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Sharp-interface limits of a phase-field model with a generalized Navier slip boundary condition for moving contact lines

Published online by Cambridge University Press:  26 June 2018

Xianmin Xu ,
Yana Di  and
Haijun Yu Open the ORCID record for Haijun Yu [Opens in a new window]
Xianmin Xu
Affiliation:
NCMIS & LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Beijing 100190, China School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
Yana Di
Affiliation:
NCMIS & LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Beijing 100190, China School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
Haijun Yu*
Affiliation:
NCMIS & LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Beijing 100190, China School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
*
†Email address for correspondence: [email protected]
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Abstract

The sharp-interface limits of a phase-field model with a generalized Navier slip boundary condition for binary fluids with moving contact lines are studied by asymptotic analysis and numerical simulations. The effects of the mobility number as well as a phenomenological relaxation parameter on the boundary condition are considered. In asymptotic analysis, we consider both the cases that the mobility number is proportional to the Cahn number and the square of the Cahn number, and derive the sharp-interface limits for several set-ups of the boundary relaxation parameter. It is shown that the sharp-interface limit of the phase-field model is the standard two-phase incompressible Navier–Stokes equations coupled with several different slip boundary conditions. Numerical results are consistent with the analysis results and also illustrate the different convergence rates of the sharp-interface limits for different scalings of the two parameters.

JFM classification

Interfacial Flows (free surface): Contact lines Multiphase and Particle-laden Flows: Multiphase flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 849 , 25 August 2018 , pp. 805 - 833
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Copyright
© 2018 Cambridge University Press 

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