Gary W. Delaney

The packing properties of superellipsoids

We investigate the properties of packings of frictionless non-spherical particles utilizing a dynamic particle expansion technique. We employ superquadric particles (superellipsoids), which allows us to explore how a broad range of particle shapes affect both the macroscopic and the local configurational properties of the system. We smoothly transition from spherical particles possessing only translational degrees of freedom to large aspect ratio non-spherical grains where rotational degrees of freedom are highly important. We demonstrate that the degree of anisotropy and local surface curvature of the particles have a profound effect on their packing properties, determining whether a random or an ordered packing is readily formed.

Disordered spherical bead packs are anisotropic

Investigating how tightly objects pack space is a long-standing problem, with relevance for many disciplines from discrete mathematics to the theory of glasses. Here we report on the fundamental yet so far overlooked geometric property that disordered mono-disperse spherical bead packs have significant local structural anisotropy manifest in the shape of the free space associated with each bead. Jammed disordered packings from several types of experiments and simulations reveal very similar values of the cell anisotropy, showing a linear decrease with packing fraction. Strong deviations from this trend are observed for unjammed configurations and for partially crystalline packings above 64%. These findings suggest an inherent geometrical reason why, in disordered packings, anisotropic shapes can fill space more efficiently than spheres, and have implications for packing effects in non-spherical liquid crystals, foams and structural glasses.

Rocking Newton’s cradle

In textbook descriptions of Newton’s cradle, it is generally claimed that displacing one ball will result in a collision that leads to another ball being ejected from the line, with all others remaining motionless. Hermann and Schmalzle, Hinch and Saint-Jean, and others have shown that a realistic description is more subtle. We present a simulation of Newton’s cradle that reproduces the break-up of the line of balls at the first collision, the eventual movement of all the balls in phase, and is in good agreement with our experimentally obtained data. The first effect is due to the finite elastic response of the balls, and the second is a result of viscoelastic dissipation in the impacts. We also analyze a dissipation-free ideal Newton’s cradle which displays complex dynamics.

Combining tomographic imaging and DEM simulations to investigate the structure of experimental sphere packings

We introduce and describe in detail a “virtual laboratory” platform to study granular materials by combining advanced image reconstruction techniques from computed X-ray micro tomography and discrete element method simulations. This platform allows us to directly access quantities such as forces at the grain contacts, which would be otherwise hard to measure experimentally. We apply this technique to the investigation of equal sized bead packings prepared experimentally by means of different methods, and covering a broad range of packing fractions from ϕ = 0.57 to ϕ = 0.64. Results concerning the number of contacts, the distribution of forces at contact and the relation of these quantities with local and global packing properties are presented and discussed. This combined approach is found to both offer the ability to improve on previous tomographic measurements of geometric properties of the packings, and to estimate other physical properties that are not available experimentally.

Local Origin of Global Contact Numbers in Frictional Ellipsoid Packings

In particulate soft matter systems the average number of contacts Z of a particle is an important predictor of the mechanical properties of the system. Using x-ray tomography, we analyze packings of frictional, oblate ellipsoids of various aspect ratios α, prepared at different global volume fractions ϕg. We find that Z is a monotonically increasing function of ϕg for all α. We demonstrate that this functional dependence can be explained by a local analysis where each particle is described by its local volume fraction ϕl computed from a Voronoi tessellation. Z can be expressed as an integral over all values of ϕl: Z(ϕg,α,X)=∫Zl(ϕl,α,X)P(ϕl|ϕg)dϕl. The local contact number function Zl(ϕl,α,X) describes the relevant physics in term of locally defined variables only, including possible higher order terms X. The conditional probability P(ϕl|ϕg) to find a specific value of ϕl given a global packing fraction ϕg is found to be independent of α and X. Our results demonstrate that for frictional particles a local approach is not only a theoretical requirement but also feasible.

Non-universal Voronoi cell shapes in amorphous ellipsoid packs

In particulate systems with short-range interactions, such as granular matter or simple fluids, local structure determines the macroscopic physical properties. We analyse local structure metrics derived from the Voronoi diagram of oblate ellipsoids, for various aspect ratios and global packing fractions φg. We focus on jammed static configurations of frictional ellipsoids, obtained by tomographic imaging and by discrete element method simulations. The rescaled distribution of local packing fractions φl, defined as the ratio of particle volume and its Voronoi cell volume, is found to be independent of the particle aspect ratio, and coincide with results for sphere packs. By contrast, the typical Voronoi cell shape, quantified by the Minkowski tensor anisotropy index β = β02,0, points towards a difference between random packings of spheres and those of oblate ellipsoids. While the average cell shape β of all cells with a given value of is similar in dense and loose jammed sphere packings, the structure of dense and loose ellipsoid packings differs substantially such that this does not hold true.

Tomographic Analysis of Jammed Ellipsoid Packings

Disordered packings of ellipsoidal particles are an important model for disordered granular matter. Here we report a way to determine the average contact number of ellipsoid packings from tomographic analysis. Tomographic images of jammed ellipsoid packings prepared by vertical shaking of loose configurations are recorded and the positions and orientations of the ellipsoids are reconstructed. The average contact number can be extracted from a contact number scaling (CNS) function. The size of the particles, that may vary due to production inaccuracies, can also be determined by this method.

Set Voronoi diagrams of 3D assemblies of aspherical particles

Abstract Several approaches to quantitative local structure characterization for particulate assemblies, such as structural glasses or jammed packings, use the partition of space provided by the Voronoi diagram. The conventional construction for spherical mono-disperse particles, by which the Voronoi cell of a particle is that of its centre point, cannot be applied to configurations of aspherical or polydisperse particles. Here, we discuss the construction of a Set Voronoi diagram for configurations of aspherical particles in three-dimensional space. The Set Voronoi cell of a given particle is composed of all points in space that are closer to the surface (as opposed to the centre) of the given particle than to the surface of any other; this definition reduces to the conventional Voronoi diagram for the case of mono-disperse spheres. An algorithm for the computation of the Set Voronoi diagram for convex particles is described, as a special case of a Voronoi-based medial axis algorithm, based on a triangulation of the particles’ bounding surfaces. This algorithm is further improved by a pre-processing step based on morphological erosion, which improves the quality of the approximation and circumvents the problems associated with small degrees of particle–particle overlap that may be caused by experimental noise or soft potentials. As an application, preliminary data for the volume distribution of disordered packings of mono-disperse oblate ellipsoids, obtained from tomographic imaging, is computed.

Novel application of DEM to modelling comminution processes

Comminution processes in which grains are broken down into smaller and smaller sizes represent a critical component in many industries including mineral processing, cement production, food processing and pharmaceuticals. We present a novel DEM implementation capable of realistically modelling such comminution processes. This extends on a previous implementation of DEM particle breakage that utilized spherical particles. Our new extension uses super-quadric particles, where daughter fragments with realistic size and shape distributions are packed inside a bounding parent super-quadric. We demonstrate the flexibility of our approach in different particle breakage scenarios and examine the effect of the chosen minimum resolved particle size. This incorporation of the effect of particle shape in the breakage process allows for more realistic DEM simulations to be performed, that can provide additional fundamental insights into comminution processes and into the behaviour of individual pieces of industrial machinery.

An efficient computational approach to characterize DSC-MRI signals arising from three-dimensional heterogeneous tissue structures.

The systematic investigation of susceptibility-induced contrast in MRI is important to better interpret the influence of microvascular and microcellular morphology on DSC-MRI derived perfusion data. Recently, a novel computational approach called the Finite Perturber Method (FPM), which enables the study of susceptibility-induced contrast in MRI arising from arbitrary microvascular morphologies in 3D has been developed. However, the FPM has lower efficiency in simulating water diffusion especially for complex tissues. In this work, an improved computational approach that combines the FPM with a matrix-based finite difference method (FDM), which we call the Finite Perturber the Finite Difference Method (FPFDM), has been developed in order to efficiently investigate the influence of vascular and extravascular morphological features on susceptibility-induced transverse relaxation. The current work provides a framework for better interpreting how DSC-MRI data depend on various phenomena, including contrast agent leakage in cancerous tissues and water diffusion rates. In addition, we illustrate using simulated and micro-CT extracted tissue structures the improved FPFDM along with its potential applications and limitations.