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

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

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