The simplest microscopic model of a complex fluid: flow phenomena and constitutive relation

TL;DR

This paper introduces a simple microscopic 1D model that captures complex flow behaviors of fluids, revealing universal physics behind non-Newtonian phenomena like shear banding.

Contribution

It derives a compact mean-field constitutive relation for a 1D XY-model, showing its ability to reproduce various flow regimes in complex fluids.

Findings

Model exhibits shear banding and slip-plane motion

Shear banding does not require tensorial stress fields

Provides insights into universality of flow phenomena

Abstract

It was shown in [PRL 114, 138301 (2015)] that a remarkably simple dynamical model exhibits many of the complex flow regimes and non-equilibrium phase transitions characteristic of complex fluids. By removing extraneous detail, this simplest microscopic model of non-Newtonian flow can reveal the universal physics relevant to all complex fluids. Here we present more detailed results and a full derivation of the model's compact mean-field constitutive relation, with great potential scope for insights into universality and tractable mathematics. By enforcing local conservation of angular momentum, the one-dimensional (1D) XY-model (originally used for equilibrium magnetic systems) can be driven into various flow regimes, including simple Newtonian behaviour, shear banding, solid-liquid coexistence and slip-plane motion. The model demonstrates that the phenomenon of shear banding does not rely on details of tensorial stress fields, but can exist in 1D.