Structural properties of different sphere packings with arbitrary porosities for planetary-science applications

Granular solids in planetary science are found in the regolith that covers planetary surfaces as well as in the bulk of rubble-pile asteroids, comets and planetesimals. To help understand the physics of these planetary bodies, we aim at deriving the structural properties of granular packings over a large range of porosities. Relevant to fluid flow and gas diffusion are the void spaces inside the granular packings so that we analyze the mean free path of point-like particles, their diffusion constant and their total traveled path lengths. For mechanical and heat-transport properties, the coordination number and the absolute chain length of the inter-connected particles are important. Generally, we also derive the homogeneity and isotropy of the granular solids. We compare granular packings generated by four algorithms for porosities in the range between 85 and 42%, which are the upper and lower limits for natural packings of equal-sized spheres. All produced sphere packings arrive at very similar quantities for the mean free path, the free path probability distribution function, the diffusion constant and the total traveled path length for the entire range of porosities. Hence, transport processes governed by the void-space properties are independent of the specific generation algorithm for the granular packing. In contrast, heat conduction or mechanical stresses almost exclusively depend on the existence and properties of particle contacts and particle chains in the network of spheres. In this case, the four algorithms deliver very different results.