The Volume Rule in the Random Packing Ratio

TL;DR

This paper investigates how the interface effects and sphere size optimization influence the packing ratio in sphere packing systems, emphasizing the importance of precise volume and contact definitions for different scales.

Contribution

It introduces the concept of the volume rule in the context of random packing ratios and proposes optimized sphere size strategies for improved packing efficiency.

Findings

Edge effects reduce packing ratios near container boundaries

Optimized sphere size sequences enhance packing density

Clear definitions of volume and contact are crucial for packing analysis

Abstract

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.