Derivation of the Wenzel and Cassie Equations from a Phase Field Model for Two Phase Flow on Rough Surface
Xianmin Xu, Xiaoping Wang
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.
SIAM Journal on Applied Mathematics
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.
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Surface Chemistry 100%
Phase Field Mathematics 66%
Boundary Condition Mathematics 66%
Two-Phase Flow Chemistry 33%
Homogenization Chemistry 33%
Gibbs Free Energy Chemistry 33%
Procedure Chemistry 33%
Particle Size Chemistry 33%
Xu, X., & Wang, X. (2010). Derivation of the Wenzel and Cassie Equations from a Phase Field Model for Two Phase Flow on Rough Surface. SIAM Journal on Applied Mathematics, 70(8), 2929-2941. https://doi.org/10.1137/090775828
Xu, Xianmin ; Wang, Xiaoping. / Derivation of the Wenzel and Cassie Equations from a Phase Field Model for Two Phase Flow on Rough Surface. In: SIAM Journal on Applied Mathematics. 2010 ; Vol. 70, No. 8. pp. 2929-2941.
@article{59a402bb2cea41d781c285b58222aa27,
title = "Derivation of the Wenzel and Cassie Equations from a Phase Field Model for Two Phase Flow on Rough Surface",
abstract = "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. {\textcopyright} 2010 Society for Industrial and Applied Mathematics.",
author = "Xianmin Xu and Xiaoping Wang",
note = "KAUST 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.",
journal = "SIAM Journal on Applied Mathematics",
publisher = "Society for Industrial and Applied Mathematics",
Xu, X & Wang, X 2010, 'Derivation of the Wenzel and Cassie Equations from a Phase Field Model for Two Phase Flow on Rough Surface', SIAM Journal on Applied Mathematics, vol. 70, no. 8, pp. 2929-2941. https://doi.org/10.1137/090775828
Derivation of the Wenzel and Cassie Equations from a Phase Field Model for Two Phase Flow on Rough Surface. / Xu, Xianmin; Wang, Xiaoping.
In: SIAM Journal on Applied Mathematics, Vol. 70, No. 8, 01.2010, p. 2929-2941.
T1 - Derivation of the Wenzel and Cassie Equations from a Phase Field Model for Two Phase Flow on Rough Surface
AU - Xu, Xianmin
AU - Wang, Xiaoping
N1 - KAUST 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.
N2 - 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.
AB - 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.
UR - http://epubs.siam.org/doi/10.1137/090775828
JO - SIAM Journal on Applied Mathematics
JF - SIAM Journal on Applied Mathematics
Xu X, Wang X. Derivation of the Wenzel and Cassie Equations from a Phase Field Model for Two Phase Flow on Rough Surface. SIAM Journal on Applied Mathematics. 2010 Jan;70(8):2929-2941. doi: 10.1137/090775828