Interaction of vortex rings generated by two unsynchronised drop impacts
Abstract
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 ≥ 7 ms). At 7 ≤ Δt<80 ms, the creation of the second vortex ring is impaired, whereas at Δt≥ 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.
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BibTeX
@misc{huttunen2026interaction,
title = {{Interaction of vortex rings generated by two unsynchronised drop impacts}},
author = {Anna A. L. Huttunen and Guilherme Moreira Bessa and Matilda Backholm},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2607.07214},
eprint = {2607.07214},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.07214},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Interaction of vortex rings generated by two unsynchronised drop impacts
AU - Anna A. L. Huttunen
AU - Guilherme Moreira Bessa
AU - Matilda Backholm
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2607.07214
UR - https://arxiv.org/abs/2607.07214
AB - 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 ≥ 7 ms). At 7 ≤ Δt<80 ms, the creation of the second vortex ring is impaired, whereas at Δt≥ 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.
ER -