Science China Technological Sciences

, Volume 61, Issue 2, pp 309–316 | Cite as

The effect of surface anisotropy on contact angles and the characterization of elliptical cap droplets

  • ZhanLong Wang
  • EnHui Chen
  • YaPu Zhao


In this paper, the variation of contact angles of a droplet on grooved surfaces was studied from microscale to macroscale experimentally and theoretically. The experimental results indicated that the contact angle changes nonlinearly with anisotropic factor. To get clear of the changing process of contact angle on grooved surfaces from microscale to macroscale, we carried out theoretical analysis with moment equilibrium method being adopted. In addition, the variation of contact angles in different directions was investigated and a mathematic model to calculate arbitrary contact angles around the elliptic contact line was suggested. For the convenience of potential applications, a symbolic contact angle was proposed to characterize the ellipsoidal cap droplet on grooved surfaces. Our results will offer help to the future design of patterned surfaces in practical applications, and deepen the understanding of wetting behavior on grooved surfaces.


droplet contact angle ellipse contact line grooved surface 


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  1. 1.
    Zhao Y P. Physical Mechanics of Surfaces and Interfaces (in Chinese). Beijing: Science Press, 2012Google Scholar
  2. 2.
    Sun G, Fang Y, Cong Q, et al. Anisotropism of the non-smooth surface of butterfly wing. J Bionic Eng, 2009, 6: 71–76CrossRefGoogle Scholar
  3. 3.
    Vernik L, Liu X. Velocity anisotropy in shales: A petrophysical study. Geophysics, 1997, 62: 521–532CrossRefGoogle Scholar
  4. 4.
    Xia D, Johnson L M, López G P. Anisotropic wetting surfaces with one-dimesional and directional structures: Fabrication approaches, wetting properties and potential applications. Adv Mater, 2012, 24: 1287–1302CrossRefGoogle Scholar
  5. 5.
    Yuan Q, Huang X, Zhao Y P. Dynamic spreading on pillar-arrayed surfaces: Viscous resistance versus molecular friction. Phys Fluids, 2014, 26: 092104CrossRefGoogle Scholar
  6. 6.
    Quéré D. Wetting and roughness. Annu Rev Mater Res, 2008, 38: 71–99CrossRefGoogle Scholar
  7. 7.
    Parker A R, Lawrence C R. Water capture by a desert beetle. Nature, 2001, 414: 33–34CrossRefGoogle Scholar
  8. 8.
    Yuan Q, Zhao Y P. Wetting on flexible hydrophilic pillar-arrays. Sci Rep, 2013, 3: 1944CrossRefGoogle Scholar
  9. 9.
    Chen L, Auernhammer G K, Bonaccurso E. Short time wetting dynamics on soft surfaces. Soft Matter, 2011, 7: 9084–9089CrossRefGoogle Scholar
  10. 10.
    Kreder M J, Alvarenga J, Kim P, et al. Design of anti-icing surfaces: Smooth, textured or slippery? Nat Rev Mater, 2016, 1: 15003CrossRefGoogle Scholar
  11. 11.
    Wang S, Yang Z, Gong G, et al. Icephobicity of penguins Spheniscus Humboldti and an artificial replica of penguin feather with airinfused hierarchical rough structures. J Phys Chem C, 2016, 120: 15923–15929CrossRefGoogle Scholar
  12. 12.
    Wen C Y, Tersoff J, Hillerich K, et al. Periodically changing morphology of the growth interface in Si, Ge, and GaP nanowires. Phys Rev Lett, 2011, 107: 025503CrossRefGoogle Scholar
  13. 13.
    Jacobsson D, Panciera F, Tersoff J, et al. Interface dynamics and crystal phase switching in GaAs nanowires. Nature, 2016, 531: 317–322CrossRefGoogle Scholar
  14. 14.
    Schutzius T M, Jung S, Maitra T, et al. Spontaneous droplet trampolining on rigid superhydrophobic surfaces. Nature, 2015, 527: 82–85CrossRefGoogle Scholar
  15. 15.
    Dubov A L, Mourran A, Möller M, et al. Contact angle hysteresis on superhydrophobic stripes. J Chem Phys, 2014, 141: 074710CrossRefGoogle Scholar
  16. 16.
    Chi L F, Gleiche M, Fuchs H. Nanoscopic channel lattices with controlled anisotropic wetting. Nature, 2000, 403: 173–175CrossRefGoogle Scholar
  17. 17.
    Yu N, Wang S, Liu Y, et al. Thermal-responsive anisotropic wetting microstructures for manipulation of fluids in microfluidics. Langmuir, 2017, 33: 494–502CrossRefGoogle Scholar
  18. 18.
    Wang Z, Zhao Y P. Wetting and electrowetting on corrugated substrates. Phys Fluids, 2017, 29: 067101CrossRefGoogle Scholar
  19. 19.
    Brandon S, Haimovich N, Yeger E, et al. Partial wetting of chemically patterned surfaces: The effect of drop size. J Colloid Interface Sci, 2003, 263: 237–243CrossRefGoogle Scholar
  20. 20.
    Fürstner R, Barthlott W, Neinhuis C, et al. Wetting and self-cleaning properties of artificial superhydrophobic surfaces. Langmuir, 2005, 21: 956–961CrossRefGoogle Scholar
  21. 21.
    Liu C, Ju J, Ma J, et al. Directional drop transport achieved on high-temperature anisotropic wetting surfaces. Adv Mater, 2014, 26: 6086–6091CrossRefGoogle Scholar
  22. 22.
    Seemann R, Brinkmann M, Kramer E J, et al. Wetting morphologies at microstructured surfaces. Proc Natl Acad Sci USA, 2005, 102: 1848–1852CrossRefGoogle Scholar
  23. 23.
    Chu K H, Xiao R, Wang E N. Uni-directional liquid spreading on asymmetric nanostructured surfaces. Nat Mater, 2010, 9: 413–417CrossRefGoogle Scholar
  24. 24.
    Park K C, Kim P, Grinthal A, et al. Condensation on slippery asymmetric bumps. Nature, 2016, 531: 78–82CrossRefGoogle Scholar
  25. 25.
    Xia D, Brueck S R J. Strongly anisotropic wetting on one-dimensional nanopatterned surfaces. Nano Lett, 2008, 8: 2819–2824CrossRefGoogle Scholar
  26. 26.
    Wenzel R N. Resistance of solid surfaces to wetting by water. Ind Eng Chem, 1936, 28: 988–994CrossRefGoogle Scholar
  27. 27.
    Cassie A B D, Baxter S. Wettability of porous surfaces. Trans Faraday Soc, 1944, 40: 546–551CrossRefGoogle Scholar
  28. 28.
    Yang J, Rose F R A J, Gadegaard N, et al. Effect of sessile drop volume on the wetting anisotropy observed on grooved surfaces. Langmuir, 2009, 25: 2567–2571CrossRefGoogle Scholar
  29. 29.
    Hirvi J T, Pakkanen T A. Wetting of nanogrooved polymer surfaces. Langmuir, 2007, 23: 7724–7729CrossRefGoogle Scholar
  30. 30.
    Zhao Y, Lu Q, Li M, et al. Anisotropic wetting characteristics on submicrometer-scale periodic grooved surface. Langmuir, 2007, 23: 6212–6217CrossRefGoogle Scholar
  31. 31.
    Li W, Fang G, Li Y, et al. Anisotropic wetting behavior arising from superhydrophobic surfaces: Parallel grooved structure. J Phys Chem B, 2008, 112: 7234–7243CrossRefGoogle Scholar
  32. 32.
    Chen Y, He B, Lee J, et al. Anisotropy in the wetting of rough surfaces. J Colloid Interface Sci, 2005, 281: 458–464CrossRefGoogle Scholar
  33. 33.
    Kusumaatmaja H, Vrancken R J, Bastiaansen C W M, et al. Anisotropic drop morphologies on corrugated surfaces. Langmuir, 2008, 24: 7299–7308CrossRefGoogle Scholar
  34. 34.
    Chung J Y, Youngblood J P, Stafford C M. Anisotropic wetting on tunable micro-wrinkled surfaces. Soft Matter, 2007, 3: 1163–1169CrossRefGoogle Scholar
  35. 35.
    Zhao Y P. Bridging length and time scales in moving contact line problems. Sci China-Phys Mech Astron, 2016, 59: 114631CrossRefGoogle Scholar
  36. 36.
    Yuan Q, Zhao Y P. Topology-dominated dynamic wetting of the precursor chain in a hydrophilic interior corner. Proc R Soc A-Math Phys Eng Sci, 2012, 468: 310–322CrossRefGoogle Scholar
  37. 37.
    Bell M S, Shahraz A, Fichthorn K A, et al. Effects of hierarchical surface roughness on droplet contact angle. Langmuir, 2015, 31: 6752–6762CrossRefGoogle Scholar
  38. 38.
    Feng L, Li S, Li Y, et al. Super-hydrophobic surfaces: From natural to artificial. Adv Mater, 2002, 14: 1857–1860CrossRefGoogle Scholar
  39. 39.
    De Gennes P G, Brochard-Wyart F, Quéré D. Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves. New York: Springer, 2004CrossRefMATHGoogle Scholar
  40. 40.
    Zhao Y P. Nano and Mesoscopic Mechanics (in Chinese). Beijing: Science Press, 2014Google Scholar
  41. 41.
    Sefiane K. Effect of nonionic surfactant on wetting behavior of an evaporating drop under a reduced pressure environment. J Colloid Interface Sci, 2004, 272: 411–419CrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.State Key Laboratory of Nonlinear Mechanics, Institute of MechanicsChinese Academy of SciencesBeijingChina
  2. 2.School of Engineering ScienceUniversity of Chinese Academy of SciencesBeijingChina

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