We apply the extended kinetic theory (EKT) to the dense, simple shear flow of inelastic hard spheres. EKT is a phenomenological extension of kinetic theory which aims at incorporating in the simplest possible way the role of pre-collisional velocity correlations which are likely to occur at a concentration larger than the freezing point. The main effect of that correlation is the decrease in the rate at which fluctuating energy is dissipated in inelastic collisions. We use previously published results of numerical simulations performed using an event-driven algorithm to obtain analytical expressions for the radial distribution function at contact (which diverges at a concentration lower than the value at random close packing for sheared inelastic spheres) and the correlation length (i.e., the decreasing factor of the dissipation rate) at different values of the coefficient of restitution. With those, we show that when the diffusion of fluctuating energy of the particles is negligible, EKT implies that three branches of the analytical relation between the ratio of the shear stress to the pressure and the concentration (granular rheology) exist. Hence, for a certain value of the stress ratio, up to three corresponding values of the concentration are possible, with direct implications on the existence of multiple solutions to steady granular flows.

Extended kinetic theory applied to dense, granular, simple shear flows.

BERZI, DIEGO
2014-01-01

Abstract

We apply the extended kinetic theory (EKT) to the dense, simple shear flow of inelastic hard spheres. EKT is a phenomenological extension of kinetic theory which aims at incorporating in the simplest possible way the role of pre-collisional velocity correlations which are likely to occur at a concentration larger than the freezing point. The main effect of that correlation is the decrease in the rate at which fluctuating energy is dissipated in inelastic collisions. We use previously published results of numerical simulations performed using an event-driven algorithm to obtain analytical expressions for the radial distribution function at contact (which diverges at a concentration lower than the value at random close packing for sheared inelastic spheres) and the correlation length (i.e., the decreasing factor of the dissipation rate) at different values of the coefficient of restitution. With those, we show that when the diffusion of fluctuating energy of the particles is negligible, EKT implies that three branches of the analytical relation between the ratio of the shear stress to the pressure and the concentration (granular rheology) exist. Hence, for a certain value of the stress ratio, up to three corresponding values of the concentration are possible, with direct implications on the existence of multiple solutions to steady granular flows.
2014
File in questo prodotto:
File Dimensione Formato  
2014 Acta Mech.pdf

Accesso riservato

: Post-Print (DRAFT o Author’s Accepted Manuscript-AAM)
Dimensione 285.61 kB
Formato Adobe PDF
285.61 kB Adobe PDF   Visualizza/Apri
Acta Mech_11311-835525_Berzi.pdf

accesso aperto

: Post-Print (DRAFT o Author’s Accepted Manuscript-AAM)
Dimensione 289.59 kB
Formato Adobe PDF
289.59 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/835525
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 32
  • ???jsp.display-item.citation.isi??? 24
social impact