Analysis for wetting on rough surfaces by a three-dimensional phase field model

Xianmin  Xu

doi:10.3934/dcdsb.2016075

Article Contents

2016, Volume 21, Issue 8: 2839-2850. Doi: 10.3934/dcdsb.2016075

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Analysis for wetting on rough surfaces by a three-dimensional phase field model

Xianmin Xu^1,

1.
The State Key Laboratory of Scientic and Engineering Computing, Institute of Computational Mathematics and Scientic/Engineering Computing, Chinese Academy of Sciences, Beijing 100190

Received: September 30, 2015

Revised: February 29, 2016

Published: September 2016

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Abstract

In this paper, we consider the derivation of the modified Wenzel's and Cassie's equations for wetting phenomena on rough surfaces from a three-dimensional phase field model. We derive an effective boundary condition by asymptotic two-scale homogenization technique when the size of the roughness is small. The modified Wenzel's and Cassie's equations for the apparent contact angles on the rough surfaces are then derived from the effective boundary condition. The homogenization results are proved rigorously by the $\Gamma$-convergence theory.

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Mathematics Subject Classification: Primary: 41A60, 49J45; Secondary: 76T10.

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