A class of periodic and quasi-periodic trajectories of particles settling under gravity in a viscous fluid

TL;DR

This paper explores the dynamics of particles settling in a viscous fluid, identifying regular configurations with periodic motions and proposing mechanisms for the evolution of particle clouds.

Contribution

It introduces a family of stable, periodic particle configurations and analyzes their behavior, including effects of additional particles, in the point-particle approximation.

Findings

Identified regular configurations with periodic oscillations

Demonstrated robustness of oscillations under particle rearrangements

Proposed a mechanism for the destabilization of particle clouds

Abstract

We investigate regular configurations of a small number of particles settling under gravity in a viscous fluid. The particles do not touch each other and can move relative to each other. The dynamics is analyzed in the point-particle approximation. A family of regular configurations is found with periodic oscillations of all the settling particles. The oscillations are shown to be robust under some out-of-phase rearrangements of the particles. In the presence of an additional particle above such a regular configuration, the particle periodic trajectories are horizontally repelled from the symmetry axis, and flattened vertically. The results are used to propose a mechanism how a spherical cloud, made of a large number of particles distributed at random, evolves and destabilizes.