# Comparative Study to Evaluate Mixing Efficiency of Very Fine Particles
## 4 Numerical Analysis Models  
### Particle Modeling  
All particles were modeled as spheres to isolate the effects of CGM scaling and to ensure consistency across different mixing-system configurations. Although Ansys Rocky supports non-spherical particle modeling, it incurs a significantly higher computational cost, particularly in high-resolution or large-scale simulations. When the particle size is significantly smaller than the characteristic dimensions of the mixing equipment, such as when the particle diameters are on the order of microns or millimeters while the vessel spans several meters, the influence of the particle shape on the bulk mixing behavior is generally considered negligible. This is particularly true when mixing uniformity is evaluated using statistical indices, such as the LMI. This simplification enabled us to focus on assessing the applicability of CGM and the associated efficiency improvements.  
In real-world industrial processes, however, particles often exhibit highly irregular and diverse shapes, which render full geometric representation within DEM simulations computationally prohibitive. Nevertheless, when simulation results are intended for high-fidelity comparison with experimental data or for quantitative validation of specific equipment, incorporating realistic particle shapes may become necessary. In such cases, CGM becomes even more essential as it facilitates the simulation of complex-shaped systems by significantly reducing the particle count and enabling tractable timesteps without severely compromising physical accuracy. Therefore, integrating CGM into the modeling of realistically shaped particles represents a promising direction for future research, particularly studies aiming to bridge simulation and experiment in industrial-scale powder-mixing applications.  
To ensure consistency across simulations, we employed a two-particle system in each mixing process. Although real-world industrial scenarios might involve diverse particle types, identical material properties were assigned to all particles in these simulations to avoid variations resulting from differing material properties. Table 1 summarizes the physical properties used for both types of particles in all simulations.  
The sizes and total masses of the particles were adjusted according to the characteristics of each mixing process to maximize computational efficiency. Table 2 summarizes these parameters, while Figure 10 illustrates the initial spatial distributions of the particles before mixing.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Property** & **Particle 1** & **Particle 2** \\ \hline Bulk density (kg/m\({}^{3}\)) & 1900 & 1050 \\ Bulk Young’s modulus (N/m\({}^{2}\)) & \(5\times 10^{7}\) & \(5\times 10^{7}\) \\ Friction coefficient & 0.2 & 0.2 \\ Restitution coefficient & 0.3 & 0.3 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Material properties of particles.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Mixer Type** & \multicolumn{2}{c}{**Diameter [mm]**} & \multicolumn{2}{c}{**Total Mass [kg]**} \\ \cline{2-4}  & **Particle 1** & **Particle 2** & **Particle 1** & **Particle 2** \\ \hline Tumbling V mixer & 3 & 6 & 180 & 100 \\ Ribbon-blade mixer & 2 & 4 & 11 & 110 \\ Paddle-blade mixer & 2 & 4 & 84 & 185 \\ Vertical-blade mixer & 1 & 2 & 3 & 75 \\ Conical-screw mixer & 2 & 4 & 200 & 250 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Particle sizes and masses for each mixing process.