Hydrodynamics of fluid-solid coexistence in dense shear granular flow

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.

References in corpus (20)

• Patterns and Collective Behavior in Granular Media: Theoretical Concepts
• Granular Shear Flow Dynamics and Forces : Experiment and Continuum Theory
• Towards granular hydrodynamics in two-dimensions
• Hysteresis and competition between disorder and crystallization in sheared and vibrated granular flow
• Compaction of a granular material under cyclic shear
• Partially fluidized shear granular flows: Continuum theory and MD simulations
• Inherent Rheology of a Granular Fluid in Uniform Shear Flow
• Transport Coefficients for Granular Media from Molecular Dynamics Simulations
• Global Equation of State of two-dimensional hard sphere systems
• Close-packed floating clusters: granular hydrodynamics beyond the freezing point?
• Transport properties of dense dissipitive hard-sphere fluids for arbitrary energy loss models
• Transport coefficients of a heated granular gas
• Quantitative study of a freely cooling granular medium
• First normal stress difference and crystallization in a dense sheared granular fluid
• A Hydrodynamic model for a dynamical jammed-to-flowing transition in gravity driven granular media
• Chapman-Enskog expansion about nonequilibrium states: the sheared granular fluid
• Transport coefficients for an inelastic gas around uniform shear flow: Linear stability analysis
• Shear-induced crystallization of a dense rapid granular flow: hydrodynamics beyond the melting point?
• The Behavior of Granular Materials under Cyclic Shear
• Instability of the symmetric Couette-flow in a granular gas: hydrodynamic field profiles and transport

Cited by in corpus (7)

• Universality of shear-banding instability and crystallization in sheared granular fluid
• Navier-Stokes hydrodynamics of thermal collapse in a freely cooling granular gas
• Hydrodynamic instabilities in shear flows of cohesive granular particles
• Weakly nonlinear analysis of two dimensional sheared granular flow
• Shear-banding instability in arbitrarily inelastic granular shear flows
• Quantitative test of the time dependent Gintzburg-Landau equation for sheared granular flow in two dimension
• Noise induces rare events in granular media