Collision statistics in sheared inelastic hard spheres

Abstract

The dynamics of sheared inelastic-hard-sphere systems are studied using non-equilibrium molecular dynamics simulations and direct simulation Monte Carlo. In the molecular dynamics simulations LeesEdwards boundary conditions are used to impose the shear. The dimensions of the simulation box are chosen to ensure that the systems are homogeneous and that the shear is applied uniformly. Various system properties are monitored, including the one-particle velocity distribution, granular temperature, stress tensor, collision rates, and time between collisions. The one-particle velocity distribution is found to agree reasonably well with an anisotropic Gaussian distribution, with only a slight overpopulation of the high velocity tails. The velocity distribution is strongly anisotropic, especially at lower densities and lower values of the coefficient of restitution, with the largest variance in the direction of shear. The density dependence of the compressibility factor of the sheared inelastic hard sphere system is quite similar to that of elastic hard sphere fluids. As the systems become more inelastic, the glancing collisions begin to dominate more direct, head-on collisions. Examination of the distribution of the time between collisions indicates that the collisions experienced by the particles are strongly correlated in the highly inelastic systems. A comparison of the simulation data is made with DSMC simulation of the Enskog equation. Results of the kinetic model of Montanero et al. [Montanero et al., J. Fluid Mech. 389, 391 (1999)] based on the Enskog equation are also included. In general, good agreement is found for high density, weakly inelastic systems. * Electronic address: leo.lue@manchester.ac.uk 1

Modelling inelastic Granular Media Using Dynamical Density Functional Theory

“…To resolve the collision we apply a collision rule. A standard collision rule which maps pre-collisional velocities p in i , p in j to post-collisional velocities p out i , p out j is given by [6]:…”

“…Therefore, instead of a numerical method involving a timestep for microscopic simulation, we predict collision times of particles, then sort and schedule and process these events before advancing simulation. This methodology is at the centre of Event Driven Particle Dynamics (EDPD), which was first developed as early as the 1950s [2], but is still a modern topic of research [6].…”

Modelling inelastic granular media using Dynamical Density Functional Theory

“…To resolve the collision we apply a collision rule. A standard collision rule which maps pre-collisional velocities p in i , p in j post-collisional velocities p out i , p out j is given by [6]:…”

DynamO: a free ${\cal O}$(N) general event‐driven molecular dynamics simulator

“…DynamO is capable of simulating large ( 10 6 particles) and complex systems for extremely long simulation times. [44] This package has already been used to study sheared/damping granular materials, [45,46] square well molecules, [47] binary mixtures, [48] parallel cubes, [49] and helix forming polymers. [50] The remainder of this article is organized as follows.…”

“…For example, compression dynamics, where the particles in the system grow with time, is already implemented. DynamO is also used [45,48] as a framework to perform direct simulation Monte Carlo calculations for the Enskog equation.…”