# Comparative Study to Evaluate Mixing Efficiency of Very Fine Particles
## 6 Conclusions  
This study systematically evaluated the applicability and accuracy of CGM in DEM simulations across five representative industrial mixers: a tumbling V mixer, a ribbon-blade mixer, a paddle-blade mixer, a vertical-blade mixer, and a conical-screw mixer. By increasing the particle size through CGM, the computational demands were significantly reduced, which enabled efficient large-scale simulations. However, such upscaling can introduce inaccuracies in mixing behavior predictions, particularly during the early stages of particle motion. To assess mixing performance, we analyzed the temporal variation in the LMI under various CGM scaling conditions. For all five mixing systems, CGM yielded a substantial reduction in computational time, often exceeding 90%, while maintaining acceptable levels of LMI accuracy. Visual inspection of particle distributions and temporal LMI trends confirmed that the overall mixing patterns remained consistent across CGM conditions. Although early-stage discrepancies in the LMI were observed, especially at higher CGM values, these differences diminished as the simulations progressed. In many cases, the final LMI errors were limited to 5%, with negligible impact on the overall interpretation of mixing performance. These results demonstrate that CGM is a reliable and efficient strategy for DEM-based mixing simulations, especially when full-resolution simulations are computationally prohibitive. CGM facilitates the modeling of entire mixing systems rather than limited domains, enabling more comprehensive process analysis and design optimization. Moreover, by quantifying the trade-off between accuracy and computational efficiency, this study provides valuable guidance for selecting appropriate CGM levels for specific mixing scenarios. Beyond using fixed CGM values, more generalizable guidelines may be derived by considering the relative sizes of the particles and the mixing equipment. For example, in mixers with chambers spanning several meters in diameter, regardless of whether the particle size is on the order of a few microns or several millimeters, the global mixing behavior is typically governed more by macroscopic flow patterns than by individual particle trajectories. From this perspective, a coarse-graining approach remains valid across a wide range of CGM factors, provided that local-scale effects do not control the mixing mechanism. Therefore, the appropriate CGM value should be selected based on the characteristic ratio of the particle size and the mixer dimensions, as well as the accuracy required for the target application. While some local deviations may arise with higher CGM levels, the global trends and statistical mixing indices such as the LMI should remain largely unaltered. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Particle Count** & \multicolumn{2}{c}{**Simulation Duration**} & \multicolumn{2}{c}{**Average LMI**} & **Average** \\ \cline{2-7}  & W/O CGM & CGM Factor 7 & W/O CGM & CGM Factor 7 & W/O CGM & CGM Factor 7 & Error \\ \hline Tumbling V mixer & \(4.53\times 10^{6}\) & \(1.32\times 10^{4}\) & 58.5 h & 13 min & 0.300 & 0.324 & 12.39\% \\ Ribbon-blade mixer & \(2.71\times 10^{6}\) & \(2.28\times 10^{3}\) & 125 h & 14 min & 0.972 & 0.928 & 2.54\% \\ Paddle-blade mixer & \(9.85\times 10^{6}\) & \(2.97\times 10^{4}\) & 186 h & 26 min & 0.798 & 0.754 & 3.42\% \\ Vertical-blade mixer & \(8.93\times 10^{6}\) & \(7.14\times 10^{4}\) & 500 h & 3 h 7 min & 0.734 & 0.785 & 4.38\% \\ Conical-screw mixer & \(5.08\times 10^{6}\) & \(1.48\times 10^{4}\) & 114 h & 30 min & 0.568 & 0.576 & 4.54\% \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Summary of simulation results for all mixer types. A cross-comparison of the final LMI values and the average CGM-induced errors across all mixers revealed a clear trend.