The Johnson-Segalman model with a diffusion term in Couette flow

TL;DR

This paper investigates the Johnson-Segalman model with a diffusion term in Couette flow, revealing how the added term influences shear banding behavior, steady states, and metastability in complex fluids.

Contribution

It introduces a gradient term to the Johnson-Segalman model, showing how it reduces the degeneracy of steady states and affects shear banding in cylindrical Couette flow.

Findings

Gradient term breaks degeneracy of steady states

Curvature influences observable steady state behavior

Metastability implications discussed

Abstract

We study the Johnson-Segalman (JS) model as a paradigm for some complex fluids which are observed to phase separate, or ``shear-band'' in flow. We analyze the behavior of this model in cylindrical Couette flow and demonstrate the history dependence inherent in the local JS model. We add a simple gradient term to the stress dynamics and demonstrate how this term breaks the degeneracy of the local model and prescribes a much smaller (discrete, rather than continuous) set of banded steady state solutions. We investigate some of the effects of the curvature of Couette flow on the observable steady state behavior and kinetics, and discuss some of the implications for metastability.