Wetting on rough surfaces and contact angle hysteresis: numerical experiments based on a phase field model

Alessandro Turco; François Alouges; Antonio DeSimone

ESAIM: Mathematical Modelling and Numerical Analysis (2009)

  • Volume: 43, Issue: 6, page 1027-1044
  • ISSN: 0764-583X

Abstract

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We present a phase field approach to wetting problems, related to the minimization of capillary energy. We discuss in detail both the Γ-convergence results on which our numerical algorithm are based, and numerical implementation. Two possible choices of boundary conditions, needed to recover Young's law for the contact angle, are presented. We also consider an extension of the classical theory of capillarity, in which the introduction of a dissipation mechanism can explain and predict the hysteresis of the contact angle. We illustrate the performance of the model by reproducing numerically a broad spectrum of experimental results: advancing and receding drops, drops on inclined planes and superhydrophobic surfaces.

How to cite

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Turco, Alessandro, Alouges, François, and DeSimone, Antonio. "Wetting on rough surfaces and contact angle hysteresis: numerical experiments based on a phase field model." ESAIM: Mathematical Modelling and Numerical Analysis 43.6 (2009): 1027-1044. <http://eudml.org/doc/250551>.

@article{Turco2009,
abstract = { We present a phase field approach to wetting problems, related to the minimization of capillary energy. We discuss in detail both the Γ-convergence results on which our numerical algorithm are based, and numerical implementation. Two possible choices of boundary conditions, needed to recover Young's law for the contact angle, are presented. We also consider an extension of the classical theory of capillarity, in which the introduction of a dissipation mechanism can explain and predict the hysteresis of the contact angle. We illustrate the performance of the model by reproducing numerically a broad spectrum of experimental results: advancing and receding drops, drops on inclined planes and superhydrophobic surfaces. },
author = {Turco, Alessandro, Alouges, François, DeSimone, Antonio},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Wetting; contact angle hysteresis; super-hydrophobic surfaces.; wetting; super-hydrophobic surfaces},
language = {eng},
month = {6},
number = {6},
pages = {1027-1044},
publisher = {EDP Sciences},
title = {Wetting on rough surfaces and contact angle hysteresis: numerical experiments based on a phase field model},
url = {http://eudml.org/doc/250551},
volume = {43},
year = {2009},
}

TY - JOUR
AU - Turco, Alessandro
AU - Alouges, François
AU - DeSimone, Antonio
TI - Wetting on rough surfaces and contact angle hysteresis: numerical experiments based on a phase field model
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2009/6//
PB - EDP Sciences
VL - 43
IS - 6
SP - 1027
EP - 1044
AB - We present a phase field approach to wetting problems, related to the minimization of capillary energy. We discuss in detail both the Γ-convergence results on which our numerical algorithm are based, and numerical implementation. Two possible choices of boundary conditions, needed to recover Young's law for the contact angle, are presented. We also consider an extension of the classical theory of capillarity, in which the introduction of a dissipation mechanism can explain and predict the hysteresis of the contact angle. We illustrate the performance of the model by reproducing numerically a broad spectrum of experimental results: advancing and receding drops, drops on inclined planes and superhydrophobic surfaces.
LA - eng
KW - Wetting; contact angle hysteresis; super-hydrophobic surfaces.; wetting; super-hydrophobic surfaces
UR - http://eudml.org/doc/250551
ER -

References

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  1. G. Alberti and A. De Simone, Wetting of rough surfaces: a homogenization approach. Proc. R. Soc. A461 (2005) 79–97.  Zbl1145.82321
  2. G. Alberti and A. DeSimone, Quasistatic evolution of sessile drops and contact angle hysteresis. In preparation (2009).  Zbl1276.76016
  3. G. Alberti, G. Bouchitté and P. Seppecher, Phase transition with line-tension effect. Arch. Rat. Mech. Anal.144 (1998) 1–46.  Zbl0915.76093
  4. S. Baldo and G. Bellettini, Γ-convergence and numerical analysis: an application to the minimal partition problem. Ricerche di Matematica1 (1991) 33–64.  Zbl0755.65064
  5. W. Bao and Q. Du, Computing the ground state solution of Bose-Einstein condensates by a normalized gradient flow. SIAM J. Sci. Comp.25 (2004) 1674.  Zbl1061.82025
  6. A. Braides, Γ-convergence for beginners. Oxford University Press (2002).  Zbl1198.49001
  7. M. Callies and D. Quéré, On water repellency. Soft Matter1 (2005) 55–61.  
  8. G. Dal Maso, An introduction to Γ-convergence. Birkhaüser (1993).  
  9. P.-G. De Gennes, F. Brochard-Wyart and D. Quéré, Capillarity and Wetting Phenomena. Springer (2004).  Zbl1139.76004
  10. A. DeSimone, N. Grunewald and F. Otto, A new model for contact angle hysteresis. Networks and Heterogeneous Media2 (2007) 211–225 Zbl1125.76011
  11. R. Finn, Equilibrium Capillary Surfaces. Springer (1986).  Zbl0583.35002
  12. A. Lafuma and D. Quéré, Superhydrophobic states. Nature Materials2 (2003) 457–460.  
  13. L. Modica, Gradient theory of phase transitions with boundary contact energy. Ann. Inst. H. Poincaré Anal. Non Linéaire5 (1987) 497.  Zbl0642.49009
  14. L. Modica and S. Mortola, Un esempio di Γ-convergenza. Boll. Un. Mat. It. B14 (1977) 285–299.  
  15. N.A. Patankar, On the modeling of hydrophobic contact angles on rough surfaces. Langmuir19 (2003) 1249–1253.  
  16. S.J. Polak, An increased accuracy scheme for diffusion equations in cylindrical coordinates. J. Inst. Math. Appl.14 (1974) 197–201.  Zbl0286.65041
  17. P. Seppecher, Moving contact lines in the Cahn-Hilliard theory. Int. J. Engng. Sci.34 (1996) 977–992.  Zbl0899.76042
  18. J.C. Strikwerda, Finite Difference Schemes and PDE. SIAM (2004).  

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