Spontaneous instabilities and stick-slip motion in a generalized Hebraud-Lequeux model

TL;DR

This paper generalizes the Hebraud-Lequeux model for jammed materials, revealing oscillating instabilities that cause intermittent stick-slip flows, potentially explaining observed serrated flows in glassy materials under shear.

Contribution

The authors introduce a modification to the HL model that incorporates an additional time scale, leading to new oscillatory instabilities and intermittent flow behaviors.

Findings

Generalized HL model exhibits oscillating instabilities.

Instabilities lead to intermittent stick-slip flows.

Scenario may explain serrated flows in glassy materials.

Abstract

We revisit the H\'ebraud-Lequeux (HL) model for the rheology of jammed materials and argue that a possibly important time scale is missing from HL's initial specification. We show that our generalization of the HL model undergoes interesting oscillating instabilities for a wide range of parameters, which lead to intermittent, stick-slip flows under constant shear rate. The instability we find is akin to the synchronization transition of coupled elements that arises in many different contexts (neurons, fireflies, financial bankruptcies, etc.). We hope that our scenario could shed light on the commonly observed intermittent, serrated flows of glassy materials under shear.