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