Lacunarity as a quantitative measure of mixing—a micro-CT analysis-based case study on granular materials

In practically every industry, mixing is a fundamental process, yet its 3D analysis is scarce in the literature. High-resolution computed tomography (micro-CT) is the perfect X-ray imaging tool to investigate the mixing of granular materials. Other than qualitative analysis, 3D micro-CT images provide an opportunity for quantitative analysis, which is of utmost importance, in terms of efficiency (time and budget), and environmental impact of the mixing process. In this work, lacunarity is proposed as a measure of mixing. By the lacunarity calculation on the repeated micro-CT measurements, a temporal description of the mixing can be given in three dimensions. As opposed to traditional mixing indices, the lacunarity curve provides additional information regarding the spatial distribution of the grains. Discrete element method simulations were also performed and showed similar results to the experiments.