Optical method for measuring the volume fraction of granular media: Application to faced-centered cubic lattices of monodisperse spheres.

In order to understand the dynamics of granular flows, one must have knowledge about the solid volume fraction. However, its reliable experimental estimation is still a challenging task. Here, we present the application of a stochastic-optical method (SOM) [L. Sarno et al., Granul. Matter 18, 80 (2016)10.1007/s10035-016-0676-3] to an array of spheres arranged according to faced-centered cubic lattices, where spheres' locations are known a priori. The purpose of this study is to test the robustness of the image binarization algorithm, introduced in the SOM for the indirect estimation of the near-wall volume fraction through an optically measurable quantity, defined as two-dimensional volume fraction. A comprehensive range of volume fractions and illumination conditions are numerically and experimentally investigated. The proposed binarization algorithm is found to yield reasonably accurate estimations of the two-dimensional volume fraction with a root-mean-square error smaller than 0.03 for all investigated illumination conditions. A slightly worse performance is observed for samples with relatively low volume fractions (<0.3), where the binarization algorithm occasionally cannot identify the surface elements in the second and third layers of the regular lattice.