Hydrodynamics of fluid-solid coexistence in dense shear granular flow

TL;DR

This paper develops a granular hydrodynamics model for dense shear flows of inelastically colliding disks, introduces new constitutive relations, and reveals a transition to a two-phase flow with solid-like clusters at high inelasticity.

Contribution

It proposes new interpolation formulas for constitutive relations and demonstrates the transition to two-phase flow through stability analysis and MD simulations.

Findings

Shear viscosity diverges at lower density than other relations.

Uniform shear flow becomes unstable at high inelasticity.

Two-phase flow with dense clusters emerges at high inelasticity.

Abstract

We consider dense rapid shear flow of inelastically colliding hard disks. Navier-Stokes granular hydrodynamics is applied accounting for the recent finding \cite{Luding,Khain} that shear viscosity diverges at a lower density than the rest of constitutive relations. New interpolation formulas for constitutive relations between dilute and dense cases are proposed and justified in molecular dynamics (MD) simulations. A linear stability analysis of the uniform shear flow is performed and the full phase diagram is presented. It is shown that when the inelasticity of particle collision becomes large enough, the uniform sheared flow gives way to a two-phase flow, where a dense "solid-like" striped cluster is surrounded by two fluid layers. The results of the analysis are verified in event-driven MD simulations, and a good agreement is observed.