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. © EDP Sciences, SMAI 2013.

Macroscopic contact angle and liquid drops on rough solid surfaces via homogenization and numerical simulations / Cacace, S.; Chambolle, A.; De Simone, A.; Fedeli, L.. - In: MODÉLISATION MATHÉMATIQUE ET ANALYSE NUMÉRIQUE. - ISSN 0764-583X. - 47:3(2013), pp. 837-858. [10.1051/m2an/2012048]

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

#### 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. © EDP Sciences, SMAI 2013.
##### Scheda breve Scheda completa
2013
Augmented Lagrangian; Contact-angle hysteresis; Homogenization; Nonsmooth optimization; Super-hydrophobic surfaces; Total variation; Wetting
01 Pubblicazione su rivista::01a Articolo in rivista
Macroscopic contact angle and liquid drops on rough solid surfaces via homogenization and numerical simulations / Cacace, S.; Chambolle, A.; De Simone, A.; Fedeli, L.. - In: MODÉLISATION MATHÉMATIQUE ET ANALYSE NUMÉRIQUE. - ISSN 0764-583X. - 47:3(2013), pp. 837-858. [10.1051/m2an/2012048]
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11573/1659844`
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