Fiber buckling in confined viscous flows: an absolute instability described by the Ginzburg-Landau equation

TL;DR

This study investigates the buckling instability of flexible fibers in viscous flows within Hele-Shaw cells, revealing an absolute instability described by the Ginzburg-Landau equation, with detailed characterization of deformation dynamics.

Contribution

It demonstrates that fiber buckling in confined viscous flows is governed by an absolute instability modeled by the Ginzburg-Landau equation, providing new insights into fiber-fluid interactions.

Findings

Buckling instability occurs in long fibers aligned with flow.

Deformation characterized by wavelength, phase velocity, and envelope growth.

The instability is linear and absolute, explained by the Ginzburg-Landau equation.

Abstract

We explore the dynamics of a flexible fiber transported by a viscous flow in a Hele-Shaw cell of height comparable to the fiber height. We show that long fibers aligned with the flow experience a buckling instability. Competition between viscous and elastic forces leads to the deformation of the fiber into a wavy shape convolved by a Bell-shaped envelope. We characterize the wavelength and phase velocity of the deformation as well as the growth and spreading of the envelope. Our study of the spatio-temporal evolution of the deformation reveals a linear and absolute instability arising from a local mechanism well described by the Ginzburg-Landau equation.