# Comparative Study to Evaluate Mixing Efficiency of Very Fine Particles
## 5 Numerical Analysis Results
### Mixing Efficiency Analysis of Vertical-Blade Mixer with CGM Scaling  
This section presents the DEM simulation results for the vertical-blade mixer under various CGM scaling factors (CGM = 1, 2, 3, 4, and 5). The analysis focused on the evolution of the particle-mixing characteristics over time, the quantitative changes in the LMI, and statistical summaries from the final second of each simulation.  
Figure 19 presents the temporal evolution of the LMI. While differences in absolute values were observed across CGM factors, the LMI consistently increased over time under all conditions. During the initial mixing phase, some CGM cases showed negative LMI values, which is attributed to the statistical nature of the LMI formula. Such values can arise when the component ratio is highly unbalanced or when sampling is insufficient in the early stages. Nevertheless, the LMI values across all CGM cases increased along similar trajectories and began converging as the mixing progressed, which reinforces the robustness of LMI-based evaluation.  
Figure 20 presents the particle distribution snapshots at 6, 18, 24, and 30 s for each CGM condition. The overall mixing pattern remained consistent across all CGM levels. Although  
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & \multirow{2}{*}{**W/O CGM**} & \multicolumn{5}{c}{**CGM Scaling Factor**} \\ \cline{3-6}  & & **2** & **3** & **4** & **5** & **7** \\ \hline Particle count & 9.85 \(\times\) 10\({}^{6}\) & 1.27 \(\times\) 10\({}^{6}\) & 3.78 \(\times\) 10\({}^{5}\) & 1.36 \(\times\) 10\({}^{5}\) & 6.66 \(\times\) 10\({}^{4}\) & 2.97 \(\times\) 10\({}^{4}\) \\ Simulation duration & 186 h & 12 h & 2 h 35 min & 1 h 13 min & 41 min & 26 min \\ Average LMI & 0.798 & 0.807 & 0.793 & 0.758 & 0.760 & 0.754 \\ Minimum LMI & 0.799 & 0.811 & 0.797 & 0.772 & 0.782 & 0.771 \\ Maximum LMI & 0.795 & 0.801 & 0.785 & 0.742 & 0.726 & 0.736 \\ Error & – & 1.18\% & 0.64\% & 4.98\% & 4.81\% & 5.51\% \\ \hline \end{tabular}
\end{table}
Table 6: Particle counts, simulation times, LMI statistics, and errors for the Paddle-Blade Mixer.  
Figure 19: Time evolution of the LMI for different CGM factors for the Vertical-Blade Mixer.  
the resolution of individual particles decreased with higher CGM scaling, the general flow behavior and mixing characteristics exhibited minimal deviation. This confirms that the underlying mixing mechanisms are preserved even after CGM.  
As shown in Figure 19, extending the simulation would likely have led to further convergence of the LMI values across CGM conditions, potentially reducing the error margins. Table 7 summarizes the average, maximum, and minimum LMI values during the 29-30 s interval, along with the particle count, total simulation time, and error percentage for each CGM case. As the CGM scaling increased, the simulation time was significantly reduced, from approximately 500 h at CGM = 1 to only 3 h and 7 min at CGM = 5. The error rates largely remained within 4%, which indicates that CGM can ensure reliable numerical accuracy while providing substantial computational savings.  
Figure 20: Particle distribution snapshots at 6, 18, 24, and 30 s under various CGM factors in the Vertical-Blade Mixer.  
The negative LMI values observed during the early stages in certain CGM cases can be interpreted based on the unique flow characteristics of the vertical-blade mixer. Due to the high-speed rotation of the central vertical blade, strong centrifugal forces are generated near the core region, which mobilize the central particles. Meanwhile, the peripheral regions near the vessel wall may remain relatively stagnant. If the initial particle arrangement is inhomogeneous, especially with clusters near the wall, these dead zones can temporarily persist, causing the particle distributions to be more segregated than in a purely random state. As mixing progresses, however, these stagnant regions are gradually eliminated, and the LMI returns to physically meaningful levels.