Stability of sedimenting flexible loops

TL;DR

This study investigates the sedimentation behavior of flexible loops in viscous fluids through simulations and stability analysis, revealing stable planar shapes and regimes influenced by elastic and gravitational forces.

Contribution

It introduces a combined numerical and analytical approach to analyze the stability and dynamics of sedimenting flexible loops, identifying key governing parameters.

Findings

Loops tend to settle into stable, planar shapes.

Three distinct dynamical regimes are identified.

A semi-analytic stability criterion is developed and verified.

Abstract

We study the behaviour of circular flexible loops sedimenting in a viscous fluid by numerical simulations and linear stability analysis. The numerical model involves a local slender-body theory approximation for the flow coupled to the Euler-Bernoulli elastic forces for an inextensible fibre. Starting from an inclined circle, we simulate the dynamics using truncated Fourier modes to observe three distinct regimes of motion: absolute stability, two-, and three-dimensional dynamics, depending on therelative importance of elastic and gravitational forces. We identify the governing parameter and develop a simple semi-analytic stability criterion, which we verify numerically. In all cases, sedimenting loops converge to stable, planar shape equilibria with one free parameter related to the initial conditions and material properties of the fibre.