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Abstract
Particle packing is an important subject in scientific research and industrial applications. In the past decades, extensive efforts have been taken on particle packing, but mainly focusing on the packing of spheres.
However, the investigations regarding packing of non-spherical particles are limited because of the complexity of the problem, like contact detection, overlap and force calculation. Therefore, recent studies mainly focused on well-defined shapes. Among these well-defined shapes, the ellipsoids are regarded as the first step from spherical to non-spherical particles. More importantly, ellipsoids can represent a wide range of shapes from very platy to elongated, including spheres. Therefore, ellipsoids with a range of aspect ratios are used in both physical experiments and DEM simulations. Through the combination of vibration and so-called batch-wised feeding method, it is expected to obtain local ordered packing structures of mono-sized spheres and ellipsoids, which is obviously important for the further investigation in the field of crystallization of particles. The equivalent packing size, which is defined as an equivalent spherical diameter determined by measuring and relating its size-dependent packing property to the diameter of a sphere, is quite significant in the characterisation of the size of non-spherical particles and can be used to estimate the packing density of packing including non-spherical particles. The investigation about the segregation caused due to particle shape and the underlying mechanism will be beneficial to the process control in many industries including handling particular materials.
For the packing of mono-sized ellipsoids, both simulation and experimental results show the strong effects of some key variables on packing properties. Generally, increasing dropping height can increase the packing density, overall mean coordination number, and result in more local ordered packing structures, while increasing deposition intensity, friction coefficient and damping coefficient can decrease the packing density, overall mean coordination number of the packing and cause the decrease of the local ordered packing structures. Furthermore, the analysis regarding the order parameter implies that oblate ellipsoids prefer facing upwards and downwards and the prolate ellipsoids tend to lie flat in the plane normal to the vertical direction based on the analysis of the distributions of angle between OA, which is defined the vector pointing from particle mass centre O to polar apex A of the ellipsoid, and z-axis.
The equivalent packing size of ellipsoidal particles was confirmed from microscopic viewpoint based on the similarity between packing systems of spherical and non-spherical particles. And the similarity can be obtained from the analysis on the mean coordination number of each component in a given binary mixture of spheres and ellipsoids. Furthermore, the equivalent packing size was also demonstrated to be independent on the volume fraction of each component. The findings in this chapter indicate that the equivalent packing size can be used in the field of particle packing mainly because it is obtained from the analysis of coordination number. In other word, it is truly based on the interaction of particles and reflects the collective behaviour of particles.
The packing of mono-sized spheres with three-dimensional vibrations was investigated experimentally. The results show that the ordered packing structures can be obtained if the vibration amplitude and frequency are controlled properly and batch-wised feeding is more beneficial for obtaining the ordered packing. Furthermore, the formation of an ordered structure serves as a template for the newly added particles. By adding one layer colourful particles, it can be found that the colourful particle only slightly diffuse near the wall, which indicates that the template is quite stable. Based on these results, the binary mixtures of spheres were also studied to obtain the maximum packing density under three-dimensional vibrations. The results shows the vibration condition, volume fraction, size ratio and feeding method all play a significant role in the densification process of binary mixtures of spheres.
Vibration was also used to investigate the packing of binary mixtures of spheres and ellipsoids. The results indicate the effects of particle shape on variation of packing density and coordination number. Furthermore, segregation due to particle shape under one-dimensional vibration also shows the influence of particle shape. In both physical experiments and DEM simulations, significant convection is observed, which is considered as a responsible factor for the segregation observed. The results also indicate that it is easy for ellipsoids with small or large aspect ratios to enter the void near the wall, move downwards to the bottom of the container and to be trapped there.