Defining random loose packing for nonspherical grains

The concept of “random loose packing” (RLP) has evolved through extensive study of loose packings of spheres, which has resulted in an accepted definition as the loosest packing that can be obtained by pouring grains. We extend this consideration to packings of nonspherical grains (ellipsoids) formed by slow settling in a viscous liquid, and perform a detailed analysis of the structural properties of the resulting packings. We find that as in the case of spheres the loosest ellipsoid packings are generated for grains with high interparticle friction. However, unlike spheres, these packings cannot be considered random as they have a significant degree of orientational ordering that increases with the grain’s aspect ratio. This demonstrates that applying sedimentation or pouring techniques that have become part of the commonly held definition of RLP, will not generate random packings of ellipsoids. The consequences for the accepted definition of RLP and its applicability to nonspherical grains is discussed.

Figure 1

(a) Schematic of initial setup and final state of simulation. (b) Illustration of a frictionless elliptical grain (top) and a frictional grain (bottom) settling onto a surface composed of elliptical grains. The frictionless grain slides into the position where its center of mass is lowest, causing its axis to align in the plane normal to gravity. The frictional grain is held in place at a random angle due to frictional forces.

Figure 2

Packing fraction variation with the ellipsoid aspect ratio for high-friction and zero-friction cases. The zero-friction curves collapse onto a single line, with a maximum packing fraction at an aspect ratio of around 0.7. For the high-friction case, higher viscosities lead to looser packings across all aspect ratios. The sedimented loose packing limit (${\Phi }_{\mathrm{SLP}}$) is reached at high viscosity and high friction.

Figure 3

Variation of the average contact number $Z$ with aspect ratio for the high friction-and zero-friction cases. The average contact number for the zero-friction case varies smoothly from $Z=6$ to $Z=10$ as the aspect ratio is varied, independent of the viscosity used in the simulation. For the high-friction case ($\mu =1000$), $Z$ decreases with increasing viscosity ($\eta$), tending toward a value of $Z\simeq 4.2$.

Figure 4

Variation in the orientational order parameter ${\chi }_{{}_{\theta }}$ for packings of ellipsoids with $\mu =0$ (a) and $\mu =1000$ (b).