Characteristics of large three-dimensional heaps of particles produced by ballistic deposition from extended sources

Abstract

This paper reports a detailed numerical investigation of the geometrical and structural properties of three-dimensional heaps of particles. Our goal is the characterization of very large heaps produced by ballistic deposition from extended circular dropping areas. First, we provide an in-depth study of the formation of monodisperse heaps of particles. We find very large heaps to contain three new geometrical characteristics: they may display two external angles of repose, one internal angle of repose, and four distinct packing fraction (density) regions. Such features are found to be directly connected with the size of the dropping zone. We derive a differential equation describing the boundary of an unexpected triangular packing fraction zone formed under the dropping area. We investigate the impact that noise during the deposition has on the final heap structure. In addition, we perform two complementary experiments designed to test the robustness of the novel features found. The first experiment considers changes due to polydispersity. The second checks what happens when letting the extended dropping zone to become a point-like source of particles, the more common type of source.

Keywords:

• three-dimensional heaps of particles
• ballistic deposition
• heap formation
• static sandpiles
• granular matter

Acknowledgments

The authors thank the Deutsche Forschungsgemeinschaft (DFG) for funding through the Cluster of Excellence Engineering of Advanced Materials and within the frame of the Collaborative Research Initiative “Additive Manufacturing” (SFB 814). JACG is also supported by CNPq, Brazil.