Dynamics of ball chains and highly elastic fibres settling under gravity in a viscous fluid

Abstract

We study experimentally the dynamics of one and two ball chains settling under gravity in a highly viscous silicon oil at a Reynolds number much smaller than unity. We record the motion and shape deformation using two cameras. We demonstrate that single ball chains in most cases do not tend to be planar and often rotate, not keeping the ends at the same horizontal level. Shorter ball chains usually form shapes resembling distorted U. Longer ones in the early stage of the evolution form a shape resembling distorted W, and later deform non-symmetrically and significantly out of a plane. The typical evolution of shapes observed in our experiments with single ball chains is reproduced in our numerical simulations of a single elastic filament. In the computations, the filament is modelled as a chain of beads. Consecutive beads are connected by springs. Additional springs link consecutive pairs of beads. Elastic forces are assumed to be much smaller than gravity. As a result, the fibre is very flexible. We assume that the fluid sticks to the surfaces of the beads. We perform multipole expansion of the Stokes equations, with a lubrication correction. This method is implemented in the precise HYDROMULTIPOLE numerical codes. In our experiments, two ball chains, initially one above the other, later move away or approach each other, for a larger or smaller initial distance, respectively.