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

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

Dense, inhomogeneous shearing flows of spheres

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

Erosion and deposition in depth-averaged models of dense, dry, inclined, granular flows

We derive expressions for the rates of erosion and deposition at the interface between a dense, dry, inclined granular flow and an erodible bed. In obtaining these, we assume that the interface between the flowing grains and the bed moves with the speed of a pressure wave in the flow, for deposition, or with the speed of a disturbance through the contacting particles in the bed, for erosion. We employ the expressions for the rates of erosion and deposition to show that after an abrupt change in the angle of inclination of the bed the characteristic time for the motion of the interface is much shorter than the characteristic time of the flow. This eliminates the need for introducing models of erosion and deposition rate in the mass balance; and the instantaneous value of the particle flux is the same function of the instantaneous value of the flow depth as in a steady, uniform flow

Periodic saltation over hydrodynamically rough beds: Aeolian to aquatic

International audienceWe determine approximate, analytical solutions for average, periodic trajectories of particles that are accelerated by the turbulent shearing of a fluid between collisions with a hydrodynamically rough bed. We indicate how the viscosity of the fluid may influence the collisions with the bed. The approximate solutions compare well with periodic solutions for average periodic trajectories over rigid-bumpy and erodible beds that are generated numerically. The analytic solutions permit the determination of the relations between the particle flux and the strength of the shearing flow over a range of particle and fluid properties that vary between those for sand in air and sand in water

Fluid-solid transition in unsteady shearing flows

This paper focuses on the mechanical behaviour of granular systems under shearing, unsteady conditions. The results of numerical simulations of time evolving, homogeneous, shear flows of an assembly of frictional spheres, under constant volume conditions are illustrated. Simulations have been performed considering three volume fractions corresponding to fluid, solid and near-to-critical conditions at steady state. The three systems follow very different evolutionary paths, in terms of pressure, coordination number and stress ratio. Fluid-like and solid-like systems exhibit large and small fluctuations, respectively, in those quantities. A critical value of the coordination number seems to govern the transition from fluid to solid