Dense granular rheology from fluctuations

TL;DR

This paper introduces a comprehensive framework for understanding dense granular flows, combining theoretical analysis and simulations to explore flow behavior, critical exponents, and the non-universal nature of velocity distributions.

Contribution

It develops a unifying theoretical model for dense granular rheology, linking granular temperature dynamics with nonlocal fluidity, supported by numerical simulations.

Findings

Derived an expression for a critical exponent in granular flows.

Validated models for unclosed terms using direct numerical simulations.

Identified non-universality in velocity and strain rate distributions due to production and diffusion balance.

Abstract

A unifying framework to describe dense flows of dry, deformable grains is proposed. Perturbative analysis of a granular temperature equation describing flows with contact stresses, supported by the recovery of the nonlocal granular fluidity equation, is used to derive an expression for a recently postulated critical exponent. Direct numerical simulation justifies models for the unclosed terms that provide a material-dependent estimate. Non-universality of the velocity and strain rate distributions, arising from competition between production and diffusion, rationalizes model shortcomings.