Probability Density Function of Bead-Pack Test Planes and Resolution Limits of Tomography

Abstract

Quantitative stereology translates three-dimensional statistics into areal and lineal size distributions. Conversely, cross-sectional data are used to infer volumetric properties. One may thus infer porosity from cross-sectional areal porosity or through segment intersections with void and solid. Cross sections of uniform and spherical-bead packs result in a size distribution of circles, the statistics of which enables us to evaluate packing randomness with multiple test planes. Here, we provide cross-sectional results obtained from micro-CT scans for unimodal and bimodal packs, both of which having a narrow distribution of bead sizes. For nearly uniformly sized beads, the theoretical distributions of circle diameters agree with high-resolution data above a demonstrable threshold. Therefore, the threshold allows us to ascertain the physical resolution of scans, regardless of the voxel resolution of the scanned image. For multimodal distribution of bead sizes within the pack, theory and experiments do not always agree. For example, when beads are premixed, and later packed within a tube, a discrepancy for the number distribution of circular sizes between theory and data is evident. Smaller beads are underrepresented. Reasons for these observations and methods to overcome the underrepresentation are presented in the paper. Estimates for the respective bead fractions are best obtained by direct image analysis and not weight fractions within the premixer.