A liquid drop falling into a pool can create a vortex ring at the right impact conditions. Such drop-formed vortex rings are of importance in nature and technology and the dynamics of rings created by single and synchronised double drop impacts have been extensively studied. In practice, two neighbouring drops rarely impact a liquid surface exactly at the same time, yet the interaction of two unsynchronised vortex rings have not been studied. Here, we have performed experiments with two water drops impacting a water pool at varying time differences $Δt$. By using particle image velocimetry, we have quantified the time-evolution of the resulting vortex rings. We find four distinct categories of vortex ring evolution depending on $Δt$. At $Δt<0.5$ ms, fully symmetric merging of the vortex rings occur. At unsynchronisation larger than this, the merging either becomes asymmetric and incomplete ($0.5 < Δt<7$ ms) or non-existent ($Δt \geq 7$ ms). At $7 \leq Δt<80$ ms, the creation of the second vortex ring is impaired, whereas at $Δt\geq 80$ ms, the first impact no longer affects the formation of the second ring and the two rings evolve without influencing each other. We show that these regimes can be explained by the capillary waves created by the first droplet. Our results demonstrate the importance of the time difference between drop impacts in the creation and subsequent interaction of two adjacent drop-formed vortex rings, which is important for achieving uniform and controlled mixing in high-throughput applications.
On the vortex ring formation and mixing in thin films upon droplet impact
Institute for Fluid Mechanics and Aerodynamics, TU Darmstadt（达姆施塔特工业大学流体力学与空气动力学研究所）；Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology（韩国科学技术院机械工程系）
On angled bounce-off impact of a drop impinging on a flowing soap film
小液滴有角度地撞击在薄的流动肥皂膜上经常表现出与更常见的流体动力学相互作用一起工作的体积弹性效应的罕见出现。可观察到三种碰撞状态：（a）液滴穿透膜，（b）液滴与流聚结，以及（c）液滴从膜表面反弹。在冲击期间，液滴随着膜的大部分弹性形变而变形。对于接近切向的撞击，反弹机制占主导地位。我们概述了一个降阶的分析框架，假设一个可变形的液滴和一个可变形的三维薄膜，和理想化调用基于相位的参数研究。薄膜的倾斜角和冲击前后液滴尺寸的比值决定了相位参数。我们还进行了实验，垂直下降的液滴对倾斜的肥皂膜，恒定的压力头下流动的影响。模型预测相域的反弹比较以及我们的实验结果。此外，实验显示动量转移到薄膜的形式脱落涡偶极子，随着自由表面波的传播。在咨询以前发表的工作，我们注意到，对于运动的水行走的昆虫使用的脉冲动作，动量分布的脱落涡和波都是显着的，分别采取2/3-rd和1/3-rd的传递流向的动量。鉴于潜在的类似的脉冲行动，这一理论适用于反弹的例子在我们的实验中，和由此产生的脱落涡偶极子动量相比，从粒子成像测速数据计算的动量。幅度揭示了相同的顺序（$10^{-7}$ N $\cdot$），这表明反弹制度可以作为一个简单的模拟界面生物运动依赖于脉冲反应。
