Date of Award

Spring 1990

Document Type


Degree Name

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


Mechanical and Industrial Engineering

First Advisor

Anthony D. Rosato

Second Advisor

Ian Sanford Fischer

Third Advisor

Rajesh N. Dave


A computer based method of generating a random packing of hard spheres is described. Using a Monte Carlo method as employed in the field of Computational Statistical Physics, packing of hard spheres are generated and analyzed.

The mean packing fractions for the present assemblies of 1000 spheres are 0.555±0.015 after pouring and 0.582±0.018 after 10 cycles of shaking. These values are approximately 5 to 6 per cent lower than the experimental results of G.D. Scott[30], but similar with the result of Visscher & Bolsterli [17].

The mean coordination numbers are 5.97 and 6.33 for the pouring and shaking case, respectively. The radial distribution function was calculated and compared with other published data. The simulated results are similar with those of G.D. Scott.

The pouring simulations with 5 different system sizes verified that the resulting low packing density is independent of the number of particles In the system.

In an attempt to determine the reasons for the 5 to 6 per cent difference between existing experimental data of G.D. Scott and the simulation results, two computations were done.

The first case study measured the total void volume formed by the gaps of the neighboring spheres. It was found that the void volume occupied approximately 0.0017 per cent of the total volume. Therefore the use of the corrected diameter cannot be a factor.

The second series of computations studied the effects of allowing the system to rapidly "cool" to an equilibrated state as opposed to incrementally reducing T* from a value of 15.8 to 0.00211, whereby the system Is allowed to equlibrium at each incremental step. The result shows that the packing density increased from 0.565 to 0.617. This can account for the 5 to 6 per cent difference between the experimental result of G.D. Scott and the result of current simulation.