Unified Theory of Inertial Granular Flows and Non-Brownian Suspensions

TL;DR

This paper develops a unified theoretical framework for dense inertial granular flows and non-Brownian suspensions, predicting their rheological behavior near jamming and comparing with empirical and numerical data.

Contribution

It introduces a comprehensive scaling theory applicable to both suspensions and inertial flows of frictionless particles, highlighting differences with frictional systems.

Findings

Good agreement between theory and empirical data for frictionless systems

Frictional inertial flows exhibit different scaling properties

Predictions made for microscopic dynamical quantities accessible experimentally

Abstract

Rheological properties of dense flows of hard particles are singular as one approaches the jamming threshold where flow ceases, both for aerial granular flows dominated by inertia, and for over-damped suspensions. Concomitantly, the lengthscale characterizing velocity correlations appears to diverge at jamming. Here we introduce a theoretical framework that proposes a tentative, but potentially complete scaling description of stationary flows. Our analysis, which focuses on frictionless particles, applies {\it both} to suspensions and inertial flows of hard particles. We compare our predictions with the empirical literature, as well as with novel numerical data. Overall we find a very good agreement between theory and observations, except for frictional inertial flows whose scaling properties clearly differ from frictionless systems. For over-damped flows, more observations are needed to decide if friction is a relevant perturbation or not. Our analysis makes several new predictions on microscopic dynamical quantities that should be accessible experimentally.