Rheology of inelastic hard spheres at finite density and shear rate

Abstract

Considering a granular fluid of inelastic smooth hard spheres we discuss the conditions delineating the rheological regimes comprising Newtonian, Bagnoldian, shear thinning, and shear thickening behavior. Developing a kinetic theory, valid at finite shear rates and densities around the glass transition density, we predict the viscosity and Bagnold coefficient at practically relevant values of the control parameters. The determination of full flow curves relating the shear stress $\sigma$ to the shear rate $\dot{\gamma }$, and predictions of the yield stress complete our discussion of granular rheology derived from first principles.

arXiv comment7 pages, minor fixes and extended appendix

References in corpus (36)

• Fluctuation-Dissipation: Response Theory in Statistical Physics
• Random Packings of Frictionless Particles
• Shear thickening in concentrated suspensions: phenomenology, mechanisms, and relations to jamming
• Theory of nonlinear rheology and yielding of dense colloidal suspensions
• Local determination of the constitutive law of a dense suspension of non-colloidal particles through MRI
• A unified description of the rheology of hard-particle suspensions
• Granular Shear Flow Dynamics and Forces : Experiment and Continuum Theory
• A dynamic jamming point for shear thickening suspensions
• Shear thickening and migration in granular suspensions
• Glass Rheology: From mode-coupling theory to a dynamical yield criterion
• Schematic models for dynamic yielding of sheared colloidal glasses
• A mode coupling theory for Brownian particles in homogeneous steady shear flow
• Jamming, Yielding and Rheology of Weakly Vibrated Granular Media
• Shear thickening in granular suspensions: inter-particle friction and dynamically correlated clusters
• Shear thickening of cornstarch suspensions
• Forcing and Velocity Correlations in a Vibrated Granular Monolayer
• Approach to jamming in an air-fluidized granular bed
• Nonlinear rheology of colloidal dispersions
• Transport Coefficients for Granular Media from Molecular Dynamics Simulations
• Shear thickening in non-Brownian suspensions: an excluded volume effect
• Bagnold scaling, density plateau, and kinetic theory analysis of dense granular flow
• Transport coefficients of a heated granular gas
• Dense colloidal suspensions under time-dependent shear
• Glass Transition for Driven Granular Fluids
• Overshoots in stress strain curves: Colloid experiments and schematic mode coupling theory
• The Origin of a Repose Angle: Kinetics of Rearrangements for Granular Materials
• Shear and normal stress measurements in non-Brownian monodisperse and bidisperse suspensions
• Thinning or thickening? Multiple rheological regimes in dense suspensions of soft particles
• Rheology of Weakly Vibrated Granular Media
• The Glass Transition in Driven Granular Fluids: A Mode-Coupling Approach
• Unified rheology of vibro-fluidized dry granular media: From slow dense flows to fast gas-like regimes
• Nonequilibrium mode-coupling theory for uniformly sheared underdamped systems
• Nonequilibrium mode-coupling theory for uniformly sheared systems
• Granular Matter: a wonderful world of clusters in far-from-equilibrium systems
• Effect of Collisional Elasticity on the Bagnold Rheology of Sheared Frictionless Two Dimensional Disks
• Kinetic theory for strong uniform shear flow of granular media at high density

Cited by in corpus (10)

• Slow time scales in a dense vibrofluidized granular material
• Non-Newtonian rheology in inertial suspensions of inelastic rough hard spheres under simple shear flow
• Integration through transients approach to the $\mu (\mathcal{I})$ rheology
• From sub-aging to hyper-aging in structural glasses
• Integration through transients for inelastic hard sphere fluids
• Rheological regimes in agitated granular media under shear
• Rheology of granular liquids in extensional flows: Beyond the $\mu (\mathcal{I})$-law
• Simple shear flow in granular suspensions: Inelastic Maxwell models and BGK-type kinetic model
• A self-consistent current response theory of jamming and vibrational modes in low-temperature amorphous solids
• Mode-coupling theory of the glass transition for a liquid in a periodic potential