Wang, Xiao-Ping; Wang, Yaguang The sharp interface limit of a phase field model for moving contact problem. (English) Zbl 1157.76013 Methods Appl. Anal. 14, No. 3, 287-294 (2007). Summary: 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 T. Qian, X.-P. Wang and P. Sheng [Commun. Math. Sci. 1, No. 2, 333–341 (2003; Zbl 1160.76340)] for the moving contact line problem. We show that the leading order problem satisfies a boundary value problem for coupled Hele-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. Cited in 7 Documents MSC: 76D27 Other free boundary flows; Hele-Shaw flows 76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics Keywords:matched asymptotic expansions; diffusive interface; generalized Navier boundary condition Citations:Zbl 1160.76340 PDFBibTeX XMLCite \textit{X.-P. Wang} and \textit{Y. Wang}, Methods Appl. Anal. 14, No. 3, 287--294 (2007; Zbl 1157.76013) Full Text: DOI