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

• Volume: 47, Issue: 3, page 837-858
• ISSN: 0764-583X

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## Abstract

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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.

## How to cite

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Cacace, S., et al. "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 47.3 (2013): 837-858. <http://eudml.org/doc/273328>.

@article{Cacace2013,
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.},
author = {Cacace, S., Chambolle, A., DeSimone, A., Fedeli, L.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {wetting; super-hydrophobic surfaces; contact-angle hysteresis; homogenization; total variation; non-smooth optimization; augmented lagrangian; augmented Lagrangian},
language = {eng},
number = {3},
pages = {837-858},
publisher = {EDP-Sciences},
title = {Macroscopic contact angle and liquid drops on rough solid surfaces via homogenization and numerical simulations},
url = {http://eudml.org/doc/273328},
volume = {47},
year = {2013},
}

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 - Modélisation Mathématique et Analyse Numérique
PY - 2013
PB - EDP-Sciences
VL - 47
IS - 3
SP - 837
EP - 858
AB - 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.
LA - eng
KW - wetting; super-hydrophobic surfaces; contact-angle hysteresis; homogenization; total variation; non-smooth optimization; augmented lagrangian; augmented Lagrangian
UR - http://eudml.org/doc/273328
ER -

## References

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