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 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. The close match between both model results indicates that the considered test case lends itself well as a benchmark for further research.

翻译：本文研究了存在流体-流体-固体接触线时，描述二元流体流动的 Navier-Stokes-Cahn-Hilliard 模型在扩散界面厚度趋于零时的极限行为。为了充分模拟多相、多组分流体在固体介质周围及内部的输运过程，必须允许此类接触线相对于固体基底发生运动。尽管扩散界面模型通过迁移率诱导的扩散提供了固有的滑移机制，但在所谓的锐界面极限下，当界面厚度和迁移率参数趋于零时，这种滑移会消失。本工作的目标是提出一种在锐界面极限下保持一致的、适用于扩散界面模型的动态润湿及广义 Navier 边界条件。我们将分析集中于典型的二元流体 Couette 流动问题。为了验证扩散界面模型在界面厚度消失极限下的一致性，我们提供了相应锐界面模型的参考极限解。针对临界粘度比处及其附近的参数值，我们展示并比较了扩散界面模型与锐界面模型的结果。两种模型结果的紧密吻合表明，所考虑的测试案例非常适合作为进一步研究的基准。