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arXiv · 1710.09141

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

Xianmin Xu·Yana Di·Haijun Yu
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Abstract

The sharp-interface limits of a phase-field model with a generalized Navier slip boundary condition for moving contact line problem are studied by asymptotic analysis and numerical simulations. The effects of the {mobility} number as well as a phenomenological relaxation parameter in the boundary condition are considered. In asymptotic analysis, we focus on the case that the {mobility} number is the same order of the Cahn number and derive the sharp-interface limits for several setups 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.

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Xianmin Xu, Yana Di, Haijun Yu. 2017-10-25. Sharp-interface limits of a phase-field model with a generalized Navier slip boundary condition for moving contact lines. https://doi.org/10.1017/jfm.2018.428

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