A Numerical Study of Random Close Packing Models of Granular Systems

Abstract

Packing of equally sized spheres is an extensive field of research, and the applications range from granular media on the macroscopic scale, to theories of liquids and gases. This thesis presents results from numerical simulations of close packing of mono disperse, hard disks in two dimensions. These configurations are generated using two different close packing algorithms: The force biased Jodrey-Tory algorithm and the Lubachevsky-Stillinger algorithm. Statistical tools have been developed in order to interpret the resulting configurations, and to detect crystallization. The results indicate that the Jodrey Tory-method that produces more crystallized and ordered configurations than the Lubachevsky-Stillinger algorithm. A more suitable set of parameters might produce more disordered packings. Data from an experiments performed on two-dimensional, deformable disks is compared to the numerical data. In order to produce systems that emulate the experimental data, the Jodrey-Tory algorithm is altered to allow the disks to overlap. The resulting average contact numbers, which are the average amount of neighbours a disk is in direct contact with, are compared for the numerical and experimental data, at various packing fractions. The evolution of the contact number differ for the numerical and experimental data. This could be due to the nature of the Jodrey Tory packings, which produces configurations where the distance between the particles are large, caused by a strong repulsive force. This kind of structures might not be suitable to mimic the behavior of configuration of particles that are in mechanical equilibrium.