Date of Award

Spring 2003

Document Type


Degree Name

Master of Science in Mechanical Engineering - (M.S.)


Mechanical Engineering

First Advisor

Anthony D. Rosato

Second Advisor

Chao Zhu

Third Advisor

Kwabena A. Narh


The study of random packing of spheres has had a long history. It particularly interests many researchers because randomly packed hard spheres exhibit some features of the properties of simple liquid, e.g. the packing density and the radial distribution. Many researchers have studied random packing both experimentally and also by using computer simulation.

Monte Carlo simulation method was used to generate random loose packing of hard spheres. Packing characteristics like packing density, radial distribution function, co-ordination, angular distribution and fabric tensor have been computed for this packing system.

The packing density for a system of 8000 particles with a diameter of 0. 15 was computed to be 0.582. The packing density obtained for random packing of loose spheres is in good agreement with Owe Berg [2], Tory [18] and about 2% less than the experimental values of Scott [9].

The radial distribution function for the 8000-particle system was also computed for the packing bed. The peak occurrence in the radial distribution plot was found to be in good agreement with Scott [9], Nolan [ 11 ] and Powell [ 17].

An average co-ordination number for the same size system was computed to be 6.71291 ±0.023433 which is in good agreement with Smith [12], Visscher [1], Nolan [11].

Angular Distribution of the particles was also found by computing the contact angles for all the spheres with their neighbors. The histogram of the contact angles shows that there is no preferred direction for the particles, which shows the packing is completely random and that there is no particular pattern in their arrangement.

The fabric tensor was computed. The analysis of fabric tensor shows that all the planes in the packing assembly, generated by the Monte Carlo simulation, are principal planes. Similar situation exists in ideal fluid. Hence it is shown that the Monte Carlo simulated assembly can serve as model for ideal fluid.