| Issue |
ESAIM: M2AN
Volume 47, Number 3, May-June 2013
|
|
|---|---|---|
| Page(s) | 837 - 858 | |
| DOI | https://doi.org/10.1051/m2an/2012048 | |
| Published online | 10 March 2013 | |
Macroscopic contact angle and liquid drops on rough solid surfaces via homogenization and numerical simulations
1 Sapienza Università di Roma, Piazzale Aldo Moro 5, 00185, Rome, Italy.
cacace@mat.uniroma1.it
2 CMAP, Ecole Polytechnique, CNRS 91128, Palaiseau, France.
antonin.chambolle@cmap.polytechnique.fr
3 SISSA–International School for Advanced Studies, Via Bonomea 265, 34136, Trieste, Italy.
desimone@sissa.it
4 California Institute of Technology, 1200, E. California Blvd, 91125, Pasadena, CA .
fedeli@caltech.edu
Received: 13 March 2012
Revised: 7 August 2012
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.
Mathematics Subject Classification: 76D45 / 74N30 / 49S05 / 49Q20 / 65K15
Key words: Wetting / super-hydrophobic surfaces / contact-angle hysteresis / homogenization / total variation / non-smooth optimization / augmented Lagrangian
© EDP Sciences, SMAI, 2013
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.