Methods and Applications of Analysis

The Sharp Interface Limit of a Phase Field Model for Moving Contact Line Problem

Xiao-Ping Wang and Ya-Guang Wang

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Abstract

Using method of matched asymptotic expansions, we derive the sharp interface limit for the diffusive interface model with the generalized Navier boundary condition recently proposed by Qian, Wang and Sheng in "Molecular scale contact line hydrodynamics of immiscible flows," and "Power-law slip profile of the moving contact line in two-phase immiscible flows," for the moving contact line problem. We show that the leading order problem satisfies a boundary value problem for a coupled Hale-Shaw and Navier-Stokes equations with the interface being a free boundary, and the leading order dynamic contact angle is the same as the static one satisfying the Young’s equation.

Article information

Source
Methods Appl. Anal., Volume 14, Number 3 (2007), 287-294.

Dates
First available in Project Euclid: 24 October 2008

Permanent link to this document
https://projecteuclid.org/euclid.maa/1224877829

Mathematical Reviews number (MathSciNet)
MR2459830

Zentralblatt MATH identifier
1157.76013

Subjects
Primary: 76T05 34E05: Asymptotic expansions

Keywords
Sharp interface limit matched asymptotic expansion moving contact line

Citation

Wang, Xiao-Ping; Wang, Ya-Guang. The Sharp Interface Limit of a Phase Field Model for Moving Contact Line Problem. Methods Appl. Anal. 14 (2007), no. 3, 287--294. https://projecteuclid.org/euclid.maa/1224877829


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