# Dynamics of Ball-Chains and Very Elastic Fibres Settling under Gravity in a Viscous Fluid

## TL;DR

This study investigates the complex settling behaviors of ball-chains and elastic fibers in viscous fluids at low Reynolds numbers, combining experiments and numerical simulations to reveal their shapes, rotations, and interactions.

## Contribution

It provides new experimental and numerical insights into the dynamics and shapes of ball-chains and elastic fibers settling in viscous fluids, highlighting non-planar motions and interactions.

## Key findings

- Single ball-chains often rotate and are non-planar.
- Shorter chains form distorted U shapes.
- Longer chains form distorted W shapes and deform out of plane.

## Abstract

We study experimentally the dynamics of one and two ball-chains settling under gravity in a very viscous fluid at a Reynolds number much smaller than unity. 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, and longer ones in the early stage of the evolution form a shape resembling distorted W, and later deform non-symmetrically and significantly out of plane. This behaviour is reproduced in our numerical simulations for a single very elastic filament, with the use of the bead model and multipole expansion of the Stokes equations, corrected for lubrication and 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.