Abstract Compound droplet collision has been found in various industrial and academic applications. Such colliding phenomena of two droplets in simple shear flow are numerically resolved by a front-tracking technique. Initially, each compound droplet, assumed cylindrical, contains one concentric inner droplet. They are separated at the lateral and vertical intervals denoted by Δx0 and Δy0. Because of the shear flow, the compound droplets interact with each other and exhibit three collision modes: passing-over, merging (i.e. coalescence) and reversing. These modes and their transition are affected by many parameters including the Reynolds Re and Capillary Ca numbers (based on the properties of the outer fluid), the viscosity ratios μ13 and μ23, the interfacial tension ratio σ12 of the inner to outer interfaces, the ratio of the radii of the inner to outer droplets R12 and the initial distance between them (in terms of Δx0 and Δy0). It is found that from a merging mode, decreasing Re from 2.51 to a value less than or equal to 1.0 induces a transition to a reversing mode, whereas, increasing Ca from 0.005 to a value greater than or equal to 0.04 leads to a transition to a passing-over mode. A transition from the merging to passing-over modes also appears when varying μ23 in the range of 0.1–10.0 or varying R12 in the range of 0.2–0.8. A transition from a passing-over mode to a reversing one is available when increasing Δx0 or decreasing Δy0. Three modes of collision all occur when μ13 is varied in the range of 0.1–10.0. However, the variation of σ12 does not induce any transition between different modes. Several phase diagrams in terms of Re versus Ca, or Δx0 versus Δy0 are also proposed to show the transitions between these modes.

中文翻译：

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简单剪切流中复合液滴碰撞模式的参数研究

摘要 复合液滴碰撞在各种工业和学术应用中都有发现。简单剪切流中两个液滴的这种碰撞现象可以通过前向跟踪技术进行数值解析。最初，假设为圆柱形的每个复合液滴包含一个同心的内部液滴。它们以 Δx0 和 Δy0 表示的横向和垂直间隔分开。由于剪切流，复合液滴彼此相互作用并表现出三种碰撞模式：通过、合并（即聚结）和反向。这些模式及其转变受许多参数的影响，包括雷诺 Re 和毛细管 Ca 数（基于外部流体的性质）、粘度比 μ13 和 μ23、内外界面的界面张力比 σ12、内部和外部液滴 R12 的半径之比和它们之间的初始距离（以 Δx0 和 Δy0 表示）。发现从合并模式，将 Re 从 2.51 减小到小于或等于 1.0 的值会导致向反向模式的转变，而将 Ca 从 0.005 增加到大于或等于 0.04 的值会导致转变为一种穿越模式。当 μ23 在 0.1-10.0 的范围内变化或 R12 在 0.2-0.8 的范围内变化时，也会出现从合并模式到通过模式的转变。当增加 Δx0 或减少 Δy0 时，可以从通过模式过渡到反向模式。当 μ13 在 0.1-10.0 的范围内变化时，三种碰撞模式都会发生。然而，σ12 的变化不会引起不同模式之间的任何转变。几个 Re 与 Ca 的相图，