Bending-Filament Model for the Buckling and Coiling Instability of Viscous Fluid Rope

TL;DR

This paper introduces a simple one-dimensional model for the buckling and coiling instability of a viscous fluid rope, successfully replicating experimental observations and analyzing transition behaviors.

Contribution

The model accounts for axial and viscous forces in a viscous fluid rope, reproduces experimental regimes without adjustable parameters, and discusses unsteady motion and hysteresis effects.

Findings

Reproduces three coiling regimes observed experimentally.

Derives an expression for critical fall height affecting coiling frequency.

Identifies hysteresis in coil-uncoil transition under weak gravity.

Abstract

A simple model is proposed for the buckling and coiling instability of a viscous "fluid rope" falling on a plane. By regarding a fluid rope as a one-dimensional flow, this model accounts for only the axial and shared viscous forces. Our model successfully reproduces several experiments with no adjustable parameters, such as the existence of three distinct coiling regimes reported in Phys. Rev. Lett. 93, 214502 (2004). Our model allows for the discussion of unsteady motion. An expression for the critical fall height at which the coiling frequency changes from a decrease to increase was phenomenologically derived. It was found that the coil-uncoil transition shows remarkable hysteresis only for weak gravity condition.