Periodic and quasiperiodic motions of many particles falling in a viscous fluid

TL;DR

This study investigates the complex dynamics of many particles falling in a viscous fluid, revealing periodic, quasiperiodic, and chaotic motions, and highlighting the role of periodic orbits in cluster stability.

Contribution

It extends the analysis of particle cluster dynamics from three particles to many, identifying periodic solutions and chaotic scattering in a point-particle model.

Findings

Periodic oscillations occur in two-ring configurations.

Chaotic scattering dominates in four-ring configurations.

Long-lasting clusters are centered around periodic solutions.

Abstract

Dynamics of regular clusters of many non-touching particles falling under gravity in a viscous fluid at low Reynolds number are analysed within the point-particle model. Evolution of two families of particle configurations is determined: 2 or 4 regular horizontal polygons (called `rings') centred above or below each other. Two rings fall together and periodically oscillate. Four rings usually separate from each other with chaotic scattering. For hundreds of thousands of initial configurations, a map of the cluster lifetime is evaluated, where the long-lasting clusters are centred around periodic solutions for the relative motions, and surrounded by regions of the chaotic scattering,in a similar way as it was observed by Janosi et al. (1997) for three particles only. These findings suggest to consider the existence of periodic orbits as a possible physical mechanism of the existence of unstable clusters of particles falling under gravity in a viscous fluid.