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Issue ESAIM: M2AN
Volume 43, Number 6, November-December 2009
Page(s) 1027 - 1044
DOI 10.1051/m2an/2009016
Published online 12 June 2009

ESAIM: M2AN 43 (2009) 1027-1044
DOI: 10.1051/m2an/2009016

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

Alessandro Turco1, François Alouges2 and Antonio DeSimone1

1  Scuola Internazionale Superiore di Studi Avanzati, Via Beirut 2, 34014 Trieste, Italy. desimone@sissa.it
2  Université Paris XI, 91405 Orsay Cedex, France.

Received February 1st, 2008. Revised November 24, 2008. Published online June 12, 2009.

Abstract
We present a phase field approach to wetting problems, related to the minimization of capillary energy. We discuss in detail both the $\Gamma$-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.


Mathematics Subject Classification. 76D45, 74N30, 49S05.

Key words: Wetting, contact angle hysteresis, super-hydrophobic surfaces.


© EDP Sciences, SMAI 2009


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