Periodic motion of sedimenting flexible knots

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.

to be published in Phys. Rev. Lett

References in corpus (5)

• How knots influence properties of proteins
• Sedimentation of pairs of hydrodynamically interacting semiflexible filaments
• Dynamics and Topology of Flexible Chains: Knots in Steady Shear Flows
• Complex dynamics of knotted filaments in shear flow
• Dynamics of elastic dumbbells sedimenting in a viscous fluid: oscillations and hydrodynamic repulsion

Cited by in corpus (6)

• Flexible fibers in shear flow approach attracting periodic solutions
• Universal motion of mirror-symmetric microparticles in confined Stokes flow
• Stability of sedimenting flexible loops
• Stable Configurations Of Charged Sedimenting Particles
• Dynamical modes of highly elastic loops settling under gravity in a viscous fluid
• Hydrodynamic Inflation of Ring Polymers under Shear