Effect of aspect ratio on the development of order in vibrated granular rods

We investigate ordering of granular rods in a container subject to vibrations in a gravitational field as a function of number density of the rods. We study rods with three different length to diameter aspect ratios A(r)= 5, 10, and 15. The measurements are performed in three dimensions using x-ray computer tomography to visualize the rods in the entire container. We first discuss a method to extract the position and orientation of the rods from the scans which enables us to obtain statistical measures of the degree of order in the packing. We find that the rods with A(r)=5 phase separate into domains with vertical and horizontal orientation as the number density of the rods is increased, whereas, for A(r)=10 and 15 the rods are predominately oriented vertically in layers. By calculating two-point spatial correlation functions, we further show that long range hexagonal order occurs within a layer when the rods are oriented along the vertical axis. Thus, our experiments find that long range order increases rapidly in granular rods with growing anisotropy.