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Morphology of Liquid Drops and thin Films on a Solid Surface with Sinusoidal Microstructures

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Abstract

Surface microstructures of solid materials play a significant role in various wetting and dewetting phenomena. In the present paper, the effect of micro- and nano-structures of a substrate surface on the morphology and evolution of liquid droplets and thin films is examined. The governing equations satisfied by droplets and films on a sinusoidal surface are derived by considering van der Waals force, surface tension, gravity and hydrostatic pressure. The morphologies of both liquid droplets and thin films are numerically simulated under various characteristic sizes of roughness. It is found that the droplet shapes show a significant dependence upon the characteristic sizes of substrate microstructures. A thin liquid film on a hydrophilic substrate may have a horizontal surface or replicate the substrate morphology, depending on the wavelength of roughness.

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References

  1. de Gennes P.G., Brochard-Wyart F., Quere D. (2003) Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves. Springer, Berlin Heidelberg New York

    Google Scholar 

  2. de Gennes P.G. (1985) Wetting: statics and dynamics. Rev. Mod. Phys. 57, 827–863

    Article  Google Scholar 

  3. Quere D. (2002) Rough ideas on wetting. Phys. A 313, 32–46

    Article  Google Scholar 

  4. Ceinhuis C., Barthlott W. (1997) Characterization and distribution of water-repellent, self-cleaning plant surfaces. Ann. Bot. 79, 667–677

    Article  Google Scholar 

  5. Otten A., Herminghaus S. (2004) How plants keep dry: a physicist’s point of view. Langmuir 20, 2405–2408

    Article  Google Scholar 

  6. Hu D.L., Chan B., Bush J.W. (2004) The hydrodynamics of water strider locomotion. Nature 424, 663–666

    Article  Google Scholar 

  7. Parker A.R., Lawrence C.R. (2001) Water capture by a desert beetle. Nature 414, 33–34

    Article  Google Scholar 

  8. Lau K.K.S., Bico J., Teo K.B.K. et al (2003) Superhydrophobic carbon nanotube forests. Nano. Lett. 3, 1701–1705

    Article  Google Scholar 

  9. Zhai L., Cebeci F.C., Cohen R.E., Rubner M.F. (2004) Stable superhydrophobic coatings from polyelectrolyte multilayers. Nano. Lett. 4, 1349–1353

    Article  Google Scholar 

  10. Hosono E., Fujihara S., Honma I. et al (2005) Superhydrophobic perpendicular nano-pin film by the bottom-up process. J. Amer. Chem. Soc. 127, 13458–13459

    Article  Google Scholar 

  11. Onda T., Shibuichi S., Satoh N. et al (1996) Supper-water-repellent fractal surfaces. Langmuir 12, 2125–2127

    Article  Google Scholar 

  12. Herminghaus S. (2000) Roughness-induced non-wetting. Europhys. Lett. 52, 165–170

    Article  Google Scholar 

  13. Jeong H.E., Lee S.H., Kim J.K. et al (2006) Nanoengineered multiscale hierarchical structures with tailored wetting properties. Langmuir 22, 1640–1645

    Article  Google Scholar 

  14. Shibuichi S., Onda T., Satoh N. et al (1996) Super water-repellent surfaces resulting from fractal structure. J. Phys. Chem. 100, 19512–19517

    Article  Google Scholar 

  15. Alberti G., DeSimone A. (2005) Wetting of rough surfaces: a homogenization approach. Proc. R. Soc. Lond. A 461, 79–97

    Article  MATH  MathSciNet  Google Scholar 

  16. Bico J., Thiele U., Quere D. (2002) Wetting of textured surfaces. Colloid Surface A 206, 41–46

    Article  Google Scholar 

  17. Patankar N.A. (2003) On the modeling of hydrophobic contact angles on rough surfaces. Langmuir 19, 1249–1253

    Article  Google Scholar 

  18. Kim J., Kim C.J. Nano-structured surfaces for dramatic reduction of flow resistance in droplet-based micro-fluidics. In: Proc. IEEE Int. Conf. MEMS. Las Vegas, pp. 479–82 (2002)

  19. Lee J., He B., Patankar N.A. (2005) A roughness-based wettability switching membrane device for hydrophobic surfaces. J. Micromech Microeng 15, 591–600

    Article  Google Scholar 

  20. Blossey R. (2003) Self-cleaning surfaces - Virtual realities. Nature Mater. 2, 301–306

    Article  Google Scholar 

  21. Wenzel R.N. (1936) Resistance of solid surfaces to wetting by water. Indu. Eng. Chem. 28, 988–994

    Article  Google Scholar 

  22. Cassie A.B.D., Baxter S. (1944) Wettability of porous surfaces. Tran. Fara. Soc. 40, 546–551

    Article  Google Scholar 

  23. Zheng Q.S., Yu Y., Zhao Z.H. (2005) Effects of hydraulic pressure on the stability and transition of wetting modes of superhydrophobic surfaces. Langmuir 21, 12207–12212

    Article  Google Scholar 

  24. Bashforth F., Adams J.C. (1883) An Attempt to Test the Theories of Capillary Attraction. Cambridge University Press, Cambridge

    Google Scholar 

  25. Padday J.F. (1971) The profiles of axially symmetric menisci. Phil. T. Roy. Soc. London A 269, 265–293

    Article  Google Scholar 

  26. Hartland S., Hartley R.W. (1976) Axisymmetric Fluid-Liquid Interfaces. Elsevier, Amsterdam

    MATH  Google Scholar 

  27. Rotenberg Y., Boruvka L., Neumann A.W. (1983) Determination of surface tension and contact angle from the shapes of axisymmetric fluid interfaces. J. Colloid Inter Sci. 93, 169–183

    Article  Google Scholar 

  28. Reinstra S.W. (1990) The shape of a sessile drop for small and large surface tension. J. Eng. Math. 24, 193–202

    Article  Google Scholar 

  29. Behroozi F., Macomber H.K., Dostal J.A. et al (1996) The profile of a dew drop. Am. J. Phys. 64, 1120–1125

    Article  Google Scholar 

  30. Fan H., Gao Y.X., Huang X.Y. (2001) Thermodynamics modeling for moving contact line in gas/liquid/solid system: capillary rise problem revisited. Phys. Fluids 13, 1615–1623

    Article  Google Scholar 

  31. Johnson R.E., Dettre R.H.(1964) Contact angle hysteresis, Part I. Study of an idealized rough surfaces. Adv. Chem. Ser. 43, 112–135

    Article  Google Scholar 

  32. Carbone G., Mangialardi L. (2005) Hydrophobic properties of a wary rough substrate. Eur. Phys. J. E., 16, 67–76

    Article  Google Scholar 

  33. Taylor G.I., Michael M.A. (1973) On making holes in a sheet of fluid. J. Fluid Mech. 58, 625–639

    Article  Google Scholar 

  34. Brochard-Wyart F., Daillant J. (1990) Drying of solids wetted by thin liquid films. Can. J. Phys. 68, 1084–1088

    Google Scholar 

  35. Brochard-Wyart F., Redon C., Sykes C. (1992) Dewetting of ultrathin liquid films. C. R. Acad. Sci. II 314, 19–24

    Google Scholar 

  36. Andelman D., Joanny J.F., Robbins M.O. (1988) Complete wetting on rough surfaces: statics. Europhys. Lett. 7, 731–736

    Article  Google Scholar 

  37. Adamson A.W. Physical Chemistry of Surfaces. Wiley, New York (1990)

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Authors and Affiliations

  1. Department of Engineering Mechanics, Tsinghua University, Bei**g, 100084, China

    Jian Lin Liu, ** Qiao Feng & Shou Wen Yu

Authors
  1. Jian Lin Liu
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  2. ** Qiao Feng
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  3. Shou Wen Yu
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Corresponding author

Correspondence to ** Qiao Feng.

Additional information

The project supported by the National Natural Science Foundation of China (10525210, 10121202) and the Ministry of Education of China.

The English text was polished by Keren Wang.

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Liu, J.L., Feng, X.Q. & Yu, S.W. Morphology of Liquid Drops and thin Films on a Solid Surface with Sinusoidal Microstructures. Acta Mech Mech Sinica 22, 315–322 (2006). https://doi.org/10.1007/s10409-006-0009-6

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  • DOI: https://doi.org/10.1007/s10409-006-0009-6

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