Flow instabilities in complex fluids: Nonlinear rheology and slow relaxations

TL;DR

This paper introduces two simplified models to explain long-term irregular behaviors like oscillations and chaos in complex fluids' rheological responses, focusing on nonlinear stress evolution and coupled structural dynamics.

Contribution

The paper proposes novel simplified models that capture slow relaxations and instabilities in complex fluids' rheology through coupled nonlinear equations.

Findings

Models reproduce periodic and chaotic oscillations

Coupling of variables causes rheological instabilities

Insights into slow relaxation mechanisms

Abstract

We here present two simplified models aimed at describing the long-term, irregular behaviours observed in the rheological response of certain complex fluids, such as periodic oscillations or chaotic-like variations. Both models exploit the idea of having a (non-linear) rheological equation, controlling the temporal evolution of the stress, where one of the participating variables (a "structural" variable) is subject to a distinct dynamics with a different relaxation time. The coupling between the two dynamics is a source of instability.