In this paper, the equilibrium behavior of an immiscible two phase fluid on a rough surface is studied from a phase field equation derived from minimizing the total free energy of the system. When the size of the roughness becomes small, we derive the effective boundary condition for the equation by the multiple scale expansion homogenization technique. The Wenzel and Cassie 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 F-convergence theory. © 2010 Society for Industrial and Applied Mathematics.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): SA-C0040/UK-C0016
Acknowledgements: Received by the editors November 3, 2009; accepted for publication (in revised form) July 6, 2010; published electronically October 5, 2010. This publication was based on work supported in part by award SA-C0040/UK-C0016 from King Abdullah University of Science and Technology (KAUST), Hong Kong RGC-CERG grants 603107 and 604209, the National Basic Research Program of China under project 2009CB623200, and the State Key Laboratory of Scientific and Engineering Computing.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.