A non-invasive stochastic-optical method (SOM) for estimating the volume fraction in granular flows: application on interrogation windows with different aspect ratios

Granular flows are involved in geophysical phenomena and industrial applications. The knowledge of the volume fraction is essential for better understanding their dynamics. Indeed, this quantity is highly coupled with the rheology of granular media. Here, we investigated the performance of the stochastic-optical method (SOM), proposed by [Sarno et al. Granular Matter (2016) 18: 80]. The method works thanks to highly-controlled illumination conditions, guaranteed by a flickering-free planar lamp, and uses a high-speed digital camera. Namely, the indirect estimation of the near-wall volume fraction c_3D is made possible by the estimation of a quantity, called two-dimensional volume fraction c_2D , which is measurable through an opportune binarization of gray-scale images. With the purpose of assessing the performance of the SOM method on rectangular interrogation windows with different aspect ratios, we present a novel experimental campaign on dispersions of matte-white plastic beads immersed in a dense fluid, where the angle of incidence of light was 25. Moreover, we explored various settings of the binarization algorithm, incorporated in the SOM method. The accuracy of the method is found to be reasonably high with a root-mean-square error on c_3D lower than 0.03 for a wide range of settings and independently from the aspect ratio.