Modeling Power Consumption: A Novel Correlation for Stirred Media Mills with Variable Bead Filling Ratios

Evaluating power consumption in stirred media mills over a wide range of process parameters is crucial for analyzing breakage kinetics and milling efficiency. Despite considerable research efforts, existing models predominantly rely on power-law approaches and fail to provide a holistic understanding of the relationship between process parameters and power consumption. The aim of this study is to introduce a new mathematical model that accurately captures this relationship, across all bead filling ratios (φ), using dimensionless numbers including power number (Ne) and Reynolds number (Re). First, we considered experimental data from literature and discriminated various models to correlate either Ne or Re separately for each φ (Class 1 models) or Ne to Re–φ simultaneously (Class 2 models). The best performing model (Model 2.6 with SSR = 36.71, RMSE = 0.591, R2 = 0.99) was subsequently applied to a new set of experimental data, confirming that this model is highly robust and reliable across various conditions. To the best of our knowledge, in stirred media mill research, this work is the first to show that a simple four-parameter nonlinear model provides a robust fit for Ne data across varying rotor Re (200 to 1 × 106) and bead filling ratios (0.35–0.90).