Dense, inhomogeneous shearing flows of spheres

Diego Berzi,James T Jenkins,F Radjai,J.Y Delenne,S Nezamabadi,S Luding

doi:10.1051/epjconf/201714011006

Diego Berzi, James T Jenkins + Show 4 more

Open Access

https://doi.org/10.1051/epjconf/201714011006

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Abstract

We make use of recent extensions of kinetic theory of granular gases to include the role of particle stiffness in collisions to deal with pressure-imposed shearing flows between bumpy planes in relative motion, in which the solid volume fraction and the intensity of the velocity fluctuations are not uniformly distributed in the domain. As in previous numerical simulations on the flow of disks in an annular shear cell, we obtain an exponential velocity profile in the region where the volume fraction exceeds the critical value at which a rate-independent contribution to the stresses arises. We also show that the thickness of the inertial region, where the solid volume fraction is less than the critical value, and the shear stress at the moving boundary are determined functions of the relative velocity of the boundaries.

Highlights

[1], it has been quantified how the particle stiffness influences the frequency of collisions responsible for the rate-dependent components of particle stresses, and induces the development of rateindependent components to the stresses associated with permanent deformations
That theory has been successfully tested against discrete numerical simulations of simple shearing, in which the velocity fluctuations and the solid volume fraction were uniformly distributed
Based on the analysis reported in ref. [1], we identify the inertial region with the region where the solid volume fraction is less than the critical value, νc, necessary to develop elastic stresses associated with permanent deformations of the aggregate [6]

Summary

Introduction

[1], it has been quantified how the particle stiffness influences the frequency of collisions responsible for the rate-dependent components of particle stresses, and induces the development of rateindependent components to the stresses associated with permanent deformations. That theory has been successfully tested against discrete numerical simulations of simple shearing, in which the velocity fluctuations and the solid volume fraction were uniformly distributed. It has been briefly shown [1] how that theory can be applied to nonhomogeneous shearing flows, to explain the presence of an exponentially decaying velocity profile in very dense regions (creeping flow [2, 3]). To mimic the results of previous discrete numerical simulations of disks in an annular shear cell [4], we take the pressure constant in the flow and the shear stress inversely proportional to the square of the distance from the moving boundary.

Theory

Inertial region

Quasi-static region

Results and conclusions