Spontaneous knotting of a flexible fiber in chaotic flows

Benjamin Favier
Phys. Rev. E 103, 043101 – Published 12 April 2021
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Abstract

We consider the problem of an inextensible but flexible fiber advected by a steady chaotic flow, and ask the simple question of whether the fiber can spontaneously knot itself. Using a one-dimensional 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.

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  • Received 25 November 2020
  • Accepted 18 March 2021

DOI:https://doi.org/10.1103/PhysRevE.103.043101

©2021 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear DynamicsFluid DynamicsPolymers & Soft Matter

Authors & Affiliations

Benjamin Favier*

  • Aix Marseille Univ, CNRS, Centrale Marseille, IRPHE, Marseille, France

  • *favier@irphe.univ-mrs.fr

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Issue

Vol. 103, Iss. 4 — April 2021

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