Abstract The dynamic behavior of compound droplets on the wall of a rectangle channel by the action of an imposed shear flow is simulated using our developed three-dimensional front-tracking method combined with generalized Navier boundary condition. The validity of the present method was confirmed by comparing results of the compound droplet spreading under gravity force with analytical solutions. To determine the physical condition required for detaching/pinching-off the compound droplet, we have performed a large number of simulations with varying capillary numbers of two interfaces and obtained a phase diagram of compound droplets on solid surface in shear flow. The deformation and motion of the compound droplet including its contact line motion are investigated. It is found that the behavior of the compound droplet is controlled by two dimensionless parameters, the capillary numbers of the outer interface and the inner interface. Moreover, we also analyze the deformation and migration of the inner droplet and discuss its effect on the compound droplet. The simulation demonstrate that the lateral migration of the small inner droplet could accelerates the pinch-off process and the large inner droplet could promote the detachment for a moderate capillary number of the outer interface.

中文翻译：

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前向追踪法对剪切流中复合液滴在固体表面动态行为的数值模拟

摘要 使用我们开发的三维前向跟踪方法结合广义 Navier 边界条件，模拟了矩形通道壁上复合液滴在外加剪切流作用下的动态行为。通过将复合液滴在重力作用下扩散的结果与解析解进行比较，证实了本方法的有效性。为了确定分离/夹断复合液滴所需的物理条件，我们对两个界面的不同毛细管数进行了大量模拟，并获得了剪切流中固体表面上复合液滴的相图。研究了复合液滴的变形和运动，包括其接触线运动。发现复合液滴的行为受两个无量纲参数控制，即外界面和内界面的毛细管数。此外，我们还分析了内部液滴的变形和迁移，并讨论了其对复合液滴的影响。模拟表明，小内部液滴的横向迁移可以加速夹断过程，而大内部液滴可以促进外部界面的中等毛细管数的脱离。