Derivation of the Wenzel and Cassie Equations from a Phase Field Model for Two Phase Flow on Rough Surface

Handle URI:
http://hdl.handle.net/10754/597938
Title:
Derivation of the Wenzel and Cassie Equations from a Phase Field Model for Two Phase Flow on Rough Surface
Authors:
Xu, Xianmin; Wang, Xiaoping
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. © 2010 Society for Industrial and Applied Mathematics.
Citation:
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: 2929–2941. Available: http://dx.doi.org/10.1137/090775828.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Applied Mathematics
KAUST Grant Number:
SA-C0040/UK-C0016
Issue Date:
Jan-2010
DOI:
10.1137/090775828
Type:
Article
ISSN:
0036-1399; 1095-712X
Sponsors:
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.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorXu, Xianminen
dc.contributor.authorWang, Xiaopingen
dc.date.accessioned2016-02-25T12:59:13Zen
dc.date.available2016-02-25T12:59:13Zen
dc.date.issued2010-01en
dc.identifier.citationXu 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: 2929–2941. Available: http://dx.doi.org/10.1137/090775828.en
dc.identifier.issn0036-1399en
dc.identifier.issn1095-712Xen
dc.identifier.doi10.1137/090775828en
dc.identifier.urihttp://hdl.handle.net/10754/597938en
dc.description.abstractIn 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.en
dc.description.sponsorshipReceived 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.en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectCassie equationen
dc.subjectHomogenizationen
dc.subjectWenzel equationen
dc.titleDerivation of the Wenzel and Cassie Equations from a Phase Field Model for Two Phase Flow on Rough Surfaceen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Applied Mathematicsen
dc.contributor.institutionInstitute of Computational Mathematics and Scientific-Engineering Computing, Chinese Academy of Sciences, Beijing, Chinaen
dc.contributor.institutionHong Kong University of Science and Technology, Hong Kong, Chinaen
kaust.grant.numberSA-C0040/UK-C0016en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.