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Water droplet properties on periodically structured superhydrophobic surfaces: a lattice Boltzmann approach to multiphase flows with high water/air density ratio

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Abstract

Surface roughness affects the contact angle (CA) due to the increased area of solid–liquid interface and due to the effect of sharp edges of rough surfaces. Roughness may also lead to another non-wetting regime, by forming a composite solid–liquid–air interface between the water and the textured surface; this composite interface exhibits strong water repellency due to the various pockets of air entrapped between the surface textures. The contact between water and a hydrophobic textured surface leads to one of these two regimes depending on the thermodynamics stability of the regimes. In this study, the projection method of lattice Boltzmann method is used to analyze the large density difference at the air and water interface. The method is applied to simulate two-phase flows with the density ratio of up to 1,000. A numerical model is presented to provide a relationship between roughness and CA, which is used to develop optimized texture topography and create a biomimetic superhydrophobic surface. The numerical models encompass the effects of contact area, solid–liquid–gas composite interface and shape edges. The models are reused to analyze different possible roughness distributions and to calculate the effect of the cross-sectional area of pillars, including rectangular, triangular, cross, and pyramidal pillars. The energy barrier is investigated to predict the position of the transition between the Cassie and Wenzel regime observed for each roughness parameter as well as a theoretical free surface energy model.

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References

  • Adamson AV (1990) Physical chemistry of surfaces. Wiley, New York

    Google Scholar 

  • Barbieri L, Wagner E, Hoffmann P (2007) Water wetting transition parameters of perfluorinated substrates with periodically distributed flat-top microscale obstacles. Langmuir 23(4):1723–1734

    Article  Google Scholar 

  • Bhushan B (1999) Principles and applications of tribology. Wiley, New York

    Google Scholar 

  • Bhushan B (2002) Introduction to tribology. Wiley, New York

    Google Scholar 

  • Biben T, Joly L (2008) Wetting on nanorough surfaces. Phys Rev Lett 100:186103

    Article  Google Scholar 

  • Briant AJ, Papatzacos P, Yeomans JM (1977) Lattice Boltzmann simulations of contact line motion in a liquid-gas system. Philos Trans R Soc Lond A 360:485–495

    Article  Google Scholar 

  • Cahn JW (1977) Critical-point wetting. J Chem Phys 66:3667–3672

    Article  Google Scholar 

  • Cassie A, Baxter S (1944) Wettability of porous surfaces. Trans Faraday Soc 40:546–551

    Article  Google Scholar 

  • Chen W, Fadeev AY, Hsieh MC, Öner D, Youngblood J, McCarthy TJ (1999) Ultrahydrophobic and ultralyophobic surfaces: some comments and examples. Langmuir 15:3395–3399

    Article  Google Scholar 

  • Drelich J, Miller JD, Good RJ (1996) The effect of drop (bubble) size on advancing and receding contact angles for heterogeneous and rough solid surfaces as observed with sessile-drop and captive-bubble techniques. J Colloid Interface Sci 179:37

    Article  Google Scholar 

  • Dupuis A, Yeomans JM (2005) Modeling droplets on superhydrophobic surfaces: equilibrium states and transitions. Langmuir 21:2624–2629

    Article  Google Scholar 

  • Extrand CW (2002) Model for contact angle and hysteresis on rough and ultraphobic surfaces. Langmuir 18:7991–7999

    Article  Google Scholar 

  • Ginzburg I, Steiner K (2003) Lattice Boltzmann model for free-surface flow and its application to filling process in casting. J Comput Phys 185:61–99

    Article  MATH  MathSciNet  Google Scholar 

  • Gunstensen AK, Rothman DH, Zaleski S, Zanetti G (1991) Lattice Boltzmann model of immiscible fluids. Phys Rev A 43:4320–4327

    Article  Google Scholar 

  • He X, Chen S, Zhang R (1999) A lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh–Taylor instability. J Comput Phys 152:642–663

    Article  MATH  MathSciNet  Google Scholar 

  • He B, Lee J, Patankar NA (2004) Contact angle hysteresis on rough hydrophobic surfaces. Colloids Surf A 248:101

    Article  Google Scholar 

  • Inamuro T, Ogata T, Tajima S, Konishi N (2004) A lattice Boltzmann method for incompressible two-phase flows with large density differences. J Comput Phys 198:628–644

    Article  MATH  Google Scholar 

  • Israelachvili JN (1992) Intermolecular and surface forces, 2nd edn. Academic Press, London

    Google Scholar 

  • Jamet D, Lebaigue O, Coutris N, Delhaye JM (2001) The second gradient theory: a tool for the direct numerical simulation of liquid-vapor flows with phase-change. Nucl Eng Des 204:155–166

    Article  Google Scholar 

  • Johnson RE, Dettre RH (1964) In contact angle, wettability, and adhesion. Advances in chemistry series No. 43. American Chemical Society, Washington, DC, p 112

    Book  Google Scholar 

  • Kijlstra J, Reihs K, Klami A (2002) Roughness and topology of ultra-hydrophobic surfaces. Colloids Surf A Physicochem Eng Aspects 521–529:2006

    Google Scholar 

  • Kusumaatmaja H, Blow ML, Dupuis A, Yeomans JM (2008) The collapse transition on superhydrophobic surfaces. Europhys Lett 81:36003

    Article  Google Scholar 

  • Li W, Amirfazli A (2005) A thermodynamic approach for determining the contact angle hysteresis for superhydrophobic surfaces. J Colloid Interface Sci 292:195

    Article  Google Scholar 

  • Luo LS, Girimaji SS (2003) Theory of the lattice Boltzmann method: two-fluid model for binary mixtures. Phys Rev E 67:036302

    Article  Google Scholar 

  • Miwa M, Nakajima A, Fujishima A, Hashimoto K, Watanabe T (2000) Effects of the surface roughness on sliding angles of water droplets on superhydrophobic surfaces. Langmuir 16:5754–5760

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Nosonovsky M, Bhushan B (2005) Roughness optimization for biomimetic superhydrophobic surfaces. Microsyst Technol 11:535–549

    Article  Google Scholar 

  • Oner D, McCarthy TJ (2000) Ultrahydrophobic surfaces. Effects of topography length scales on wettability. Langmuir 16:7777–7782

    Article  Google Scholar 

  • Pooley CM, Kusumaatmaja H, Yeomans JM (2008) Contact line dynamics in binary lattice Boltzmann simulations. Phys Rev E 78:056709

    Article  Google Scholar 

  • Quéré D (2002) Surface chemistry: Fakir droplets. Nat Mater 1:14

    Article  Google Scholar 

  • Rowlinson JS, Widom B (1989) Molecular theory of capillarity, Chapter 3. Clarendon Press, Oxford

    Google Scholar 

  • Sankaranarayanan K, Sundaresan S (2002) Lift force in bubbly suspensions. Chem Eng Sci 57:3521–3542

    Article  Google Scholar 

  • Sankaranarayanan K, Shan X, Kevrekidis IG, Sundaresan S (2002) Analysis of drag and virtual mass forces in bubbly suspensions using an implicit formulation of the lattice Boltzmann method. J Fluid Mech 452:61–96

    Article  MATH  Google Scholar 

  • Shan X, Chen H (1993) Lattice Boltzmann model for simulating flows with multiple phases and components. Phys Rev E 47:1815–1819

    Article  Google Scholar 

  • Shibuichi S, Onda T, Satoh N, Tsujii K (1996) Super-water-repellent surfaces resulting from fractal structure. J Phys Chem 100:19512–19517

    Article  Google Scholar 

  • Swift MR, Osborn WR, Yeomans JM (1995) Lattice Boltzmann simulation of nonideal fluids. Phys Rev Lett 75:830–833

    Article  Google Scholar 

  • Teng S, Chen Y, Ohashi H (2000) Lattice Boltzmann simulation of multiphase fluid flows through the total variation diminishing artificial compression scheme. Int J Heat Fluid Flow 21:112–121

    Article  Google Scholar 

  • Tolke J, Krafczyk M, Schulz M, Rank E (2002) Lattice Boltzmann simulations of binary fluid flow through porous media. Philos Trans R Soc Lond A 360:535–545

    Article  MathSciNet  Google Scholar 

  • Wagner P, Furstner F, Barthlott W, Neinhuis C (2003) Quantitative assessment to the structural basis of water repellency in natural and technical surfaces. J Exp Bot 54:1295–1303

    Article  Google Scholar 

  • Wenzel RN (1936) Resistance of solid surfaces to wetting by water. Ind Eng Chem 28:988–994

    Article  Google Scholar 

  • Yan YY, Zu YQ (2007) A lattice Boltzmann method for incompressible two-phase flows on partial wetting surface with large density ratio. J Comput Phys 227:763–775

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgments

This study was supported by a grant of the Korea Healthcare technology R&D Project, Ministry for Health, Welfare & Family Affairs, Republic of Korea (Grant number: A085136). Also, the numerical method was developed by the Yan and Zu (2007) and it was implemented for this study.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Wayne State University, Detroit, MI, USA

    Yong Hyun Kim

  2. Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA, USA

    Wonjae Choi

  3. Department of Mechanical Engineering, Yonsei University, Seoul, Republic of Korea

    Joon Sang Lee

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  1. Yong Hyun Kim
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  2. Wonjae Choi
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Correspondence to Joon Sang Lee.

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Kim, Y.H., Choi, W. & Lee, J.S. Water droplet properties on periodically structured superhydrophobic surfaces: a lattice Boltzmann approach to multiphase flows with high water/air density ratio. Microfluid Nanofluid 10, 173–185 (2011). https://doi.org/10.1007/s10404-010-0658-4

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  • DOI: https://doi.org/10.1007/s10404-010-0658-4

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