G.Sign of line tension in liquid bridge stability[J].Phys Rev E,2004,70(3):031603. doi: 10.1103/PhysRevE.70.031603
    Lenz P,Lipowsky R.Morphological transitions of wetting layers on structured surfaces[J].Phys Rev Lett,1998,80(9):1920-1923. doi: 10.1103/PhysRevLett.80.1920
    Blecua P,Lipowsky R,Kierfeld J.Line tension effects for liquid droplets on circular surface domains[J].Langmuir,2006,22(26):11041-11059. doi: 10.1021/la0609773
    Brinkmann M,Kierfeld J,Lipowsky R.A general stability criterion for droplets on structured substrates[J].J Phys A:Math Gen,2004,37(48):11547-11573. doi: 10.1088/0305-4470/37/48/003
    Swain P S,Lipowsky R.Contact angles on heterogeneous surfaces:a new look at Cassie's and Wenzel's laws[J].Langmuir,1998,14(23):6772-6780. doi: 10.1021/la980602k
    Pompe T,Herminghaus S.Three-phase contact line energetics from nanoscale liquid surface topographies[J].Phys Rev Lett,2000,85(9):1930-1933. doi: 10.1103/PhysRevLett.85.1930
    Baumgart T,Hess S T,Webb W W.Imaging coexisting fluid domains in biomembrane models coupling curvature and line tension[J].Nature,2003,425(6960):821-824. doi: 10.1038/nature02013
    Akimov S A,Kuzmin P I,Zimmerberg J,et al.An elastic theory for line tension at a boundary separating two lipid monolayer regions of different thickness[J].J Electroanalytical Chemistry,2004,564:13-18. doi: 10.1016/j.jelechem.2003.10.030
    Kang K H,Kang Is,Lee C M.Electrostatic contribution to line tension in a wedge-shaped contact region[J].Langmuir,2003,19(22):9334-9342. doi: 10.1021/la034539x
    Churaev N V,Starov V M,Derjaguin B V.The shape of the transition zone between a thin film and bulk liquid and the line tension[J].J Colloid Interface Sci,1982,89(1):16-24.[JP2]. Sagis L M C,Slattery J C.Incorporation of line quantities in the continuum description for muitiphase,multiphase,multicomponent bodies with intersecting dividing surfaces—Ⅲ Determination of line tension and fluid-solid surface tensions using small sessile drops[J].J Colloid Interface Sci,1995,176(1):173-182. doi: 10.1006/jcis.1995.0020
    Hoorfar M,Amirfazli A,Gaydos J A,et al.The effects of line tension on the shape of liquid menisci near stripwise heterogeneous walls[J].Advances in Colloid and Interface Science,2005,114/115:103-118. doi: 10.1016/j.cis.2004.06.004
    Bier M,Chen W,Gowrishankar T R,et al.Resealing dynamics of a cell membrane after electroporation[J].Phys Rev E,2002,66(6):062905. doi: 10.1103/PhysRevE.66.062905
    Pompe T.Line tension behavior of a first-order wetting system[J].Phys Rev Lett,2002,89(7):076102. doi: 10.1103/PhysRevLett.89.076102
    Aiwei T,Johnson C,Wang Z W,et al.Line tension at fluid membrane domain boundaries measured by micropipette aspiration[J].Phys Rev Lett,2007,98(20):208102. doi: 10.1103/PhysRevLett.98.208102
    Drelich J,Wilbur J L,Miller J D,et al.Contact angles for liquid drops at a model heterogeneous surface consisting of alternating and parallel hydrophobic/hydrophilic strips[J].Langmuir,1996,12(7):1913-1922. doi: 10.1021/la9509763
    Yongan G.Drop size dependence of contact angles of oil drops on a solid surface in water[J].Colloids Surf A,2001,181(1/3):215-224. doi: 10.1016/S0927-7757(00)00804-9
    Amirfazli A,Keshavarz A,Zhang L,et al.Determination of line tension for systems near wetting[J].J Colloid Interface Sci,2003,265(1):152-160. doi: 10.1016/S0021-9797(03)00521-6
    Chen P,Susnar S S,Amirfazli A,et al.Line tension measurements:an application of the quadrilateral relation to a liquid lens system[J].Langmuir,1997,13(11):3035-3042. doi: 10.1021/la961077x
    Rodrigues J F,Saramago B,Fortes M A.Apparent contact angle and triple-line tension of a soap bubble on a substrate[J].J Colloid Interface Sci,2001,239(2):577-580. doi: 10.1006/jcis.2001.7578
    Vera-Graziano R,Muhl S,Rivera-Torres F.The effect of illumination on contact angles of pure water on crystalline silicon[J].J Colloid Interface Sci,1995,170(2):591-597. doi: 10.1006/jcis.1995.1139
    Amirfazli A,Chatain D,Neumann A W.Drop size dependence of contact angles for liquid tin on silica surface:line tension and its correlation with solid-liquid interfacial tension[J].Colloid Surf A,1998,142(2/3):183-188. doi: 10.1016/S0927-7757(98)00265-9
    Wang J Y,Betelu S,Law B M.Line tension effects near first-order wetting transitions[J].Phys Rev Lett,1999,83(18):3677-3680. doi: 10.1103/PhysRevLett.83.3677
    Dussaud A,Vignes-Adler M.Wetting transition of n-alkanes on concentrated aqueous salt solutions,line tension effect[J].Langmuir,1997,13(3):581-589. doi: 10.1021/la951508w
    Stckelhuber K W,Radoev B,Schulze H J.Some new observations on line tension of microscopic droplets[J].Colloids Surf A,1999,156(1/3):323-333. doi: 10.1016/S0927-7757(99)00084-9
  • 加载中


    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (2606) PDF downloads(673) Cited by()
    Proportional views


    DownLoad:  Full-Size Img  PowerPoint