Investigations of Random Packings

Abstract

In agglomeration and briquetting, in the drying of solids, in filtration, in flows trough a bed — the packing structure, ie. the arrangement of the particles relative to one another, plays a major part in all these examples. In the analysis of such packings an important problem is the determination of the porosity and of the grain-size distribution. The data necessary for the calculation of these values are often obtained by sections through the bed and the section area distributions resulting therefrom. These section area distributions depend of course on the particular state of packing. In the text below it will always be assumed that the packings are random. If it is assumed that all the particles are spheres and so distributed that the average number of midpoints per unit volume is equal to λ, then, in the case of a random packing, these midpoints are poisson-distributed22). The spheres forming the packing have a numerical density distribution q(d), where d is the measure dispersity, ie., in the case of spheres, the diameter. Sectioning such a packing density function z*(θ) as sections of these spheres.