# Comparative Study to Evaluate Mixing Efficiency of Very Fine Particles
## 5 Numerical Analysis Results
### Mixing Efficiency Analysis of Conical-Screw Mixer with CGM Scaling  
This section presents the DEM simulation results for the conical-screw mixer under various CGM scaling factors (CGM = 1, 2, 3, 4, 5, and 7). We analyzed the mixing efficiency across different CGM conditions based on the time-dependent particle behavior and the LMI. The results are presented through particle distribution visualizations, LMI time-series plots, and statistical summaries for the final second of each simulation. Figure 21 presents the temporal evolution of the LMI. In the early stages of mixing, fluctuations or negative LMI values were observed in some CGM cases. These anomalies are attributable to the statistical nature of the LMI formula, especially when the sample size is small or the composition is significantly imbalanced. Despite such early irregularities, all CGM cases demonstrated a steady upward trend in LMI over time, and values converged as mixing progressed. The overall LMI improvement pattern was similar across CGM levels, which confirms that adequate mixing performance can be achieved even at higher CGM values. Figure 22 displays the particle distributions at 6, 18, 24, and 30 s for each CGM level. Across all CGM conditions, the overall particle flow and mixing patterns remained visually consistent. Although the particle resolution decreased as the CGM factor increased, the general mixing structure was preserved. This visual consistency supports the conclusion that the fundamental mixing mechanism is retained even after CGM. As inferred from Figure 21, extending the simulation would likely have resulted in further convergence of LMI values across CGM conditions, which would reduce the error margins. Table 8 summarizes the particle count, total simulation time, and the average, maximum, and minimum LMI values during the final second (29-30 s), along with the calculated error for each CGM condition. As the CGM factor increased, the simulation time was dramatically reduced, from approximately 114 h at CGM = 1 to only 30 m at CGM = 7. While the error varied among the CGM cases, it was relatively high under certain conditions. However, extending the simulation is expected to reduce these discrepancies further. These findings confirm the effectiveness of CGM in enhancing computational efficiency while maintaining the reliability of mixing performance evaluations. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{4}{c}{**CGM Scaling Factor**} \\ \cline{2-6}  & & **2** & **3** & **4** & **5** \\ \hline Particle count & 8.93 \(\times\) 10\({}^{6}\) & 1.12 \(\times\) 10\({}^{6}\) & 3.30 \(\times\) 10\({}^{5}\) & 1.39 \(\times\) 10\({}^{5}\) & 7.14 \(\times\) 10\({}^{4}\) \\ Simulation duration & 500 h & 70 h & 13 h 20 min & 4 h 27 min & 3 h 7 min \\ Average LMI & 0.734 & 0.762 & 0.762 & 0.755 & 0.785 \\ Minimum LMI & 0.739 & 0.766 & 0.767 & 0.771 & 0.831 \\ Maximum LMI & 0.727 & 0.756 & 0.753 & 0.742 & 0.749 \\ Error & – & 3.84\% & 3.86\% & 2.88\% & 6.95\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Particle counts, simulation times, LMI statistics, and errors for the Vertical-Blade Mixer. The occurrence of negative LMI values during the early simulation stages can be explained by the specific dynamics of the conical-screw mixer. Due to the combined effects of orbital motion and multi-axis screw rotation, the initial flow field is highly asymmetric. Specifically, particles near the outer cone wall tend to move slowly in the vertical direction, whereby a stratified distribution is maintained. When particles are initially layered or segregated in this manner, the system can temporarily exhibit more structured heterogeneity than a purely random mixture, which leads to negative LMI values. As mixing continues and the screw mechanism circulates material through the entire domain, these structured layers gradually dissolve, and the LMI converges toward positive, physically meaningful levels. Figure 21: Temporal evolution of LMI for different CGM factors for the Conical-Screw Mixer.