Non-axisymmetric instability of shear-banded Taylor-Couette flow

TL;DR

This paper investigates the non-axisymmetric flow instabilities in shear-banded Taylor-Couette flow of worm-like micelles, revealing different instability mechanisms depending on shear rate and challenging previous axisymmetric stability models.

Contribution

It provides the first non-axisymmetric linear stability analysis of shear-banded Taylor-Couette flow using the diffusive Johnson-Segalman model, highlighting new instability behaviors.

Findings

Instability driven by interface at the start of the stress plateau.

Bulk instability dominates most of the stress plateau.

Results challenge previous axisymmetric stability diagrams.

Abstract

Recent experiments show that shear-banded flows of semi-dilute worm-like micelles in Taylor-Couette geometry exhibit a flow instability in the form of Taylor-like vortices. Here we perform the non-axisymmetric linear stability analysis of the diffusive Johnson-Segalman model of shear banding and show that the nature of this instability depends on the applied shear rate. For the experimentally relevant parameters, we find that at the beginning of the stress plateau the instability is driven by the interface between the bands, while most of the stress plateau is occupied by the bulk instability of the high-shear-rate band. Our work significantly alters the recently proposed stability diagram of shear-banded flows based on axisymmetric analysis.