Coupled tomography and distinct-element-method approach to exploring the granular media microstructure in a jamming hourglass

We describe an approach for exploring microscopic properties of granular media that couples x-ray microtomography and distinct-element-method (DEM) simulations through image analysis. We illustrate it via the study of the intriguing phenomenon of instant arching in an hourglass (in our case a cylinder filled with a polydisperse mixture of glass beads that has a small circular shutter in the bottom). X-ray tomography provides three-dimensional snapshots of the microscopic conditions of the system both prior to opening the shutter, and thereafter, once jamming is completed. The process time in between is bridged using DEM simulation, which settles to positions in remarkably good agreement with the x-ray images. Specifically designed image analysis procedures accurately extract the geometrical information, i.e., the positions and sizes of the beads, from the raw x-ray tomographs, and compress the data representation from initially 5 gigabytes to a few tens of kilobytes per tomograph. The scope of the approach is explored through a sensitivity analysis to input data perturbations in both bead sizes and positions. We establish that accuracy of size--much more than position--estimates is critical, thus explaining the difficulty in considering a mixture of beads of different sizes. We further point to limits in the replication ability of granular flows away from equilibrium; i.e., the difficulty of numerically reproducing chaotic motion.

Vertical ordering of rods under vertical vibration

Granular media composed of elongated particles rearrange and order vertically upon vertical vibration. We perform pseudo-two-dimensional discrete element model simulations and show that this phenomenon also takes place with no help from vertical walls. We quantitatively analyze the sizes of voids forming during vibrations and consider a void-filling mechanism to explain the observed vertical ordering. Void filling can explain why short rods are less prone to align vertically than long ones. We cannot, however, explain, invoking just void filling, the existence of an optimum acceleration to promote vertical ordering and its dependence on particle length. We finally introduce an interpretation of the phenomenon, by considering the energetic barriers that particles have to overcome to exit a horizontal or a vertical lattice. By comparing these energetic thresholds with the peak mean particle fluctuant kinetic energy, we identify three different regimes. In the intermediate regime a vertical lattice is stable, while a horizontal is not. This interpretation succeeds in reconciling both dependencies on vibration acceleration and on particle length.

About the influence of friction and polydispersity on the jamming behavior of bead assemblies

We study the jamming of bead assemblies placed in a cylindrical container whose bottom is pierced with a circular hole. Their jamming behavior is quantified here by the median jamming diameter, that is the diameter of the hole for which the jamming probability is 0.5. Median jamming diameters of monodisperse assemblies are obtained numerically using the Distinct Element Method and experimentally with steel beads. We obtain good agreement between numerical and experimental results. The influence of friction is then investigated. In particular, the formation of concentric bead rings is observed for low frictions. We identify this phenomenon as a boundary effect and study its influence on jamming. Relying on measures obtained from simulation runs, the median jamming diameter of bidisperse bead assemblies is finally found to depend only on the volume-average diameter of their constituting beads. We formulate this as a tentative law and validate it using bidisperse assemblies of steel beads.

Molecular-dynamics force models for better control of energy dissipation in numerical simulations of dense granular media

We first describe the three-dimensional extension of the molecular-dynamics models for granular media simulations. We then discuss the known energy dissipation problem occurring when simulating dense granular media with the usual molecular-dynamics forces models. We finally propose a force model able to control the energy dissipation in the multiparticle contact situations typical to dense granular media, together with appropriate numerical results.