A Unified Glassy Rheology for Granular Matter

TL;DR

This paper introduces a universal, microscopically-based rheological model for dense granular flows, unifying granular physics with disordered systems and explaining glassy behaviors.

Contribution

It develops a new constitutive law based on structural relaxation, bridging microscopic dynamics with macroscopic flow regimes in granular matter.

Findings

Established a universal constitutive law for granular flows.

Linked granular rheology to glassy behaviors via a statistical framework.

Unified granular rheology with disordered systems physics.

Abstract

Granular flows are ubiquitous in nature and industrial applications, yet a complete continuum theory remains a long-standing challenge. The leading empirical approach, {\mu}(I) rheology, lacks microscopic foundations and becomes multivalued in dense, slowly sheared flows where nonlocal corrections are required. Exploiting state-of-the-art high-speed X-ray tomography to investigate microscopic dynamics of dense granular flows in a Couette geometry, we establish a new, universal constitutive law spanning quasi-static to inertial regimes based on structural relaxation, resolving the fundamental difficulty in the original {\mu}(I) framework. By further establishing a non-equilibrium statistical framework for granular flows, we demonstrate an intrinsic analogy between driven granular matter and hard-sphere liquids owing to their identical Carnahan-Starling equation of state, naturally explaining our rheological approach and the emergence of glassy behaviors. Our framework unifies granular rheology with the broader physics of disordered systems and provides a complete, microscopically-based theoretical framework for dense granular flow.