Interaction of vortex rings generated by two unsynchronised drop impacts

Abstract

A liquid drop falling into a deep 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. An unsynchronisation larger than this drastically influences the collision and merging, which either becomes asymmetric and incomplete ($0.5 < Δt<7$ ms) or does not happen at all ($Δt \geq 7$ 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 eventually the two rings evolve without influencing each other. We show that these different 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.