Partially fluidized shear granular flows: Continuum theory and MD simulations

TL;DR

This paper develops and tests a continuum theory for partially fluidized shear granular flows, using MD simulations to calibrate the model and explore flow behavior in different regimes.

Contribution

It introduces a new continuum model based on an order parameter for static-to-flow transition, validated by MD simulations and applied to gravity-driven granular flows.

Findings

The rheology of the fluid component aligns with kinetic theory even in dense regimes.

The order parameter's free energy is constructed from hysteretic bifurcation data.

The model successfully describes surface-driven granular flows under gravity.

Abstract

The continuum theory of partially fluidized shear granular flows is tested and calibrated using two dimensional soft particle molecular dynamics simulations. The theory is based on the relaxational dynamics of the order parameter that describes the transition between static and flowing regimes of granular material. We define the order parameter as a fraction of static contacts among all contacts between particles. We also propose and verify by direct simulations the constitutive relation based on the splitting of the shear stress tensor into a``fluid part'' proportional to the strain rate tensor, and a remaining ``solid part''. The ratio of these two parts is a function of the order parameter. The rheology of the fluid component agrees well with the kinetic theory of granular fluids even in the dense regime. Based on the hysteretic bifurcation diagram for a thin shear granular layer obtained in simulations, we construct the ``free energy'' for the order parameter. The theory calibrated using numerical experiments with the thin granular layer is applied to the surface-driven stationary two dimensional granular flows in a thick granular layer under gravity.