PREPARATION, MECHANICS and STRUCTURE of SPHERE PACKINGS Near the RANDOM LOOSE PACKING LIMIT

Packings of monodisperse, hard spheres serve as an important model system in the understanding of granular materials which are ubiquitous in nature and industry from sedimented river beds, to construction aggregates, to pharmaceuticals. Unlike frictionless hard spheres which are only stable at densities near the random close packing volume fraction, packings of real spheres form stable packings over a range of volume fractions. We report experimental investigations of sedimented packings of noncohesive polymethyl-methacrylate spheres over a range of volume fractions near the lower limit of this range of volume fractions. We create packings by slow sedimentation in a viscous fluid and find that a limiting low volume fraction is achieved when the Stokes\u27 number drops below ten. This threshold value is consistent with the vanishing of the interparticle restitution coefficient. We observe that the lower limit of packing achieved depends on the type of sphere used. We develop a new in situ measurement of the effective interparticle friction coefficient and find that lower limiting volume fractions are obtained with higher static friction particles. Thus a random loose packing limit (RLP) in which non-cohesive spheres are stabilized by frictional contacts can be achieved by gentle sedimentation and yields volume fractions distinct from random close packing. We also report experiments on the mechanical response of these sedimented sphere packings. We observe that the yield-stress scales with identical cube-root power-laws of strain-rate and age. We introduce a modification of the Maxwell model of viscoelasticity that accounts for this exponent as well as for mechanical responses that we observe under constant strain and those observed elsewhere under constant stress. We investigate the internal 3-dimensional structure of sedimented packings using refractive index matching and laser-sheet illumination. Despite these sedimented packings having been deposited in gravity, we find that the structure is isotropic and homogeneous in the bulk. We find spatial autocorrelations and cross-correlations to be short ranged and that the radial distribution function is largely determined by local structure. We report distributions of local volume and crystalline order parameters and find that the distributions of order parameters are not predicted solely by hard-sphere constraints