Effects of bead packing limit concentration on microhydrodynamics-based prediction of breakage kinetics in wet stirred media milling

We studied wet-milling kinetics of a drug in a stirred mill using a microhydrodynamic model with various radial distribution functions (RDFs). An n^th-order kinetics model was fitted to the median size evolution data at several stirrer speeds and loadings of polystyrene/zirconia beads to identify the breakage rate constant k. Microhydrodynamic parameters were calculated using three RDFs: Carnahan–Starling, Lun, and Ma–Ahmadi. The first one, used in previous microhydrodynamic studies, does not account for the bead packing limit concentration. The Lun and the Ma–Ahmadi RDFs similarly predicted much higher frequency of less energetic–forceful bead–bead collisions than the Starling RDF. A subset selection algorithm determined the best multiple linear regression models (MLRMs) of k with the microhydrodynamic parameters (semi-theoretical) or the process–bead parameters (empirical) as predictors. The Lun RDF-based MLRM had the best fitting–predictions of the kinetics among the semi-theoretical MLRMs, which outperformed the empirical MLRMs.