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The sharp interface limit of a phase field model for moving contact problem. (English) Zbl 1157.76013

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.

MSC:

76D27 Other free boundary flows; Hele-Shaw flows
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics

Citations:

Zbl 1160.76340
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