Abstract The rheological behaviors of a compound droplet in a confined geometry are of importance in many industrial and natural processes. However, a detailed numerical simulation of the finite deformation and its transition to the breakup of the multi-core compound droplet in an axisymmetric T-junction channel is still lacking. The present study is to fill this gap through the numerical simulations of a two-core compound droplet that deforms and breaks up in this channel configuration. The numerical results are obtained by the axisymmetric front-tracking method. Our new finding is that the compound droplet in the channel can experience the finite deformation or the breakup depending on the flow condition or the configuration of the channel. In the finite deformation mode (i.e. non-breakup mode), the droplet rapidly reaches the maximum deformation before approaching the perpendicular rigid wall. The most deformation occurs with the outer droplet, and the inner droplet closer to the wall is less deformed than the other inner core droplet. In the breakup mode, three breakup patterns are recognized: (i) breakup type I occurring when breaking up only the outer droplet; (ii) breakup type 2 occurring when breaking up only the inner droplets; (iii) breakup type 3 occurring when breaking up both inner and outer droplets. The transition from the non-breakup mode to the breakup mode is available when increasing the Reynolds number Re (from 0.16 to 40.0), the capillary number Ca (from 0.04 to 4.0), the size Ro of the outer droplet and the middle-to-outer fluid viscosity ratio μ21, or decreasing the size Ri of the inner droplets, the radial size C2 of the channel (normalized by the channel axial size C1) and the interfacial tension ratio of the inner to the outer droplets. The transition diagrams based on some of these parameters are also proposed to provide a more complete picture of the two-core compound droplet behaving in the axisymmetric T-junction channel. .

中文翻译：

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轴对称 T 型接头通道中双核复合液滴变形和破碎的数值模拟

摘要 受限几何形状中复合液滴的流变行为在许多工业和自然过程中具有重要意义。然而，仍然缺乏对有限变形及其向轴对称 T 型接头通道中多核复合液滴破裂的转变的详细数值模拟。目前的研究是通过对在这种通道配置中变形和破裂的双核复合液滴的数值模拟来填补这一空白。数值结果是通过轴对称前跟踪方法获得的。我们的新发现是通道中的复合液滴可以根据流动条件或通道的配置经历有限变形或破裂。在有限变形模式（即非破碎模式）下，液滴在接近垂直刚性壁之前迅速达到最大变形。大多数变形发生在外部液滴，靠近壁的内部液滴比其他内核液滴变形更小。在破碎模式中，识别出三种破碎模式：（i）仅破碎外部液滴时发生的破碎类型 I；(ii) 仅分解内部液滴时发生的分解类型 2；(iii) 分解内部和外部液滴时发生的分解类型 3。当雷诺数 Re（从 0.16 到 40.0）、毛细管数 Ca（从 0.04 到 4.0）、外部液滴的尺寸 Ro 和中间到- 外部流体粘度比 μ21，或减小内部液滴的尺寸 Ri，通道的径向尺寸 C2（由通道轴向尺寸 C1 归一化）和内部液滴与外部液滴的界面张力比。还提出了基于这些参数中的一些参数的过渡图，以提供更完整的双核复合液滴在轴对称 T 型连接通道中的行为图。.