Plane shear flows of frictionless spheres: Kinetic theory and 3D soft-sphere discrete element method simulations

TL;DR

This study combines 3D discrete element simulations with extended kinetic theory to accurately predict shear flow behavior of frictionless spheres, accounting for wall bumpiness and inelastic collisions, with good agreement across various conditions.

Contribution

It introduces boundary conditions for shear flows with bumpy walls and validates extended kinetic theory against detailed simulations for inelastic, frictionless spheres.

Findings

Extended kinetic theory matches simulation results well.

Wall bumpiness affects particle trapping and dissipation.

Flow characteristics become uniform with increased bumpiness.

Abstract

We use existing 3D Discrete Element simulations of simple shear flows of spheres to evaluate the radial distribution function at contact that enables kinetic theory to correctly predict the pressure and the shear stress, for different values of the collisional coefficient of restitution. Then, we perform 3D Discrete Element simulations of plane flows of frictionless, inelastic spheres, sheared between walls made bumpy by gluing particles in a regular array, at fixed average volume fraction and distance between the walls. The results of the numerical simulations are used to derive boundary conditions appropriated in the cases of large and small bumpiness. Those boundary conditions are, then, employed to numerically integrate the differential equations of Extended Kinetic Theory, where the breaking of the molecular chaos assumption at volume fraction larger than 0.49 is taken into account in the expression of the dissipation rate. We show that the Extended Kinetic Theory is in very good agreement with the numerical simulations, even for coefficients of restitution as low as 0.50. When the bumpiness is increased, we observe that some of the flowing particles are stuck in the gaps between the wall spheres. As a consequence, the walls are more dissipative than expected, and the flows resemble simple shear flows, i.e., flows of rather constant volume fraction and granular temperature.