Linear instability of planar shear banded flow

TL;DR

This paper investigates the linear stability of planar shear banded flow using the non local Johnson Segalman model, revealing that the interface is linearly unstable to in-plane perturbations over a range of wavevectors.

Contribution

It demonstrates the linear instability of shear band interfaces within the Johnson Segalman model, providing insights into the nature of the instability and its implications for shear flow stability.

Findings

Interface linearly unstable to perturbations

Perturbations grow over a range of wavevectors

Discussion on stability of phase separated domains

Abstract

We study the linear stability of planar shear banded flow with respect to perturbations with wavevector in the plane of the banding interface, within the non local Johnson Segalman model. We find that perturbations grow in time, over a range of wavevectors, rendering the interface linearly unstable. Results for the unstable eigenfunction are used to discuss the nature of the instability. We also comment on the stability of phase separated domains to shear flow in model H.