Random packing of colloids and granular matter

This thesis deals with the random packing of colloids and granular matter. A random packing is a stable disordered collection of touching particles, without long-range positional and orientational order. Experimental random packings of particles with the same shape but made of different materials show large similarities, independent of particle size, indicating that particle shape is an important factor for their packing. The particle shapes that have been investigated are spheres, spherocylinders, spheroids and cut spheres. It was found that the packing density increases upon slightly deviating from spherical shape and for high aspect ratio the density is inversely proportional to the aspect ratio of the particles. The random contact equation for thin rod packings has been reproduced with a newly developed simulation method and contact numbers calculated agree well with experimental results. Packings of cut spheres were investigated to study the influence of a flat face on the packing structure. At aspect ratio two the flat face becomes important and order is induced by the flat face for higher aspect ratios resulting in columnar structures. Furthermore, the jamming of random packings was studied with the so-called caging number. The caging number is the average minimum number of neighbouring particles that need to be placed at random in fixed contact with a central particle such that all translations and rotations of the particle are blocked. The caging number was calculated analytically for 2-dimensional disks with varying radii and it was numerically calculated for spheres and spherocylinders. Contact numbers were used to construct geometric ensemble average of clusters of spheres to model random loose and random close packings of spheres. A lower bound on volume fraction for random loose packing was found that is surprisingly close to the freezing volume fraction for hard spheres. The ensemble analysis also highlights the importance of collective and global effects in random sphere packings by comparing clusters generated via local rules to random sphere packings and clusters that do include collective effects. Finally, some preliminary results are presented that show the possible relevance of random rod packings to the motility of certain biological cells.