PhD thesis – Simon Weis

Abstract

Particulate and granular materials are ubiquitous in nature, industry and science. In such systems the spatial structure plays a central, often dominant, role in determining physical properties. In this thesis, I develop X-ray tomography methods and quantitative structure measures to examine various experimental particulate systems, such as dry and wet monodisperse sphere packings, bidisperse sphere packings, packings of frictional emulsion droplets or tetrahedral packings.

The properties of particulate systems depend strongly on the local environment of each particle, as interactions between particles are local in most cases, e.g. repulsive contact forces or cohesive liquid bridges. Therefore geometric approaches to characterize the local environment are needed. This local environment is characterized by the Set-Voronoi tessellation. While a Voronoi cell of a particle is the volume that is closer to the center of this particle than to any other particle, the Set-Voronoi cell is the volume that is closer to the boundary of the particle than to any other particle surface. Set-Voronoi tessellations can be used on arbitrary particle shapes and configurations. The Set-Voronoi tessellation allows for a local description by geometric measures, mainly the local packing fraction and different shape measures based on Minkowski functionals and Minkowski tensors. Independent of the Set-Voronoi tessellations the contact number is measured. As contacts are a key mechanism of transmitting forces through the system, the contact number is an important measure for the mechanical stability. In this work four different physical systems are investigated using structure measures:

Tribo-charging in bidisperse sphere packings Tribo-charging describes the genera- tion of electrical charge on particles by collisions. It can lead to either repulsive or attractive forces within a packing. Packings of bidisperse spheres made of polytetrafluorethylene are analyzed in order to determine the influence of tribocharging on segregation, packing fraction and contact numbers. By controlling the humidity while shaking the beads the tribocharging can be controlled. For such systems, we here show that the contact numbers are charge dependent: With increasing charge density the same-type contact numbers decrease while the opposite-type contact numbers increase.

Tetrahedral packings When compared to sphere packings, tetrahedral particles show an increased complexity due to the fact that different contact types (face-to-face, edge- to-face, edge-to-edge, vertex-to-face contacts) impose a different number of mechanical constraints. History dependence is defined as the fact that apparently identical granular samples will differ depending on their history of preparation. The effect of history de- pendence is visible in the investigated packings of plastic, injection-moulded tetrahedral particles. We perform a local analysis of the contact distribution by grouping the par- 6ticles together according to their individual local packing fractions, as obtained by the Set-Voronoi tessellation. We then show that for sufficiently tapped packings the number of face-to-face contacts becomes a universal function of the global packing fraction, while the edge-to-face and point contacts vary with the applied packing protocol.

“Skinny” emulsions Frictional emulsions are a new, interesting type of soft and de- formable particulate system. We present a first systematic analysis of the structural features of such systems using X-ray tomography on polyethylene glycol drops. While in normal granular systems the particles are assumed to be ideally hard, the droplets in emulsions are deformable. Systems with different drop sizes are investigated with respect to the pair correlation function and packing fraction distributions. The local structural properties of these system are quite interesting as some aspects are similar to packings of hard, frictional particles, like the local packing fraction distributions and the constant global packing fraction with emulsion height (Janssen effect). Other properties are quite different from hard frictional particles, for example the flat pair correlation function. When compared to other emulsion systems it becomes obvious that friction and adhesion have a major impact on the local structure of the packing.

Liquid-stabilized sphere packings The mechanical properties of granular systems change significantly when small amounts of liquid are present in the packing due to the formation of capillary bridges. The structural differences between dry and wet sphere packings are examined using a model system of monodisperse polyoxymethylene beads and bromodecane as a wetting liquid. Our analysis demonstrates that no visible struc- tural differences are found with respect to the contact numbers and packing anisotropy. Additionally the bridge number, the average amount of bridges per particle, is reported to be higher by a value of 2 than the contact number, independent of packing fraction, preparation method and liquid content.

All systems investigated in this thesis have in common that the structural properties play a governing role for the physical properties. Thus gaining insight into the internal structure by using X-ray tomography will help to get a better understanding for granular and particulate systems. The importance of Set-Voronoi tessellations as a description of the local environment and their general applicability is demonstrated in the investigated systems. Our investigations focus on granular and particulate systems. Other disciplines, for example in soft matter physics, are likely to benefit from the methods and results, which are discussed in this thesis as X-ray tomography and Set-Voronoi cells are easily applicable to those systems.