Some geometrical properties of packings of equal spheres in cylindrical vessels

Abstract

Experimental and analytical methods are described for establishing some of the mean geometrical properties of unbiased random packings of equal spheres in cylindrical vessels. Experimental determinations have been made of the volumes of the spheres in an outer region of thickness equal to the sphere diameter, and in the remaining central region. Related properties, such as the mean void fractions of the two regions, can be calculated from these. Several preparation methods were used, including some which give rise to packings with axial or radial bias. A model is developed for computing the relevant properties of packings in a semi-infinite vessel with a plane wall. The model is then adapted to unbiased packings in cylindrical vessels, by means of quadratic equations whose coefficients depend on the cylinder-to-sphere diameter ratio. It is shown that commonly used preparation methods, such as placing or pouring spheres on the top surface, can result in packings with radial bias. Two methods of preparing unbiased random packings are described.