Macroscopic contact angle and liquid drops on rough solid surfaces via homogenization and numerical simulations

Creators: Cacace, S.; Chambolle, A.; DeSimone, A.; Fedeli, L.

Abstract

We discuss a numerical formulation for the cell problem related to a homogenization approach for the study of wetting on micro rough surfaces. Regularity properties of the solution are described in details and it is shown that the problem is a convex one. Stability of the solution with respect to small changes of the cell bottom surface allows for an estimate of the numerical error, at least in two dimensions. Several benchmark experiments are presented and the reliability of the numerical solution is assessed, whenever possible, by comparison with analytical one. Realistic three dimensional simulations confirm several interesting features of the solution, improving the classical models of study of wetting on roughness.

Additional Information

© 2013 EDP Sciences, SMAI. Article published by EDP Sciences. Received March 13, 2012. Revised August 7, 2012. Published online March 10, 2013. The authors thank François Alouges and Luca Heltai for stimulating discussions. The fourth author is grateful to the SISSA in Trieste, where he was a Ph.D. student when this work was done. We also are very grateful to the anonymous reviewers who made precise and very helpful comments on the first version of this work. Part of this research was funded by the ANR "MICA", grant number ANR-08-BLAN-0082. Finally, a special acknowledgement goes to the open source C++ finite element library deal.II (www.dealii.org), without which the simulations contained in this paper would not have been (almost) so easily realized.

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