Velocity Correlations in Driven Two-Dimensional Granular Media

Simulations of volumetrically forced granular media in two dimensions produce s tates with nearly homogeneous density. In these states, long-range velocity correlations with a characteristic vortex structure develop; given sufficient time, the correlations fill the entire simulated area. These velocity correlations reduce the rate and violence of collisions, so that pressure is smaller for driven inelastic particles than for undriven elastic particles in the same thermodynamic state. As the simulation box size increases, the effects of veloc ity correlations on the pressure are enhanced rather than reduced.Comment: 12 pages, 6 figures, 21 reference

The minimization of mechanical work in vibrated granular matter

Experiments and computer simulations are carried out to investigate phase separation in a granular gas under vibration. The densities of the dilute and the dense phase are found to follow a lever rule and obey an equation of state. Here we show that the Maxwell equal-areas construction predicts the coexisting pressure and binodal densities remarkably well, even though the system is far from thermal equilibrium. This construction can be linked to the minimization of mechanical work associated with density fluctuations without invoking any concept related to equilibrium-like free energies

Extended kinetic theory applied to inclined granular flows: role of boundaries

We compare the predictions of extended kinetic theory (EKT), where the roles of surface friction and correlation in fluctuation velocities are taken into account, with discrete element simulations of steady, fully-developed, inclined flows of identical spheres over bumpy bases, in the presence and absence of flat, frictional sidewalls. We show that the constitutive relation for the pressure of EKT must be modified in the proximity of the boundary, because of the influence of excluded volume and shielding associated with collisions of particles with the boundary itself. We also note that currently available boundary conditions for flows over bumpy planes in kinetic theory underestimate the energy dissipation. These two observations explain the lack of agreement of EKT with the simulations, in terms of the maximum angles of inclination for which steady, fully-developed flows are possible. That is, for some high angles of inclination, EKT does not have solutions, while steady flows are predicted in DEM. However, whenever a solution to the system of differential equations of EKT does exist, the predicted distributions of velocity, solid volume fraction and granular temperature satisfactorily match the numerical measurements. The incompressible, algebraic approximation of EKT, which ignores the conduction of energy in the energy balance, admits solutions for a wider range of angles of inclination, as in the simulations, but fails to reproduce the quantitative and qualitative behaviour of solid volume fraction and granular temperature in the two conductive layers at the top and bottom of the flow. When frictional sidewalls are added to the domain, we show that the spanwise ratio of shear stress to pressure is linearly distributed in the dense core region of the flow, confirming that the sidewalls exert, on average, a Coulomb-like resistance to the flow with an effective friction coefficient which is less than half the actual particle-wall friction

Velocity correlations in driven twodimensional granular media

Abstract. Simulations of volumetrically forced granular media in two dimensions produce states with nearly homogeneous density. In these states, long-range velocity correlations with a characteristic vortex structure develop; given sufficient time, the correlations fill the entire simulated area. These velocity correlations reduce the rate and violence of collisions, so that pressure is smaller for driven inelastic particles than for undriven elastic particles in the same thermodynamic state. As the simulation box size increases, the effects of velocity correlations on the pressure are enhanced rather than reduced. 1