There are many interesting and unusual effects related to the levitating droplet cluster. Most of these have been discovered very recently. Besides the regular (hexagonally arranged) cluster, there is a chain cluster including the branched cluster, small clusters, and the ring cluster. Now we are reporting a new phenomenon – a hierarchical cluster built of small groups of droplets. The droplets permanently keep rearranging, so the phenomenon is the “deterministic chaos” (remember the Lorenz “strange” attractor?).

When I was a student in the 1990s, one of my teachers told that the Mechanics of the 21st century will be the mechanics of the instability (as opposed to the theory of stability which he taught then). I think he was right. In an unstable system you cannot predict what will happen with a small fluctuation. But you can use new Big Data / Machine Learning paradigm to establish correlations in such quasi-chaotic systems. Saying that, applying the ML may be the next step of our research, but today our paper which reports the discovery of the new phenomenon – the hierarchical cluster – has been accepted!

A. Fedorets, L. A. Dombrovsky, E Bormashenko, and M. Nosonovsky “A hierarchical levitating cluster containing transforming small aggregates of water droplets” Microfluidics and Nanofluidics 26 (7), 52 (2022) https://doi.org/10.1007/s10404-022-02557-9

Abstract
A new type of levitating droplet cluster composed of often transforming small aggregates of water droplets is described for the first time. Unlike earlier observed droplet clusters controlled by aerodynamic forces, which formed either an ordered hexagonal structure or a chain structure, the cluster under consideration has a hierarchical organization. Small groups of closely spaced or packed droplets with interactions controlled by the electrostatic force are combined into larger structures controlled by aerodynamic forces. Since charged droplets in the nucleus of the cluster do not have dynamically stable configurations, droplet aggregates keep continuously restructuring. However, droplets with lower charges in external layers of the cluster form a stable hexagonal structure.

Rearrangement of water droplet groups in the hierarchical cluster within 0.07 s