The Volume Rule in the Random Packing Ratio
  The study on the relationship between the spheres and voids in packing system suggests that the edge effect at the interface between the container and the particles is an important factor lowering the packing ratio. To pack spheres in a container with high packing ratio, an optimized sphere size and an optimized sequence of sphere sizes exist for the packing of single-sized and multi-sized spheres, respectively. We suggest that the concepts of volume and contact should be clearly defined for the packing problem in specific scale. 
Honghai Liu, Enyong Jiang, Chang Q. Sun and Bruce Z. Gao
cond-mat.stat-mech