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.