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

Abstract

The dynamics of regular clusters of many nontouching particles falling under gravity in a viscous fluid at low Reynolds number are analyzed within the point-particle model. The evolution of two families of particle configurations is determined: two or four regular horizontal polygons (called "rings") centered 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 in which the long-lasting clusters are centered around periodic solutions for the relative motions, and they are surrounded by regions of chaotic scattering in a similar way to what was observed by Janosi et al. [Phys. Rev. E. 56, 2858 (1997)] for three particles only. These findings suggest that we should 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.

Stokesian dynamics of sedimenting elastic rings

“…44,73 It is very interesting that such a swirling motion is also typical in completely different systems such as knotted vortex lines 74 propagating in inviscid fluid or horizontal coaxial rings made of many separated particles, sedimenting in a very viscous fluid. 75,76 Finally, probably the most intriguing mode, tank treading, is also chiral, and thus rotates. Such a tank treading motion can be found in vesicles and red blood cells.…”

Periodic Motion of Sedimenting Flexible Knots

“…Moreover, the existence of periodic solutions for flexible knotted chains is essential for such general features of the dynamics as bifurcations, instabilities and transition to chaos, which can be further analyzed in analogy to previous studies performed for simple model systems [28][29][30][31][32] of many particles settling under gravity in a viscous fluid, with a striking coexistence of both periodic oscillations and chaotic trajectories [28,32].…”

“…Closer beads exhibit stronger hydrodynamic interactions, which results in faster sedimentation and overtaking of the slower strand. Actually, the same mechanism of hydrodynamic interactions induced by gravity is responsible for swirling motions of many rigid particle systems settling under gravity [28][29][30][31][32], and also swirling motions of two elastic filaments [33], and two elastic dumbbells [36].…”