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

Published online by Cambridge University Press:  10 March 2013

S. Cacace ,
A. Chambolle ,
A. DeSimone  and
L. Fedeli
S. Cacace
Affiliation:
Sapienza Università di Roma, Piazzale Aldo Moro 5, 00185, Rome, Italy.. cacace@mat.uniroma1.it
A. Chambolle
Affiliation:
CMAP, Ecole Polytechnique, CNRS 91128, Palaiseau, France.; antonin.chambolle@cmap.polytechnique.fr
A. DeSimone
Affiliation:
SISSA–International School for Advanced Studies, Via Bonomea 265, 34136, Trieste, Italy.; desimone@sissa.it
L. Fedeli
Affiliation:
California Institute of Technology, 1200, E. California Blvd, 91125, Pasadena, CA .; fedeli@caltech.edu
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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.

Keywords

Wettingsuper-hydrophobic surfacescontact-angle hysteresishomogenizationtotal variationnon-smooth optimizationaugmented Lagrangian
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 3 , May 2013 , pp. 837 - 858
Copyright
© EDP Sciences, SMAI, 2013

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