Cacace, S.; Chambolle, A.; DeSimone, A.; Fedeli, L. Macroscopic contact angle and liquid drops on rough solid surfaces via homogenization and numerical simulations. (English) Zbl 1307.76040 ESAIM, Math. Model. Numer. Anal. 47, No. 3, 837-858 (2013). Summary: 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. Cited in 1 Document MSC: 76D45 Capillarity (surface tension) for incompressible viscous fluids 74N30 Problems involving hysteresis in solids 49S05 Variational principles of physics 49Q20 Variational problems in a geometric measure-theoretic setting 65K15 Numerical methods for variational inequalities and related problems Keywords:wetting; super-hydrophobic surfaces; contact-angle hysteresis; homogenization; total variation; non-smooth optimization; augmented Lagrangian PDFBibTeX XMLCite \textit{S. Cacace} et al., ESAIM, Math. Model. Numer. Anal. 47, No. 3, 837--858 (2013; Zbl 1307.76040) Full Text: DOI