Periodic motion of sedimenting flexible knots

TL;DR

This study investigates the sedimentation behavior of flexible knotted chains, revealing a spontaneous formation of regular oscillating toroidal structures and analyzing how chain properties influence this motion.

Contribution

It provides the first experimental and numerical analysis of sedimenting flexible knots, highlighting the emergence of stable oscillating structures and their dependence on physical parameters.

Findings

Knots form stable, oscillating toroidal structures during sedimentation.

The oscillation mode can spontaneously develop from different initial configurations.

The characteristic time scales depend on chain flexibility and aspect ratio.

Abstract

We study the dynamics of knotted deformable closed chains sedimenting in a viscous fluid. We show experimentally that trefoil and other torus knots often attain a remarkably regular horizontal toroidal structure while sedimenting, with a number of intertwined loops, oscillating periodically around each other. We then recover this motion numerically and find out that it is accompanied by a very slow rotation around the vertical symmetry axis. We analyze the dependence of the characteristic time scales on the chain flexibility and aspect ratio. It is observed in the experiments that this oscillating mode of the dynamics can spontaneously form even when starting from a qualitatively different initial configuration. In numerical simulations, the oscillating modes are usually present as transients or final stages of the evolution, depending on chain aspect ratio and flexibility, and the number of loops.