A Numerical Investigation into the Correlation Function of Inelastic Hard Spheres Using Event Driven Particle Dynamics

The modelling of a collection of interacting particles has attracted the attention of a number of researchers worldwide, and various methodologies have been proposed [1, 2, 3, 4]. In the 80s, the development of the kinetic-collisional theory for granular flow (KTGF) [5] represented a major breakthrough in the modelling of the hydrodynamics of particulate flow. Despite the great success of KTGF, in practical situations, the flow of particles presents complexities that cannot be described by the KTGF alone. Many complicated phenomena happen at the meso-scale, the scale between “small” and “large”. As an example, clusters or agglomerates are formed at a length scale between particle size and equipment size; particle-particle interactions, other than inelastic and instantaneous collisions (e.g. adhesion) might be necessary to capture the observed behaviour. Additionally, a number of functions and parameters appearing in continuum models require accurate approximations and physical understanding.

In this work we present the study of the radial correlation function which describes how the particle density varies as a function of the distance from a fixed particle. Such function is of great importance: in granular media, collisional interactions at the microscopic level can change the value of the correlation function at contact. We construct the radial correlation function in one, two, and three dimensions for various packing fractions and coefficients of restitution, and consider the effect of external friction on the result, using novel applications of event driven particle dynamics. This systematic quantification allows us to implement a novel continuum model (dynamical density functional theory), for which the value at contact is a required input; the results show that the properties of the correlation function depend strongly on the parameters considered. We have also demonstrated that including these accurate, microscopically-determined values in continuum models is crucial in correctly describing granular media at the meso-macroscale.

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