Macroscopic contact angle and liquid drops on rough solid surfaces via homogenization and numerical simulations
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 47 (2013) no. 3, p. 837-858

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.

DOI : https://doi.org/10.1051/m2an/2012048
Classification:  76D45,  74N30,  49S05,  49Q20,  65K15
Keywords: wetting, super-hydrophobic surfaces, contact-angle hysteresis, homogenization, total variation, non-smooth optimization, augmented lagrangian
@article{M2AN_2013__47_3_837_0,
     author = {Cacace, S. and Chambolle, A. and DeSimone, A. and Fedeli, L.},
     title = {Macroscopic contact angle and liquid drops on rough solid surfaces via homogenization and numerical simulations},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {47},
     number = {3},
     year = {2013},
     pages = {837-858},
     doi = {10.1051/m2an/2012048},
     mrnumber = {3056411},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2013__47_3_837_0}
}
Cacace, S.; Chambolle, A.; DeSimone, A.; Fedeli, L. Macroscopic contact angle and liquid drops on rough solid surfaces via homogenization and numerical simulations. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 47 (2013) no. 3, pp. 837-858. doi : 10.1051/m2an/2012048. http://www.numdam.org/item/M2AN_2013__47_3_837_0/

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