Abstract The dynamics of compound droplets is more and more attractive because of their applications in a wide range of industrial and natural processes. This study aims to improve the understanding of dynamical rheological behaviors of a compound droplet moving in a nozzle with a conical shape in the downstream region via front-tracking-based simulations. The numerical results show that the compound droplet experiences three stages of deformation: the entrance stage (in front of the conical region), the transit stage (within the conical region), and the exit stage (in the exit of the nozzle). The droplet receives the maximum deformation in the axial direction during the transit stage, and the radially maximum deformation occurs during the exit stage. Because of the acceleration induced by the conical region, the inner droplet of the compound droplet can break up into smaller droplets during the exit stage. To reveal the transition between the finite deformation and the breakup, many parameters including the Capillary number Ca (varied in the range of 0.0125–1.6), the droplet size relative to the nozzle size R1/R0 (varied in the range of 0.2–0.9), the droplet radius ratio R21 (varied in the range of 0.3–0.8), the viscosity ratios μ21 and μ31 (varied in the range of 0.05–3.2), the interfacial tension ratio σ21 (varied in the range of 0.125–8.0), the conical angle α (varied in the range of 4°–34°) and the initial location of the inner droplet (i.e. the droplet eccentricity) are considered. From the finite deformation mode, the transition to the breakup mode of the inner droplet occurs when increasing any of Ca, R1/R0, R21 and α, or decreasing any of μ21 and σ21. The breakup mode is also enhanced when the inner droplet is initially located closer to the leading side of the outer droplet. However, varying μ31 induces no transition between these modes. The regime diagrams of these modes, based on these parameters, are also proposed.

中文翻译：

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锥形喷嘴中复合液滴流变行为的数值研究

摘要 复合液滴的动力学因其在广泛的工业和自然过程中的应用而越来越有吸引力。本研究旨在通过基于前端跟踪的模拟，提高对在下游区域锥形喷嘴中移动的复合液滴的动态流变行为的理解。数值结果表明，复合液滴经历了三个变形阶段：入口阶段（圆锥区域前）、过渡阶段（圆锥区域内）和出口阶段（喷嘴出口）。液滴在过渡阶段受到轴向最大变形，而径向最大变形发生在出口阶段。由于锥形区域引起的加速度，在退出阶段，复合液滴的内部液滴可以分解成更小的液滴。为了揭示有限变形和破裂之间的过渡，许多参数包括毛细管数 Ca（在 0.0125-1.6 的范围内变化）、相对于喷嘴尺寸的液滴尺寸 R1/R0（在 0.2-0.9 的范围内变化） )、液滴半径比 R21（在 0.3-0.8 范围内变化）、粘度比 μ21 和 μ31（在 0.05-3.2 范围内变化）、界面张力比 σ21（在 0.125-8.0 范围内变化） ，锥角α（在4°-34°的范围内变化）和内部液滴的初始位置（即液滴偏心率）被考虑在内。从有限变形模式，当增加 Ca、R1/R0、R21 和 α 中的任何一个时，就会发生内部液滴向破碎模式的转变，或减少 μ21 和 σ21 中的任何一个。当内部液滴最初位于更靠近外部液滴的前导侧时，破碎模式也会增强。然而，改变 μ31 不会引起这些模式之间的转换。还提出了基于这些参数的这些模式的状态图。