An area-weighted particle-size peak from image analysis predicts total dissolved solids across grinder types

Abstract

Coffee extraction is rate-limited by solute diffusion from particle surfaces, yet the particle size distribution (PSD) is commonly summarized by a single central value such as D50, which discards information about the shape of the distribution. Image analysis now enables inexpensive acquisition of the full PSD, but it remains unclear which of the many computable features best predicts total dissolved solids (TDS). In this study, 12 samples from two grinders (conical burr and flat burr, six settings each) were imaged and processed through a pipeline based on Fiji/ImageJ and Python. Spearman rank correlations between PSD features and TDS were compared. The area-weighted KDE peak (area_weighted_peak), defined as the mode of a kernel density estimate weighted by each particle's measured projected area, yielded the strongest and most consistent correlation (pooled ρ = −0.949; |ρ| > 0.94 for both grinders). Other features, including volume-weighted D50 (Dv50), De Brouckere mean diameter (D43), and count-weighted KDE peak (kde_peak), showed weaker or grinder-dependent correlations, whereas the Sauter mean diameter (D32) and area-weighted D50 (Da50) — the area-weighted mean and median of the same distribution — performed nearly as well as the area-weighted KDE peak (its mode). Among the evaluated descriptors, the area-weighted KDE peak showed the strongest and most consistent performance. It is independent of grinder geometry and can be computed from low-cost imaging equipment.