Novel Properties of Granular Materials Composed of Aspherical Particles

An introduction to the study of granular materials is presented along with a review of preceding work. Granular materials exhibit an incredibly rich set of phenomena despite the relatively small number of degrees of freedom available to these systems. In addition, granular systems are represented in nearly every part of the natural world. Examples include rice, soil, rocks, ceramics, metals, sand and cereal. In addition, many models of fluids reduce to simple collections of hard particles in certain limits. In this sense, granular materials bridge the gap between solids and fluids. The study of granular materials, therefore, sheds light on some very fundamental questions, while retaining a great deal of applicability to real world problems. I examine the structure of three dimensional random packings of hard ellipsoids formed by pouring into a container. Both oblate and prolate ellipsoids of revolution are examined. Oblate ellipsoids pack so that their symmetry (semiminor) axes are preferentially aligned with the direction of gravity, and their orientational alignment increases with increasing aspect ratio, which is similar to the case in two dimensions. Conversely, for prolate ellipsoids, the symmetry (semimajor) axes tend to lie within the plane perpendicular to gravity. In this case, the orientational order achieves a maximum and then decreases with increasing aspect ratio. No translational order is present for any degree of elongation. The density of the packings is not a monotone function of the aspect ratio, and exhibits a global maximum for slightly elongated particles. Energy minimization arguments explain the behavior of these three-dimensional packings. The conductivity of the pore space is examined numerically. The orientational order present in these packings leads to an anisotropic conductivity tensor even though the positions of the centers of mass are essentially isotropic. For packings of prolate ellipsoids, the degree of anisotropy first increases and then decreases to zero as a function of elongation of the particles. In the case of oblate ellipsoids, the degree of anisotropy increases monotonically with increasing aspect ratio.