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Simulation of selected interfacial dynamic problems using Cahn-Hilliard diffuse-interface method Mehrabian, Hadi


Using the Cahn-Hilliard diffuse-interface model, I have studied three interfacial dynamic problems for incompressible immiscible two-phase flows. As the first problem, capillary instability of a liquid torus is computed. The main differences between the torus and a straight thread are the presence of an axial curvature and an external flow field caused by the retraction of the torus. We show that the capillary wave initially grows linearly as on a straight thread. The axial curvature decreases the growth rate of the capillary waves while the external flow enhances it. Breakup depends on the competition of two time scales: one for torus retraction and the other for neck pinch-off. The outcome is determined by the initial amplitude of the disturbance, the thickness of the torus relative to its circumference, and the viscosity ratio. The second problem concerns interfacial dynamics and three-phase contact line motion of wicking through micropores of two types of geometries: axisymmetric tubes with contractions and expansions of the cross section, and two-dimensional planar channels with a Y-shaped bifurcation. Results show that the liquid meniscus undergoes complex deformation during its passage through contraction and expansion. Pinning of the interface at protruding corners limits the angle of expansion into which wicking is allowed. Capillary competition between branches downstream of a Y-shaped bifurcation may result in arrest of wicking in the wider branch. As the third problem, auto-ejection of drops from capillary tubes is studied. This study focuses on two related issues: the critical condition for autoejection, and the role of geometric parameters in the hydrodynamics. From analyzing the dynamics of the meniscus in the straight tube and the nozzle, we develop a criterion for the onset of auto-ejection based on a Weber number defined at the exit of the nozzle and an effective length that encompasses the geometric features of the tube-nozzle combination. In particular, this criterion shows that ejection is not possible in straight tubes. With steeper contraction in the nozzle, we predict two additional regimes of interfacial rupture: rapid ejection of multiple droplets and air bubble entrapment.

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