Dynamics and Topology of Flexible Chains: Knots in Steady Shear Flows

TL;DR

This study uses numerical simulations to explore how flexible elastic fibers in steady shear flows form, unform, and re-form knots, revealing two main conformational modes and the dynamic nature of their topology.

Contribution

It introduces a detailed analysis of knot formation and unknots in flexible chains under shear flow, highlighting the dynamic topological transitions and their dependence on elastic parameters.

Findings

Identification of two distinct conformational modes.

Observation of knotting and unknotting cycles in flow.

Correlation between topology changes and flow properties.

Abstract

We use numerical simulations of a bead-spring model chain to investigate the evolution of the conformation of long and flexible elastic fibers in a steady shear flow. In particular, for rather open initial configurations, and by varying a dimensionless elastic parameter, we identify two distinct conformational modes with different final size, shape, and orientation. Through further analysis we identify slipknots in the chain. Finally, we provide examples of initial configurations of an "open" trefoil knot that the flow unknots and then knots again, sometimes repeating several times. These changes in topology should be reflected in changes in bulk rheological and/or transport properties.