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

Xianmin Xu, Xiaoping Wang

Research output: Contribution to journalArticlepeer-review

29 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)2929-2941
Number of pages13
JournalSIAM Journal on Applied Mathematics
Volume70
Issue number8
DOIs
StatePublished - Jan 2010
Externally publishedYes

Fingerprint Dive into the research topics of 'Derivation of the Wenzel and Cassie Equations from a Phase Field Model for Two Phase Flow on Rough Surface'. Together they form a unique fingerprint.

Cite this