Relation between Packing Density and Particle Size Distribution in Random Packing Models of Powders

Abstract

A previous study reported on the relationship between the packing density and the particle size ratio and/or the volume fraction in binary mixture as a part of the investigation for the effect of the particle size distribution on the packing density. In the present study a similar investigation was repeated for the particles which have continuous size distributions, the modified Rosin-Rammler ones. According to the computer simulation using a random packing model the packing density was related to the parameter m (distribution constant) of the modified Rosin-Rammler distribution function. Subsequently the relationship was introduced by using an analytical method based on the binary packing results, and the adequency of the analytical method was also confirmed. The study was further developed onto the packing density of the particle assembly composed of a mixture of two powders with different modified Rosin-Rammler size distributions to investigate the blending effects.
The results are summarized as follows:
(1) For the powder of modified Rosin-Rammler size distribution the packing density decreases with increase in m.
(2) The packing densities of powders with any continuous size distributions can be obtained from the loose binary packing results by an improved analytical method.
(3) For the loosely packed bed of two mixed powders with modified Rosin-Rammler size distributions, the packing density was calculated by the above analytical method. The densities change with the parameters, m₁ and m₂ (distribution constants), D_e2⁄D_e1 (ratio of absolute size constants) and X₂ (volume fraction). These results give important information on practical use.