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.
2 CMAP, Ecole Polytechnique, CNRS 91128, Palaiseau, France.
3 SISSA–International School for Advanced Studies, Via Bonomea 265, 34136, Trieste, Italy.
4 California Institute of Technology, 1200, E. California Blvd, 91125, Pasadena, CA .
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