Nonlinear dynamics of a shear banding interface

TL;DR

This paper investigates the nonlinear behavior of shear banding interfaces in a 2D shear flow using the Johnson Segalman model, revealing instabilities, wave transitions, and chaotic dynamics.

Contribution

It provides the first numerical analysis of nonlinear shear band interface dynamics, including instability mechanisms and transition to chaos.

Findings

Flat interfaces become unstable with small undulations for small interfacial width ratios.

Transition from steady traveling waves to rippling waves with periodic stress response.

Presence of multiple bands leads to erratic interfacial behavior and low-dimensional chaos.

Abstract

We study numerically the nonlinear dynamics of a shear banding interface in two dimensional planar shear flow, within the non-local Johnson Segalman model. Consistent with a recent linear stability analysis, we find that an initially flat interface is unstable with respect to small undulations for sufficiently small ratio of the interfacial width $\ell$ to cell length $L_x$. The instability saturates in finite amplitude interfacial fluctuations. For decreasing $\ell/L_x$ these undergo a non equilibrium transition from simple travelling interfacial waves with constant average wall stress, to periodically rippling waves with a periodic stress response. When multiple shear bands are present we find erratic interfacial dynamics and a stress response suggesting low dimensional chaos.