The Rheology of Granular Mixtures with Varying Size, Density, Particle Friction and Flow Geometry

TL;DR

This study uses discrete element simulations to analyze how granular mixture rheology depends on particle properties and flow conditions, proposing a unified model that combines $(I)$-rheology and kinetic theory.

Contribution

It introduces a power-law scaling model that unifies local and non-local rheology data for granular mixtures, accounting for particle size, density, and friction effects.

Findings

Stress ratio and concentration scale with inertial number using volume averaging.

Critical packing fraction correlates with skewness, polydispersity, and friction.

A unified power-law model collapses diverse rheology data onto a master curve.

Abstract

Employing the discrete element method, we study the rheology of dense granular media mixtures, varying in size, density, and frictional properties of particles, across a spectrum from quasi-static to inertial regimes. By accounting for the volumetric contribution of each solid phase, we find that the stress ratio, $\mu$, and concentration $\phi$, scale with the inertial number when using volume averaging to calculate mean particle density, friction and size. Moreover, the critical packing fraction correlates with skewness, polydispersity, and particle friction, irrespective of the size distribution. Notably, following the work of Kim and Kamrin [2020] we introduce a rheological power-law scaling to collapse all or monodisperse and polydisperse data, reliant on concentration, dimensionless granular temperature, and the inertial number. This model seamlessly merges the $\mu(I)$-rheology and Kinetic Theory, enabling the unification of all local and non-local rheology data onto a single master curve.