Computation of the effective slip of rough hydrophobic surfaces via homogenization

Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2014, 24 (11), pp.2259-2285 We present a quantitative analysis of the effect of rough hydrophobic surfaces on viscous newtonian flows. We use a model introduced by Ybert and coauthors in which the rough surface is repl...

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Bibliographic Details
Main Authors Bonnivard, Matthieu, Dalibard, Anne-Laure, Gérard-Varet, David
Format Journal Article
LanguageEnglish
Published 17.01.2013
Subjects
Mathematics - Analysis of PDEs
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Summary:Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2014, 24 (11), pp.2259-2285 We present a quantitative analysis of the effect of rough hydrophobic surfaces on viscous newtonian flows. We use a model introduced by Ybert and coauthors in which the rough surface is replaced by a flat plane with alternating small areas of slip and no-slip. We investigate the averaged slip generated at the boundary, depending on the ratio between these areas. This problem reduces to the homogenization of a non-local system, involving the Dirichlet to Neumann map of the Stokes operator, in a domain with small holes. Pondering on works by Allaire, we compute accurate scaling laws of the averaged slip for various types of roughness (riblets, patches). Numerical computations complete and confirm the analysis.
DOI:10.48550/arxiv.1301.4067