Shape-corrected, volume-weighted mean diameter: A robust method for reliable 3-D mean diameter calculations from 2-D datasets

Particle-size analysis is an essential technique in many scientific research areas, including Earth sciences, engineering, material sciences, soil sciences, and pharmacology, among others. Over the past few decades, various techniques and methodologies have been developed to calculate particle-size distributions in different sample types (e.g., cohesive versus loose), using volumetric (3-D) or image-aided (2-D) analyses. Quantitative comparison between 2-D and 3-D datasets has always been an issue. Here we illustrate an equation designed to extract reliable average 3-D particle diameters from 2-D datasets acquired by image analysis. We propose the shape-corrected, volume-weighted mean diameter (Dw) as a new particle-size descriptor resulting from the summation of products between the equivalent particle diameter and volume, divided by the total volume of particles analyzed. In this calculation, particles were approximated to perfect circular-spherical shapes, but a shape correction factor (λ) was applied to account for deviations from the perfect spherical shape. We tested the accuracy of Dw by analyzing 2-D datasets acquired from thin sections of two artificial granular samples with different mean particle diameters and shapes. More than 10,000 particles were manually digitized per each thin section. Two-dimensional particle-size distributions were cross-checked with the results provided by laser diffraction granulometry and compared with previously published and widely used calculation and conversion methods. Our promising results encourage the use of Dw because it provides size data that match well with 3-D laser granulometry and requires basic input parameters that can be easily extracted from any image analysis software.