We modeled the joint (bivariate) distribution of fiber length and diameter with a parametric copula as a basic example, which is equally suitable for more complex distributions of irregularly shaped particles.
In contrast, the spherical particle system could only be described with sufficient accuracy by combining micro-CT with high-resolution nano-CT measurements on subvolumes of reduced sample size. Fiber diameter and length could be described well on the basis of the low-resolution micro-CT measurements on the entire sample volume. We immobilized the particles within a wax matrix and created sample volumes suitable for computed tomographic (CT) measurements at two different magnification scales (X-ray micro- and nano-CT). In this study, we mixed spherical glass particles (0.4–5.8 μm diameter) with glass fibers (diameter 10 μm, length 18–660 μm) to investigate a borderline case of maximum difference in the aspect ratio and a significant difference in the characteristic length to characterize the system over several size scales. Both performance measures play a decisive role in the development and improvement of modern functional materials. The three-dimensional characterization of distributed particle properties in the micro- and nanometer range is essential to describe and understand highly specific separation processes in terms of selectivity and yield.
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