# Comparative Study to Evaluate Mixing Efficiency of Very Fine Particles
###### Abstract  
This study evaluates the applicability and accuracy of coarse-grain modeling (CGM) in discrete-element method (DEM)-based simulations, focusing on particle-mixing efficiency in five representative industrial mixers: the tumbling V mixer, ribbon-blade mixer, paddle-blade mixer, vertical-blade mixer, and conical-screw mixer. Although the DEM is widely employed for particulate system simulations, the high computational cost associated with fine particles significantly hinders large-scale applications. CGM addresses these issues by scaling up particle sizes, thereby reducing particle counts and allowing longer simulation timesteps. We utilized the Lacey mixing index (LMI) as a statistical measure to quantitatively assess mixing uniformity across various CGM scaling factors. Based on the results, CGM significantly reduced computational time (by over 90% in certain cases) while preserving acceptable accuracy levels in terms of LMI values. The mixing behaviors remained consistent under various CGM conditions, based on both visually inspected particle distributions and the temporal LMI trends. Although minor deviations occurred in early-stage mixing, these discrepancies diminished with time, with the final LMI errors remaining below 5% in most scenarios. These findings indicate that CGM effectively enhances computational efficiency in DEM simulations without significantly compromising physical accuracy. This research provides practical guidelines for optimizing industrial-scale particle-mixing processes and conducting computationally feasible, scalable, and reliable DEM simulations. discrete-element method (DEM); coarse-grain modeling (CGM); Lacey mixing index (LMI); particle mixing; computational efficiency; powder blending 20251587120  
efficiency for the active materials, binders, and conductive additives critically impacts the final product performance. Similarly, in the pharmaceutical industry, mixing processes are paramount. Over 80% of pharmaceutical products are prepared in solid powder form, which necessitates the blending of various functional powders to achieve the final formulation [3]. Effective mixing ensures sufficient therapeutic efficacy for multifunctional drugs, whereas poor mixing can lead to segregation, thereby degrading clinical performance. Hence, selecting proper mixing equipment and optimizing the operating conditions based on the powder properties is essential. As shown in Figure 1, mixing processes vary significantly across applications, from mechanical vibration and rotational mixing to gas-solid interactions. Ongoing efforts to optimize mixing processes continue to enhance product quality and reduce manufacturing costs. Historically, mixing was regarded as a secondary step rather than a core production process; hence, limited attention was paid to its economic impact. Consequently, across industries, inefficient mixing was typically addressed by simply prolonging the process instead of optimizing the process parameters. Recently, however, the significance of mixing efficiency has been increasingly recognized, especially as production volumes grow and cycle times shorten. Excessive power consumption from unnecessarily prolonged mixing has emerged as a critical issue that contributes significantly to operational costs. Therefore, evaluating and optimizing mixing efficiency has become increasingly important [7; 8; 9; 10]. Mixing efficiency can be assessed experimentally or through numerical simulations. Experimental evaluations usually involve visual observation of particle motion using imaging tools or powder sampling at specific locations. Imaging-based techniques utilize spatiotemporal diagrams to analyze particle movement [11; 12; 13] and image processing algorithms for quantitative assessments [14; 15]. However, these methods are limited to visually accessible regions, which complicates the evaluation of mixing performance in obstructed zones.