Dynamic vorticity banding in discontinuously shear thickening suspensions

TL;DR

This paper presents a continuum model and particle simulations demonstrating that shear thickening suspensions can develop unsteady, dynamic vorticity bands due to stress-concentration coupling, challenging previous beliefs about steady-state band formation.

Contribution

It introduces a coupled continuum model and particle simulations showing unsteady vorticity banding in shear thickening suspensions, highlighting the role of stress-concentration interactions.

Findings

Homogeneous flow is unstable to vorticity banding in negative slope regime.

Vorticity bands are unsteady and exhibit spatiotemporal patterns.

Particle simulations confirm the dynamical banding behavior predicted by the model.

Abstract

It has recently been argued that steady-state vorticity bands cannot arise in shear thickening suspensions, because the normal stress imbalance across the interface between the bands will set up particle migrations. In this Letter, we develop a simple continuum model that couples shear thickening to particle migration. We show by linear stability analysis that homogeneous flow is unstable towards vorticity banding, as expected, in the regime of negative constitutive slope. In full nonlinear computations, we show however that the resulting vorticity bands are unsteady, with spatiotemporal patterns governed by stress-concentration coupling. We furthermore show that these dynamical bands also arise in direct particle simulations, in good agreement with the continuum model.