Spontaneous knotting of a flexible fiber in chaotic flows

TL;DR

This study investigates how flexible fibers in chaotic flows can spontaneously form knots, revealing the influence of flow dynamics, fiber length, and contact forces on knot formation and stability.

Contribution

It introduces a combined modeling approach to analyze knot formation in fibers within chaotic flows, highlighting the roles of flow chaos, fiber length, and contact forces.

Findings

Longer fibers increase knotting probability.

Finite-time Lyapunov exponent enhances knot formation.

Contact forces stabilize knotted configurations.

Abstract

We consider the problem of an inextensible but flexible fiber advected by a steady chaotic flow, and ask the simple question whether the fiber can spontaneously knot itself. Using a 1D Cosserat model, a simple local viscous drag model and discrete contact forces, we explore the probability of finding knots at any given time when the fiber is interacting with the ABC class of flows. The bending rigidity is shown to have a marginal effect compared to that of increasing the fiber length. Complex knots are formed up to 11 crossings, but some knots are more probable than others. The finite-time Lyapunov exponent of the flow is shown to have a positive effect on the knot probability. Finally, contact forces appear to be crucial since knotted configurations can remain stable for times much longer than the turnover time of the flow, something that is not observed when the fiber can freely cross itself.