Steady inhomogeneous shear flows as mechanical phase transitions

TL;DR

This paper introduces a mechanical phase transition framework to understand inhomogeneous shear flows and shear banding in complex fluids, providing a new theoretical approach to these non-equilibrium phenomena.

Contribution

It develops a novel mechanical phase transition approach by mapping non-local constitutive relations onto dynamical systems, advancing the theoretical understanding of shear banding and solid-melt coexistence.

Findings

Framework successfully describes shear banding in complex fluids

Reveals coexistence conditions for solid and sheared melt

Provides a mechanical analogy for non-equilibrium inhomogeneous flows

Abstract

Inhomogeneous flows and shear banding are of interest for a range of applications but have been eluding a comprehensive theoretical understanding, mostly due to the lack of a framework comparable to equilibrium statistical mechanics. Here we revisit models of fluids that reach a stationary state obeying mechanical equilibrium. Starting from a non-local constitutive relation, we apply the idea of a "mechanical phase transition" and map the constitutive relation onto a dynamical system through an integrating factor. We illustrate this framework for two applications: shear banding in strongly thinning complex fluids and the coexistence of a solid with its sheared melt. Our results contribute to the growing body of work following a mechanical route to describe inhomogeneous systems away from thermal equilibrium.