Substrate elastic deformation due to vertical component of liquid-vapor interfacial tension

Applied Mathematics and Mechanics (English Edition)

Volumn 33, Issue 9, 2012, Pages 1095-1114

  Yu, Ying Song ^a  

^a HUBEI UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Contact angle (CA); Liquid vapor interfacial tension; Soft substrate; Surface deformation; Vertical component; Wetting

Indexed keywords

FUNDAMENTAL EQUATIONS; HISTORICAL DEVELOPMENT; LIQUID-VAPOR; MICRO-CANTILEVERS; MICRO-FLUIDIC DEVICES; NUMERICAL ASPECTS; SOFT MATERIAL; SOFT SUBSTRATES; SOLID SUBSTRATES; SURFACE DEFORMATION; VERTICAL COMPONENT; YOUNG'S EQUATION;

CAPILLARITY; CONTACT ANGLE; ELASTIC DEFORMATION; WETTING;

VAPORS;

EID: 84867219792     PISSN: 02534827     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10483-012-1608-x     Document Type: Article

References (76)

1. Bonn, D., Eggers, J., Indekeu, J., Meunier, J., and Rolley, E. Wetting and spreading. Reviews of Modern Physics, 81(2), 739-805 (2009)
2. De Gennes, P. G. Wetting: statics and dynamics. Reviews of Modern Physics, 57(3), 827-863 (1985)
3. Adamson, A. W. and Gast, A. P. Physical Chemistry of Surfaces, 6th ed., Wiley, New York (1997)
4. Leger, L. and Joanny, J. F. Liquid spreading. Reports on Progress in Physics, 55(4), 431-486 (1992)
5. Finn, R. Equilibrium Capillary Surfaces, Springer, New York (1986)
6. Young, T. An essay on the cohesion of fluids. Philosophical Transactions of the Royal Society of London, 95, 65-87 (1805)
7. Hondros, E. D. Dr. Thomas Young-natural philosopher. Journal of Materials Science, 40(9-10), 2119-2123 (2005)
8. Finn, R. The contact angle in capillarity. Physics of Fluids, 18(4), 047102 (2006)
9. Maxwell, J. C. The Encyclopedia Britannica: Capillary Action, 9th ed., Encyclopedia Britannica, Inc., London, 566 (1875)
10. De Gennes, P. G., Brochard-Wyart, F., and Quéré, D. Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves, Springer, Berlin (2004)
11. Hu,W. R. and Xu, S. C. Microgravity Fluid Mechanics (in Chinese), Science Press, Beijing (1999)
12. Lester, G. R. Contact angles of liquids at deformable solid surfaces. Journal of Colloid Science, 16(4), 315-326 (1961)
13. Rusanov, A. I. Theory of wetting of elastically deformed bodies, 1. deformation with a finite contact-angle (in Russian). Colloid Journal of the USSR, 37(4), 614-622 (1975)
14. Fortes, M. A. Deformation of solid surfaces due to capillary forces. Journal of Colloid and Interface Science, 100(1), 17-26 (1984)
15. Yu, Y. S. and Zhao, Y. P. Elastic deformation of soft membrane with finite thickness induced by a sessile liquid droplet. Journal of Colloid and Interface Science, 339(2), 489-494 (2009)
16. Liu, J. L., Nie, Z. X., and Jiang, W. G. Deformation field of the soft substrate induced by capillary force. Physica B, 404(8-11), 1195-1199 (2009)
17. Shanahan, M. E. R. and de Gennes, P. G. Equilibrium of the triple line solid/liquid/fluid of a sessile drop. Adhesion (ed. Allen, K. W.), Elsevier Applied Science, London, 71-81 (1987)
18. Shanahan, M. E. R. and Carré, A. Spreading and dynamics of liquid drops involving nanometric deformations on soft substrates. Colloids and Surfaces A, 206(1-3), 115-123 (2002) (Pubitemid 34628543)
19. Shanahan, M. E. R. and Carré, A. Nanometric solid deformation of soft materials in capillary phenomena. Nano-Surface Chemistry (ed. Rosoff, M.), Marcel Dekker Inc., New York (2002)
20. White, L. R. The contact angle on the elastic substrate, 1. the role of disjoining pressure in the surface mechanics. Journal of Colloid and Interface Science, 258(1), 82-96 (2003)
21. Das, S., Marchand, A., Andreotti, B., and Snoeijer, J. H. Elastic deformation due to tangential capillary forces. Physics of Fluids, 23(7), 072006 (2011)
22. Kern, R. and Müller, P. Deformation of an elastic thin solid induced by a liquid droplet. Surface Science, 264(3), 467-494 (1992)
23. Treloar, L. R. G. The Physics of Rubber Elasticity, Clarendon, Oxford, 66 (1949)
24. Shanahan, M. E. R. The influence of solid micro-deformation on contact angle equilibrium. Journal of Physics D: Applied Physics, 20(7), 945-950 (1987)
25. Shanahan, M. E. R. Statics and dynamics of wetting on thin solids. Revue de Physique Appliquée, 23(6), 1031-1037 (1988)
26. Shanahan, M. E. R. The spreading dynamics of a liquid drop on a viscoelastic solid. Journal of Physics D: Applied Physics, 21(6), 981-985 (1988)
27. Carré, A. and Shanahan, M. E. R. Direct evidence for viscosity-independent spreading on a soft solid. Langmuir, 11(1), 24-26 (1995)
28. Shanahan, M. E. R. and Carré, A. Viscoelastic dissipation in wetting and adhesion phenomena. Langmuir, 11(4), 1396-1402 (1995)
29. Carré, A., Gastel, J. C., and Shanahan, M. E. R. Viscoelastic effects in the spreading of liquids. nature, 379(6564), 432-434 (1996) (Pubitemid 126598936)
30. Carré, A. and Shanahan, M. E. R. Effect of cross-linking on the dewetting of an elastomeric surface. Journal of Colloid and Interface Science, 191(1), 141-145 (1997) (Pubitemid 27472996)
31. Long, D., Ajdari, A., and Leibler, L. Static and dynamic wetting properties of thin rubber films. Langmuir, 12(21), 5221-5230 (1996) (Pubitemid 126536524)
32. Andrade, J. D., King, R. N., Gregonis, D. E., and Coleman, D. L. Surface characterization of poly (hydroxyethyl methacrylate) and related polymers, I. contact angle methods in water. Journal of Polymer Science: Polymer Symposium, 66, 313-336 (1979)
33. Métois, J. J. Elastic straining of a thin graphite layer by a liquid droplet or a non-epitaxed Pb crystallite. Surface Science, 241(3), 279-288 (1991) (Pubitemid 21650614)
34. Extrand, C. W. and Kumagai, Y. Contact angle and hysteresis on soft surfaces. Journal of Colloid and Interface Science, 184(1), 191-200 (1996) (Pubitemid 26413178)
35. Saiz, E., Tomsia, A. P., and Cannon, R. M. Ridging effects on wetting and spreading of liquids on solids. Acta Materialia, 46(7), 2349-2361 (1998) (Pubitemid 128395144)
36. Pu, G., Guo, J. H., Gwin, L. E., and Severtson, S. J. Mechanical pinning of liquids through inelastic wetting ridge formation on thermally stripped acrylic polymers. Langmuir, 23(24), 12142-12146 (2007) (Pubitemid 350197383)
37. Pericet-Cámara, R., Auernhammer, G. K., Koynov, K., Lorenzoni, S., Raiteri, R., and Bonaccurso, E. Solid-supported thin elastomer films deformed by microdrops. Soft Matter, 5(19), 3611-3617 (2009)
38. Pericet-Cámara, R., Best, A., Butt, H. J., and Bonaccurso, E. Effect of capillary pressure and surface tension on the deformation of elastic surfaces by sessile liquid microdrops: an experimental investigation. Langmuir, 24(19), 10565-10568 (2008)
39. Jerison, E. R., Xu, Y., Wilen, L. A., and Dufresne, E. R. Deformation of an elastic substrate by a three-phase contact line. Physical Review Letters, 106(18), 186103 (2011)
40. Saiz, E., Cannon, R. M., and Tomsia, A. P. Reactive spreading: adsorption, ridging and compound formation. Acta Materialia, 48(18-19), 4449-4462 (2000) (Pubitemid 32029838)
41. Madasu, S. and Cairncross, R. A. Static wetting on flexible substrates: a finite element formulation. International Journal for Numerical Methods in Fluids, 45(3), 301-319 (2004) (Pubitemid 38587467)
42. Yu, Y. S., Yang, Z. Y., and Zhao, Y. P. Role of vertical component of surface tension of the droplet on the elastic deformation of PDMS membrane. Journal of Adhesion Science and Technology, 22(7), 687-698 (2008)
43. Yu, Y. S. and Zhao, Y. P. Deformation of PDMS membrane and microcantilever by a water droplet: comparison between Mooney-Rivlin and linear elastic constitutive models. Journal of Colloid and Interface Science, 332(2), 467-476 (2009)
44. Wang, F. C. Boundary Slip and Contact Angle Hysteresis in the Nanoscale Liquid-Solid Interfacial Mechanics (in Chinese), Ph. D. dissertation, Graduate University of Chinese Academy of Sciences, Beijing (2012)
45. Rugar, D. and Hansma, P. Atomic force microscopy. Physics Today, 43(10), 23-30 (1990)
46. Dimitriadis, E. K., Horkay, F., Maresca, J., Kachar, B., and Chadwick, R. S. Determination of elastic moduli of thin layers of soft material using the atomic force microscopy. Biophysical Journal, 82(5), 2798-2810 (2002) (Pubitemid 34441316)
47. Magonov, S. N. and Reneker, D. H. Characterization of polymer surfaces with atomic force microscopy. Annual Review of Materials Science, 27, 175-222 (1997) (Pubitemid 127668331)
48. Zhao, L. M., Schaefer, D., and Marten, M. R. Assessment of elasticity and topography of aspergillus nidulans spores via atomic force microscopy. Applied and Environmental Microbiology, 71(2), 955-960 (2005) (Pubitemid 40223584)
49. Jensenius, H., Thaysen, J., Rasmussen, A. A., Veje, L. H., Hansen, O., and Boisen, A. A microcantilever-based alcohol vapor sensor-application and response model. Applied Physics Letters, 76(18), 2615-2617 (2000)
50. Bonaccurso, E. and Butt, H. J. Microdrops on atomic force microscope cantilevers: evaporation of water and spring constant calibration. Journal of Physics and Chemistry B, 109(1), 253-263 (2005) (Pubitemid 40120969)
51. Haschke, T., Bonaccurso, E., Butt, H. J., Lautenschlager, D., Schönfeld, F., and Wiechert, W. Sessile-drop-induced bending of atomic force microscope cantilevers: a model system for monitoring microdrop evaporation. Journal of Micromechanics and Microengineering, 16(11), 2273-2280 (2006) (Pubitemid 44679445)
52. Butt, H. J., Golovko, D. S., and Bonaccurso, E. On the derivation of Young's equation for sessile drops: nonequilibrium effects due to evaporation. Journal of Physics and Chemistry B, 111(19), 5277-5283 (2007) (Pubitemid 46854516)
53. Golovko, D. S., Bonanno, P., Lorenzoni, S., Stefani, F., Raiteri, R., and Bonaccurso, E. Evaporative cooling of sessile water microdrops measured with atomic force microscope cantilevers. Journal of Micromechanics and Microengineering, 18(9), 095026 (2008)
54. Golovko, D. S., Butt, H. J., and Bonaccurso, E. Transition in the evaporation kinetics of water microdrops on hydrophilic surfaces. Langmuir, 25(1), 75-78 (2009)
55. Jeon, S., Desikan, R., Tian, F., and Thundat, T. Influence of nanobubbles on the bending of microcantilevers. Applied Physics Letters, 88(10), 103118 (2006)
56. Lee, H. J., Chang, Y. S., Lee, Y. P., Jeong, K. H., and Kim, H. Y. Deflection of microcantilever by growing vapor bubble. Sensors and Actuators A, 136(2), 717-722 (2007) (Pubitemid 46678747)
57. Zheng, X. P., Zhao, H. P., Gao, L. T., Liu, J. L., Yu, S. W., and Feng, X. Q. Elasticity-driven droplet movement on a microbeam with gradient stiffness: a biomimetic self-propelling mechanism. Journal of Colloid and Interface Science, 323(1), 133-140 (2008)
58. Mastrangelo, C. H. and Hsu, C. H. Mechanical stability and adhesion of micro structures under capillary forces- part I: basic theory. Journal of Microelectromechanical Systems, 2(1), 33-43 (1993)
59. Mastrangelo, C. H. and Hsu, C. H. Mechanical stability and adhesion of micro structures under capillary forces- part II: experiments. Journal of Microelectromechanical Systems, 2(1), 44-55 (1993)
60. Syms, R. R. A., Yeatman, E. M., Bright, V. M., and Whitesides, G. M. Surface tension-powered self-assembly of microstructures- the state-of-the-art. Journal of Microelectromechanical Systems, 12(4), 387-417 (2003)
61. Syms, R. R. A. and Yeatman, E. M. Self-assembly of three-dimensional microstructures using rotation by surface tension forces. Electronics Letters, 29(8), 662-664 (1993)
62. Green, P. W., Syms, R. R. A., and Yeatman, E. M. Demonstration of three-dimensional microstructure self-assembly. Journal of Microelectromechanical Systems, 4(4), 170-176 (1995)
63. Syms, R. R. A. Equilibrium of hinged and hingeless structures rotated using surface tension forces. Journal of Microelectromechanical Systems, 4(4), 177-184 (1995)
64. Bico, J., Roman, B., Moulin, L., and Boudaoud, A. Adhesion: elastocapillary coalescence in wet hair. nature, 432(7018), 690 (2004) (Pubitemid 39656283)
65. Py, C., Reverdy, P., Doppler, L., Bico, J., Roman, B., and Baroud, C. N. Capillary origami: spontaneous wrapping of a droplet with an elastic sheet. Physical Review Letters, 98(15), 156103 (2007)
66. Py, C., Reverdy, P., Doppler, L., Bico, J., Roman, B., and Baroud, C. N. Capillary origami. Physics of Fluids, 19(9), 091104 (2007)
67. Guo, X. Y., Li, H., Ahn, B. Y., Duoss, E. B., Hsia, K. J., Lewis, J. A., and Nuzzo, R. Two- and three-dimensional folding of thin film single-crystalline silicon for photovoltaic power applications. Proceedings of the National Academy of Sciences of the United States of America, 106(48), 20149- 20154 (2009)
68. Li, H., Guo, X. Y., Nuzzo, R. G., and Hsia, K. J. Capillary induced self-assembly of thin foils into 3D structures. Journal of the Mechanics and Physics of Solids, 58(12), 2033-2042 (2010)
69. Patra, N., Wang, B. Y., and Král, P. Nanodroplet activated and guided folding of graphene nanostructures. Nano Letters, 9(11), 3766-3771 (2009)
70. Yuan, Q. Z. and Zhao, Y. P. Precursor film in dynamic wetting, electrowetting and electro-elastocapillarity. Physical Review Letters, 104(24), 246101 (2010)
71. Wang, Z. Q., Wang, F. C., and Zhao, Y. P. Tap dance of water droplet. Proceedings of the Royal Society A, 468(2145), 2485-2495 (2012)
72. Yu, Y. S., Wang, Z. Q., and Zhao, Y. P. Experimental and theoretical investigations of evaporation of sessile water droplet on hydrophobic surfaces. Journal of Colloid and Interface Science, 365(1), 254-259 (2012)
73. Deegan, R. D., Bakajin, O., Dupont, T. F., Huber, G., Nagel, S. R., and Witten, T. A. Capillary flow as the cause of ring stains from dried liquid drops. nature, 389(6653), 827-829 (1997) (Pubitemid 27462971)
74. Yunker, P. J., Still, T., Lohr, M. A., and Yodh, A. G. Suppression of the coffee-ring effect by shape-dependent capillary interactions. nature, 476(7360), 308-311 (2011)
75. Wang, Y. and Zhao, Y. P. Electrowetting on curved surfaces. Soft Matter, 8(9), 2599-2606 (2012)
76. Roman, B. and Bico, J. Elasto-capillarity: deforming an elastic structure with a liquid droplet. Journal of Physics: Condensed Matter, 22(49), 493101 (2010)