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: 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 }, pages = {837--858}, publisher = {EDP-Sciences}, volume = {47}, number = {3}, year = {2013}, doi = {10.1051/m2an/2012048}, mrnumber = {3056411}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2012048/} }
TY - JOUR AU - Cacace, S. AU - Chambolle, A. AU - DeSimone, A. AU - Fedeli, L. TI - Macroscopic contact angle and liquid drops on rough solid surfaces via homogenization and numerical simulations JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2013 SP - 837 EP - 858 VL - 47 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2012048/ DO - 10.1051/m2an/2012048 LA - en ID - M2AN_2013__47_3_837_0 ER -
%0 Journal Article %A Cacace, S. %A Chambolle, A. %A DeSimone, A. %A Fedeli, L. %T Macroscopic contact angle and liquid drops on rough solid surfaces via homogenization and numerical simulations %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2013 %P 837-858 %V 47 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2012048/ %R 10.1051/m2an/2012048 %G en %F 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 , Volume 47 (2013) no. 3, pp. 837-858. doi : 10.1051/m2an/2012048. http://www.numdam.org/articles/10.1051/m2an/2012048/
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