Biomimetics pp 51-80 | Cite as

Modeling of Contact Angle for a Liquid in Contact with a Rough Surface for Various Wetting Regimes

  • Bharat BhushanEmail author
Part of the Springer Series in Materials Science book series (SSMATERIALS, volume 279)


The roughness distribution affects contact angle and surface wetting. Three surface wetting regimes are discussed, which include Wenzel, Cassie-Baxter, and Cassie regimes. In the Wenzel regime, a liquid droplet completely wets the rough surface with a homogeneous interface. In the Cassie-Baxter regime, a heterogeneous or composite interface with air pockets trapped between the asperities is formed. In a Cassie regime, a liquid film impregnates some of the cavities in an area surrounding the droplet as well.


  1. Adamson A. V. (1990), Physical Chemistry of Surfaces, Wiley, New York.Google Scholar
  2. Anisimov, M. A. (2007), “Divergence of Tolman’s Length for a Droplet Near the Critical Point,” Phys. Rev. Lett. 98, 035702.Google Scholar
  3. Antonini, C., Carmona, F. J., Pierce, E., Marengo, M., and Amirfazli, A. (2009), “General Methodology for Evaluating the Adhesion Force of Drops and Bubbles on Solid Surfaces,” Langmuir 25, 6143–6154.CrossRefGoogle Scholar
  4. Bahadur, V. and Garimella, S. V. (2007), “Electrowetting-Based Control of Static Droplet States on Rough Surfaces,” Langmuir 23, 4918–4924.CrossRefGoogle Scholar
  5. Barbieri, L., Wagner, E., and Hoffmann, P. (2007), “Water Wetting Transition Parameters of Perfluorinated Substrates with Periodically Distributed Flat-Top Microscale Obstacles,” Langmuir 23, 1723–1734.CrossRefGoogle Scholar
  6. Bartell, F. E. and Shepard, J. W. (1953), “Surface Roughness as Related to Hysteresis of Contact Angles” J. Phys. Chem. 57, 455–458.CrossRefGoogle Scholar
  7. Bhushan, B. (2012), “Bioinspired Structured Surfaces,” Langmuir 28, 1698–1714.CrossRefGoogle Scholar
  8. Bhushan, B. (2013a), Principles and Applications of Tribology, second ed., Wiley, New York.Google Scholar
  9. Bhushan, B. (2013b), Introduction to Tribology, second ed., Wiley, New York.CrossRefGoogle Scholar
  10. Bhushan, B. (2017), Nanotribology and Nanomechanics—An Introduction, fourth ed., Springer International, Switzerland.Google Scholar
  11. Bhushan, B. and Jung, Y. C. (2007), “Wetting Study of Patterned Surfaces for Superhydrophobicity,” Ultramicroscopy 107, 1033–1041.CrossRefGoogle Scholar
  12. Bhushan, B. and Jung, Y. C. (2008), “Wetting, Adhesion and Friction of Superhydrophobic and Hydrophilic Leaves and Fabricated Micro/nanopatterned Surfaces,” J. Phys.: Condens. Matter 20, 225010.Google Scholar
  13. Bhushan, B. and Jung, Y. C. (2011), “Natural and Biomimetic Artificial Surfaces for Superhydrophobicity, Self-Cleaning, Low Adhesion, and Drag Reduction,” Prog. Mater. Sci. 56, 1–108.CrossRefGoogle Scholar
  14. Bhushan, B. and Nosonovsky, M. (2010), “The Rose Petal Effect and the Modes of Superhydrophobicity,” Phil. Trans. R. Soc. A 368, 4713–4728.CrossRefGoogle Scholar
  15. Bhushan, B., Nosonovsky, M., and Jung, Y. C. (2007), “Towards Optimization of Patterned Superhydrophobic Surfaces” J. R. Soc. Interface 4, 643–648.CrossRefGoogle Scholar
  16. Bormashenko, E., Pogreb, R., Whyman, G., and Erlich, M. (2007), “Cassie-Wenzel Wetting Transition in Vibrated Drops Deposited on the Rough Surfaces: Is Dynamic Cassie-Wenzel Transition 2D or 1D Affair?” Langmuir 23, 6501–6503.Google Scholar
  17. Boruvka, L. and Neumann, A. W. (1977), “Generalization of the Classical Theory of Capillarity,” J. Chem. Phys. 66, 5464–5476.CrossRefGoogle Scholar
  18. Brown, P. S. and Bhushan, B. (2016), “Designing Bioinspired Superoleophobic Surfaces,” APL Mater. 4, 015703.CrossRefGoogle Scholar
  19. Cassie, A. B. D. (1948), “Contact Angles,” Discuss. Faraday Soc. 3, 11–16.CrossRefGoogle Scholar
  20. Cassie, A. B. D. and Baxter, S. (1944), “Wettability of Porous Surfaces,” Trans. Faraday Soc. 40, 546–551.CrossRefGoogle Scholar
  21. Checco, A., Guenoun, P., and Daillant, J. (2003), “Nonlinear Dependence of the Contact Angle of Nanodroplets on Contact Line Curvatures,” Phys. Rev. Lett. 91, 186101.Google Scholar
  22. Cheng, Y. T., Rodak, D. E., Angelopoulos, A., and Gacek, T. (2005), “Microscopic Observations of Condensation of Water on Lotus Leaves,” Appl. Phys. Lett. 87, 194112.CrossRefGoogle Scholar
  23. de Gennes, P. G., Brochard-Wyart, F., and Quėrė, D. (2003) Capillarity and Wetting Phenomena, Springer, Berlin.Google Scholar
  24. Derjaguin, B. V. and Churaev, N. V. (1974), “Structural Component of Disjoining Pressure,” J. Colloid Interface Sci. 49, 249–255.CrossRefGoogle Scholar
  25. Eustathopoulos, N., Nicholas, M. G., and Drevet, B. (1999), Wettability at High Temperatures, Pergamon, Amsterdam.Google Scholar
  26. Extrand, C. W. (2002), “Model for Contact Angle and Hysteresis on Rough and Ultraphobic Surfaces,” Langmuir 18, 7991–7999.CrossRefGoogle Scholar
  27. Extrand, C. W. (2003), “Contact Angle Hysteresis on Surfaces with Chemically Heterogeneous Islands,” Langmuir 19, 3793–3796.CrossRefGoogle Scholar
  28. Feng, X. J., Feng, L., Jin, M. H., Zhai, J., Jiang, L., and Zhu, D. B. (2004), “Reversible Super-hydrophobicity to Super-hydrophilicity Transition of Aligned ZnO Nanorod Films,” J. Am. Chem. Soc. 126, 62–63.CrossRefGoogle Scholar
  29. Gao, L. and McCarthy, T. J. (2007). “How Wenzel and Cassie Were Wrong,” Langmuir 23, 3762–3765.CrossRefGoogle Scholar
  30. Gupta, P., Ulman, A., Fanfan, F., Korniakov, A., and Loos, K. (2005), “Mixed Self-Assembled Monolayer of Alkanethiolates on Ultrasmooth Gold do not Exhibit Contact Angle Hysteresis,” J. Am. Chem. Soc. 127, 4–5.CrossRefGoogle Scholar
  31. Israelachvili, J. N. (1992), Intermolecular and Surface Forces, second ed., Academic Press, London, UK.Google Scholar
  32. Israelachvili, J. N. and Gee, M. L. (1989), “Contact Angles on Chemically Heterogeneous Surfaces,” Langmuir 5, 288–289.CrossRefGoogle Scholar
  33. Johnson, R. E. and Dettre, R. H. (1964), “Contact Angle Hysteresis,” in Contact Angle, Wettability, and Adhesion, Adv. Chem. Ser. (ed. F. M. Fowkes), Vol. 43, pp. 112–135, American Chemical Society, Washington, D. C.Google Scholar
  34. Jung, Y. C. and Bhushan, B. (2006), “Contact Angle, Adhesion, and Friction Properties of Micro- and Nanopatterned Polymers for Superhydrophobicity,” Nanotechnology 17, 4970–4980.CrossRefGoogle Scholar
  35. Jung, Y. C. and Bhushan, B. (2007), “Wetting Transition of Water Droplets on Superhydrophobic Patterned Surfaces,” Scripta Mater. 57, 1057–1060.CrossRefGoogle Scholar
  36. Jung, Y. C. and Bhushan, B. (2008a), “Wetting Behavior during Evaporation and Condensation of Water Microdroplets on Superhydrophobic Patterned Surfaces” J. Micros. 229, 127–140.CrossRefGoogle Scholar
  37. Jung, Y. C. and Bhushan, B. (2008b), “Dynamic Effects of Bouncing Water Droplets on Superhydrophobic Surfaces,” Langmuir 24, 6262–6269.CrossRefGoogle Scholar
  38. Kamusewitz, H., Possart, W., and Paul, D. (1999), “The Relation between Young’s Equilibrium Contact Angle and the Hysteresis on Rough Paraffin Wax Surfaces,” Colloid Surf. A-Physicochem. Eng. Asp. 156, 271–279.CrossRefGoogle Scholar
  39. Kijlstra, J., Reihs, K., and Klami, A. (2002), “Roughness and Topology of Ultra-Hydrophobic surfaces,” Colloid Surf. A-Physicochem. Eng. Asp. 206, 521–529.CrossRefGoogle Scholar
  40. Krasovitski, B. and Marmur, A. (2005) “Drops Down the Hill:  Theoretical Study of Limiting Contact Angles and the Hysteresis Range on a Tilted Plate,” Langmuir 21, 3881–3885.CrossRefGoogle Scholar
  41. Krupenkin, T. N., Taylor, J. A., Schneider, T. M., and Yang, S. (2004), “From Rolling Ball to Complete Wetting: The Dynamic Tuning of Liquids on Nanostructured Surfaces,” Langmuir 20, 3824–3827.CrossRefGoogle Scholar
  42. Lafuma, A. and Quéré, D. (2003), “Superhydrophobic States,” Nat. Mater. 2, 457–460.CrossRefGoogle Scholar
  43. Li, W. and Amirfazli, A. (2006), “A Thermodynamic Approach for Determining the Contact Angle Hysteresis for Superhydrophobic Surfaces,” J. Colloid. Interface Sci. 292, 195–201.CrossRefGoogle Scholar
  44. Marmur, A. (2003), “Wetting on Hydrophobic Rough Surfaces: To be Heterogeneous or Not to be?” Langmuir 19, 8343–8348.CrossRefGoogle Scholar
  45. Nosonovsky, M. (2007a), “Multiscale Roughness and Stability of Superhydrophobic Biomimetic Interfaces,” Langmuir 23, 3157–3161.CrossRefGoogle Scholar
  46. Nosonovsky, M. (2007b), “Model for Solid-Liquid and Solid-Solid Friction for Rough Surfaces with Adhesion Hysteresis,” J. Chem. Phys. 126, 224701.CrossRefGoogle Scholar
  47. Nosonovsky, M. (2007c), “On the Range of Applicability of the Wenzel and Cassie Equations” Langmuir 23, 9919–9920.CrossRefGoogle Scholar
  48. Nosonovsky, M. and Bhushan, B. (2005), “Roughness Optimization for Biomimetic Superhydrophobic Surfaces,” Microsyst. Technol. 11, 535–549.CrossRefGoogle Scholar
  49. Nosonovsky, M. and Bhushan, B. (2006a), “Stochastic Model for Metastable Wetting of Roughness-Induced Superhydrophobic Surfaces,” Microsyst. Technol. 12, 231–237.CrossRefGoogle Scholar
  50. Nosonovsky, M. and Bhushan, B. (2006b), “Wetting of Rough Three-Dimensional Superhydrophobic Surfaces,” Microsyst. Technol. 12, 273–281.CrossRefGoogle Scholar
  51. Nosonovsky, M. and Bhushan, B. (2007a), “Multiscale Friction Mechanisms and Hierarchical Surfaces in Nano- and Bio-Tribology,” Mater. Sci. Eng.:R 58, 162–193.CrossRefGoogle Scholar
  52. Nosonovsky, M. and Bhushan, B. (2007b), “Hierarchical Roughness Makes Superhydrophobic Surfaces Stable,” Microelectronic Eng. 84, 382–386.Google Scholar
  53. Nosonovsky, M. and Bhushan, B. (2007c), “Biomimetic Superhydrophobic Surfaces: Multiscale Approach,” Nano Lett. 7, 2633–2637.CrossRefGoogle Scholar
  54. Nosonovsky, M. and Bhushan, B. (2007d), “Hierarchical Roughness Optimization for Biomimetic Superhydrophobic Surfaces,” Ultramicroscopy 107, 969–979.CrossRefGoogle Scholar
  55. Nosonovsky, M. and Bhushan, B. (2008a), Multiscale Dissipative Mechanisms and Hierarchical Surfaces: Friction, Superhydrophobicity, and Biomimetics, Springer-Verlag, Heidelberg, Germany.CrossRefGoogle Scholar
  56. Nosonovsky, M. and Bhushan, B. (2008b), “Roughness-Induced Superhydrophobicity: A Way to Design Non-Adhesive Surfaces,” J. Phys.: Condens. Matter 20, 225009.Google Scholar
  57. Nosonovsky, M. and Bhushan, B. (2008c), “Biologically-Inspired Surfaces: Broadening the Scope of Roughness,” Adv. Func. Mater. 18, 843–855.CrossRefGoogle Scholar
  58. Nosonovsky, M. and Bhushan, B. (2008d), “Patterned Non-Adhesive Surfaces: Superhydrophobicity and Wetting Regime Transitions,” Langmuir 24, 1525–1533.CrossRefGoogle Scholar
  59. Nosonovsky, M. and Bhushan, B. (2008e), “Do Hierarchical Mechanisms of Superhydrophobicity Lead to Self-Organized Criticality?” Scripta Mater. 59, 941–944.CrossRefGoogle Scholar
  60. Nosonovsky, M. and Bhushan, B. (2008f), “Energy Transitions in Superhydrophobicity: Low Adhesion, Easy Flow and Bouncing,” J. Phys.: Condens. Matter 20, 395005.Google Scholar
  61. Nosonovsky, M. and Bhushan, B. (2009), “Superhydrophobic Surfaces and Emerging Applications: Non-Adhesion, Energy, Green Engineering,” Curr. Opin. Colloid Interface Sci. 14, 270–280.CrossRefGoogle Scholar
  62. Patankar, N. A. (2004), “Transition between Superhydrophobic States on Rough Surfaces” Langmuir 20, 7097–7102.CrossRefGoogle Scholar
  63. Pompe, T., Fery, A., and Herminghaus, S. (2000), “Measurement of Contact Line Tension by Analysis of the Three-Phase Boundary with Nanometer Resolution,” in Apparent and Microscopic Contact Angles (eds. J. Drelich, J. S. Laskowski, and K. L. Mittal), pp. 3–12, VSP Publishing, Utrecht, Netherlands.Google Scholar
  64. Quéré, D. (2005), “Non-Sticking Drops,” Rep. Prog. Phys. 68, 2495–2535.CrossRefGoogle Scholar
  65. Sun, M., Luo, C., Xu, L., Ji, H., Ouyang, Q., Yu, D., and Chen, Y. (2005), “Artificial Lotus Leaf by Nanocasting,” Langmuir 21, 8978–8981.CrossRefGoogle Scholar
  66. Tretinnikov, O. N. (2000), “Wettability and Microstructure of Polymer Surfaces: Stereochemical and Conformational Aspects” in Apparent and Microscopic Contact Angles (eds. J. Drelich, J. S. Laskowski, and K. L. Mittal), pp. 111–128, VSP Publishing, Utrecht, Netherlands.Google Scholar
  67. Wenzel, R. N. (1936), “Resistance of Solid Surfaces to Wetting by Water,” Indust. Eng. Chem. 28, 988–994.CrossRefGoogle Scholar
  68. Yoshimitsu, Z., Nakajima, A., Watanabe, T., and Hashimoto, K. (2002), “Effects of Surface Structure on the Hydrophobicity and Sliding Behavior of Water Droplets,” Langmuir 18, 5818–5122.CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Nanoprobe Laboratory for Bio/Nanotechnology and Biomimetics (NLBB)The Ohio State UniversityColumbusUSA

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