An optical method for measuring the near-wall volume fraction in granular dispersions

The volume fraction plays a crucial role in the dynamics of granular flows. This work is devoted to developing a novel cost-effective optical method for determining the near-wall volume fraction. By means of a numerical investigation, performed by Monte Carlo generations of mono-disperse sphere distributions under controlled illumination conditions, the stochastic relationship between the near-wall volume fraction and a measurable quantity, referred to as two-dimensional volume fraction, is figured out. A binarization algorithm is proposed for estimating the two-dimensional volume fraction from gray-scale digital images. The relation is found to be of exponential type, with parameters only depending on the angle of incidence of light. An experimental investigation is designed for implementing the proposed method to a real laboratory context. The laboratory campaign, performed on dispersions of white plastic grains immersed in different ambient fluids, enables us to validate the proposed approach. It is found that the exponential law provides results in sound agreement with experimental data. Sensitivity analyses are also performed to confirm and evaluate the robustness and the accuracy of the proposed method.