Self-sustaining oscillations of a falling sphere through Johnson-Segalman fluids

TL;DR

This paper demonstrates through numerical simulations that the Johnson-Segalman model can reproduce self-sustaining oscillations in the falling speed of a sphere in viscoelastic fluids, capturing complex oscillatory behaviors.

Contribution

It shows that the Johnson-Segalman model can replicate continual oscillations of a falling sphere, expanding understanding of viscoelastic fluid dynamics.

Findings

Reproduces oscillatory falling speeds in simulations

Shows sphere slows down then accelerates repeatedly

Validates Johnson-Segalman model for dynamic behaviors

Abstract

We confirm numerically that the Johnson-Segalman model is able to reproduce the continual oscillations of the falling sphere observed in some viscoelastic models. The empirical choice of parameters used in the Johnson-Segalman model is from the ones that show the non-monotone stress-strain relation of the steady shear flows of the model. The carefully chosen parameters yield continual, self-sustaining, (ir)regular and periodic oscillations of the speed for the falling sphere through the Johnson-Segalman fluids. In particular, our simulations reproduce the phenomena: the falling sphere settles slower and slower until a certain point at which the sphere suddenly accelerates and this pattern is repeated continually.