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

摘要

We investigate regular configurations of a small number of particles settlingunder gravity in a viscous fluid. The particles do not touch each other and canmove relative to each other. The dynamics is analyzed in the point-particleapproximation. A family of regular configurations is found with periodicoscillations of all the settling particles. The oscillations are shown to berobust under some out-of-phase rearrangements of the particles. In the presenceof an additional particle above such a regular configuration, the particleperiodic trajectories are horizontally repelled from the symmetry axis, andflattened vertically. The results are used to propose a mechanism how aspherical cloud, made of a large number of particles distributed at random,evolves and destabilizes.