skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Different singularities in the functions of extended kinetic theory at the origin of the yield stress in granular flows

Abstract

We use previous results from discrete element simulations of simple shear flows of rigid, identical spheres in the collisional regime to show that the volume fraction-dependence of the stresses is singular at the shear rigidity. Here, we identify the shear rigidity, which is a decreasing function of the interparticle friction, as the maximum volume fraction beyond which a random collisional assembly of grains cannot be sheared without developing force chains that span the entire domain. In the framework of extended kinetic theory, i.e., kinetic theory that accounts for the decreasing in the collisional dissipation due to the breaking of molecular chaos at volume fractions larger than 0.49, we also show that the volume fraction-dependence of the correlation length (measure of the velocity correlation) is singular at random close packing, independent of the interparticle friction. The difference in the singularities ensures that the ratio of the shear stress to the pressure at shear rigidity is different from zero even in the case of frictionless spheres: we identify that with the yield stress ratio of granular materials, and we show that the theoretical predictions, once the different singularities are inserted into the functions of extended kinetic theory, are in excellent agreement withmore » the results of numerical simulations.« less

Authors:
;  [1]
  1. Politecnico di Milano, 20133 Milan (Italy)
Publication Date:
OSTI Identifier:
22403207
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Fluids (1994); Journal Volume: 27; Journal Issue: 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 42 ENGINEERING; CHAOS THEORY; COMPUTERIZED SIMULATION; FLOW MODELS; FRICTION; GRANULAR MATERIALS; KINETIC EQUATIONS; RANDOMNESS; SHEAR; SINGULARITY; SPHERES; STOWING; STRESSES

Citation Formats

Berzi, Diego, and Vescovi, Dalila. Different singularities in the functions of extended kinetic theory at the origin of the yield stress in granular flows. United States: N. p., 2015. Web. doi:10.1063/1.4905461.
Berzi, Diego, & Vescovi, Dalila. Different singularities in the functions of extended kinetic theory at the origin of the yield stress in granular flows. United States. doi:10.1063/1.4905461.
Berzi, Diego, and Vescovi, Dalila. Thu . "Different singularities in the functions of extended kinetic theory at the origin of the yield stress in granular flows". United States. doi:10.1063/1.4905461.
@article{osti_22403207,
title = {Different singularities in the functions of extended kinetic theory at the origin of the yield stress in granular flows},
author = {Berzi, Diego and Vescovi, Dalila},
abstractNote = {We use previous results from discrete element simulations of simple shear flows of rigid, identical spheres in the collisional regime to show that the volume fraction-dependence of the stresses is singular at the shear rigidity. Here, we identify the shear rigidity, which is a decreasing function of the interparticle friction, as the maximum volume fraction beyond which a random collisional assembly of grains cannot be sheared without developing force chains that span the entire domain. In the framework of extended kinetic theory, i.e., kinetic theory that accounts for the decreasing in the collisional dissipation due to the breaking of molecular chaos at volume fractions larger than 0.49, we also show that the volume fraction-dependence of the correlation length (measure of the velocity correlation) is singular at random close packing, independent of the interparticle friction. The difference in the singularities ensures that the ratio of the shear stress to the pressure at shear rigidity is different from zero even in the case of frictionless spheres: we identify that with the yield stress ratio of granular materials, and we show that the theoretical predictions, once the different singularities are inserted into the functions of extended kinetic theory, are in excellent agreement with the results of numerical simulations.},
doi = {10.1063/1.4905461},
journal = {Physics of Fluids (1994)},
number = 1,
volume = 27,
place = {United States},
year = {Thu Jan 15 00:00:00 EST 2015},
month = {Thu Jan 15 00:00:00 EST 2015}
}
  • In this work we quantitatively assess, via instabilities, a Navier–Stokes-order (small- Knudsen-number) continuum model based on the kinetic theory analogy and applied to inelastic spheres in a homogeneous cooling system. Dissipative collisions are known to give rise to instabilities, namely velocity vortices and particle clusters, for sufficiently large domains. We compare predictions for the critical length scales required for particle clustering obtained from transient simulations using the continuum model with molecular dynamics (MD) simulations. The agreement between continuum simulations and MD simulations is excellent, particularly given the presence of well-developed velocity vortices at the onset of clustering. More specifically, spatialmore » mapping of the local velocity-field Knudsen numbers (Knu) at the time of cluster detection reveals Knu » 1 due to the presence of large velocity gradients associated with vortices. Although kinetic-theory-based continuum models are based on a small- Kn (i.e. small-gradient) assumption, our findings suggest that, similar to molecular gases, Navier–Stokes-order (small-Kn) theories are surprisingly accurate outside their expected range of validity.« less
  • Flows of granular materials are widespread in the environment, for example, in natural phenomena like avalanches or sand storms, or in industrial and technological processes, where bulk materials like grains, coal, ore, etc., are transported, screened, or crushed. Here, discrete element based simulations of granular flow in a 2d velocity space are compared with a particle code that solves kinetic granular flow equations in two and three dimensions. The binary collisions of the latter are governed by the same forces as those governing the discrete elements. Both methods are applied to a granular shear flow of equally sized discs andmore » spheres. The two dimensional implementation of the kinetic approach shows excellent agreement with the results of the discrete element simulations. During change to a three dimensional velocity space, the qualitative features of the flow are maintained. However, some flow properties change quantitatively.« less
  • Here, granular materials are characterized by large collections of discrete particles, where the particle-particle interactions are significantly more important than the particle-fluid interactions. The current kinetic theory captures fairly accurately the granular flow behavior in the dilute case, when only binary interactions are significant, but is not accurate at all in the dense flow regime, where multi-particle interactions and contacts must be modeled. To improve the kinetic theory results for granular flows in the dense flow regime, we propose a Modified Kinetic Theory (MKT) model that utilizes the contact duration or cut-off time to account for the complex particle-particle interactionsmore » in the dense regime. The contact duration model, also called TC model, is originally proposed by Luding and McNamara to solve the inelastic collapse issue existing in the Inelastic Hard Sphere (IHS) model. This model defines a cut-off time t c such that dissipation is not counted if the time between two consecutive contacts is less than t c. As shown in their study, the use of a cut-off time t c can also reduce the dissipation during multi-particle contacts. In this paper we relate the TC model with the Discrete Element Method (DEM) by choosing the cut-off time t c to be the duration of contact calculated from the linear-spring-dashpot soft-sphere model of the DEM. We examine two types of granular flows: simple shear flow and the plane shear flow, and compare the results of the classical Kinetic Theory (KT) model, the present MKT model, and the DEM model. Here, we show that the MKT model entails a significant improvement over the KT model for simple shear flows at inertial regimes. With the MKT model the calculations are close to the DEM results at solid fractions as high as 0.57. Even for the plane shear flows, where shear rate and solid fraction are inhomogeneous, the results of the MKT model agree very well with the DEM results.« less
  • Cited by 1
  • No abstract prepared.