Phase-field modeling of two-phase displacement in a capillary tube

Contact lines, where fluid interfaces meet solid surfaces, pose a fundamental challenge to modeling fluid-fluid displacement in confined geometries, as they violate the classical no-slip boundary condition. Recent experiments reveal that contact-line motion in a capillary tube produces compact displacement at low flow rates and unstable fingering at high flow rates. We present a phase-field model with a novel formulation of the boundary wetting conditions. Our model captures the equilibrium configurations at arbitrary wettability, and also predicts dynamic configurations, including wetting transitions, thin-film formation and interface pinch-off, in quantitative agreement with experiments.