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Uniaxially variable (rod-like) particles are common in nature and industry. However, the aspect ratio effects on the random packings for differently shaped rod-like particles are not uniform by their innate definitions of aspect ratios. In this work, we propose new definitions of effective aspect ratios that take the surface shape information into account and observe uniform shape elongation effects on the random packing densities. The packing density reaches a maximal value with the effective aspect ratio to be about 1.5. We also observe symmetric high-density regions on the packing-density map. Finally, we carry out the Voronoi analysis and find that the surface shape of particles plays a more important role in changing the local packing properties than the aspect ratio. Our work provides a uniform definition for the aspect ratio of differently shaped rod-like particles and leads to a better understanding towards the particle shape effects on random packings. Unlabelled Image • We obtain the random packings of uniaxially variable superellipsoids. • We propose new definitions of effective aspect ratio for superellipsoids. • We observe uniform shape elongation effects on the random packing densities. • Symmetric high-density regions are observed on the packing density map. [ABSTRACT FROM AUTHOR]

We generate the maximally random jammed (MRJ) packings and maximally dense random packings (MDRPs) of bi-axially elongated superballs with different shape parameters. On the MRJ packing state, the packings of ellipsoids, general superellipsoids and cuboids are on different random degrees and the shape elongation effects on the disordered-packing densities are not uniform. The effects of order degree and particle shape are compounded. However, we find uniform shape elongation effects on the MDRP state. Bi-axial elongation will improve the random-packing densities. The packing densities reach the maximum when the aspect ratio is about 1.5 for all the surface shape parameters and oblateness. The influence of order degree is eliminated on the MDRP state, which demonstrates the advantages of the MDRP state as a platform for comparing the packing density of disordered packings. Our work helps to explore the shape effects on disordered packings of non-spherical particles. Unlabelled Image • We obtain the MRJ packings and MDRPs of biaxially elongated superballs. • We find uniform biaxial elongation effects for all the superballs on the MDRP state. • 1.5 is a special aspect ratio value which corresponds to the maximal random-packing density. • Biaxial shape elongation effects are weakened with the increase of the surface shape parameter. [ABSTRACT FROM AUTHOR]

• A new approach to determining the random packing densities via binary mixtures with spheres. • We obtain the equivalent packing diameters of superballs. • The random packing densities of superballs obtained are surprisingly close to those of the MDRPs. • The linear fitting method can be used to verify the randomicity of non-spherical particle packings. We propose a new approach to determining the random packing densities of superballs via binary mixtures with spheres. The main idea of the approach is to suppress order formations in non-spherical particle packings via the polydispersity of particle shapes, which avoids using order metrics. The packing density of superballs in a mixture can be segregated using a linear fitting method with the concept of equivalent packing size (or size ratio with unit spheres) which represents the effective size (or volume) of a non-spherical particle in a binary mixture with spheres. We systemically study the packing properties of binary mixtures consisting of spheres and superballs and obtain the equivalent packing sizes of superballs. Our results show that the equivalent packing size ratio always corresponds to the minimal packing density or specific volume (reciprocal of packing densities) variation, and is independent of the solid volume fraction. The specific volumes of mixtures with the equivalent packing size ratio are always the upper bound for all the solid volume fractions. The linear relationship between the specific volume and solid volume fraction is only observed in the mixtures with superballs of small surface shape parameters (shapes close to a sphere), which results from the highly disordered nature in the mixtures. Moreover, the ideal random packing densities of mono-sized superballs obtained via the linear fitting method are surprisingly close to those of the MDRPs (maximally dense random packings), further verifying that the MDRPs of non-spherical particles correspond to the ideal random packings whose degrees of order are at the same level with that of the random close packing of spheres. Our work leads to a better understanding towards the random and binary packings and sheds new light on the essence of the MDRP. Our work also guides the optimal particle size distributions of powders in chemical engineering process. [ABSTRACT FROM AUTHOR]

The superellipsoid model is a rich geometric model and is convenient to study the particle shape effects on random packings. The particle shape significantly influences the macroscopic and microscopic structure properties of random packings. In this work, we find uniform and decoupled shape effects on the maximally dense random packings (MDRPs) of hard superellipsoids. Slightly changing the surface shape or elongating (compressing) the particles may influence the random packing density significantly. The influences of surface shape parameter p and aspect ratio w on the random packing densities are decoupled. For the aspect ratio effects, all the packing density curves show “M” type with various p . Meanwhile, the aspect ratio effects are applicable to all the symmetric particles with three equal main cross sections when w  = 1.0. For the surface shape effects, the packing density curve is also in “M” type with various w . The maximum of the random packing density is obtained at p  ≈ 0.7, 2.0 and w  ≈ 0.7, 1.5. Moreover, we obtain the MDRPs of hard superellipsoids via the inverse Monte Carlo packing method with a wide range of the surface shape parameter. The normalized local cubatic order parameter and a new normalized local bond-orientational order parameter are used to evaluate the order degrees of orientations and bond-orientations in random packings, respectively. The local analyses of the MDRPs of superellipsoids are carried out via the Voronoi tessellation. Two linear relationships between the mean and standard deviation of the reduced Voronoi cell volumes are obtained. Our findings should lead to a better understanding of random packings and are helpful in guiding the granular material design. [ABSTRACT FROM AUTHOR]