On the consistency of dynamic wetting boundary conditions for the Navier–Stokes–Cahn–Hilliard equations

We investigate the limiting behavior of the Navier–Stokes–Cahn–Hilliard model for binary-fluid flows as the diffuse-interface thickness passes to zero, in the presence of fluid–fluid–solid contact lines. Allowing for motion of such contact lines relative to the solid substrate is required to adequately model multi-phase and multi-species fluid transport past and through solid media. Even though diffuse-interface models provide an inherent slip mechanism through the mobility-induced diffusion, this slip vanishes as the interface thickness and mobility parameter tend to zero in the so-called sharp-interface limit. The objective of this work is to present and analyze dynamic wetting and generalized Navier boundary conditions for diffuse-interface models that are consistent in the sharp-interface limit. We concentrate our analysis on the prototypical binary-fluid Couette-flow problems. To verify the consistency of the diffuse-interface model in the limit of vanishing interface thickness, we provide reference limit solutions of a corresponding sharp-interface model. For parameter values both at and away from the critical viscosity ratio, we present and compare the results of both the diffuse- and sharp-interface models. As a corollary of the close agreement between the diffuse-interface and sharp-interface results, the presented results can serve as a benchmark for future investigations.