# Comparative Study to Evaluate Mixing Efficiency of Very Fine Particles
###### Abstract
Sampling-based approaches [16; 17; 18] are more practical but inherently limited since the results depend on the sampling technique, position, quantity, and sample size, even within the same system [19; 20]. Even with multiple sampling points, fully capturing both microscopic and macroscopic particle behaviors remains challenging [21]. Numerical simulation is generally more cost-effective for complex systems and serves as a foundational tool for scale-up, design, and process control. Computational methods for mixing simulations include continuum-based and discrete approaches. Continuum models,  
Figure 1: Common industrial mixers for mixing powders and granular materials: (**a**) tumbling-cylinder mixer; (**b**) tumbling-double-cone mixer; (**c**) tumbling V mixer; (**d**) vertical-blade mixer; (**e**) ribbon-blade mixer; (**f**) paddle-blade mixer; (**g**) screw mixer; (**h**) fluidized-bed mixer. based on Eulerian-Eulerian frameworks, analyze interactions between particulate flows and surrounding fluids without modeling individual particles explicitly [22]. However, since these models treat particles as a continuous phase, their ability to capture microscopic particle behaviors is limited. By contrast, discrete methods explicitly track individual particles. Common examples include Monte Carlo methods, cellular automata, and the discrete-element method (DEM). Among these, the DEM is widely used in particle-mixing simulations, such as for drum mixers [23; 24; 25], tote blenders [26], and V-blenders [27]. The DEM calculates particle motion at discrete timesteps by solving [PERSON]'s second law while accounting for particle-particle and particle-wall interactions. However, it requires significant computational resources; as the particle size decreases, the timesteps must be shortened to maintain contact resolution, which increases the particle count exponentially. These factors significantly increase computational costs, often necessitating high-performance computing resources. Recent studies highlight the DEM's potential in battery manufacturing optimization. The DEM has been employed to simulate dry mixing in next-generation battery production and evaluate parameters such as viscosity, mixing index, porosity, and stress distribution. These studies emphasize the DEM's utility in understanding microscale interactions and their macroscale implications. Additionally, research on the synthesis of lithium-ion battery cathodes has shown that powder mixing significantly influences electrochemical performance, which underscores the criticality of powder mixing and sets the groundwork for DEM-based modeling [28]. This study verifies the accuracy of DEM simulations incorporating coarse-grain modeling (CGM), which scales up particle sizes to improve computational efficiency. CGM reduces the particle count and allows larger timesteps by increasing the effective particle size, with each scaled-up particle representing a cluster of real particles. We systematically examine five industrial-scale mixing processes via DEM simulations to investigate the impact of varying CGM scaling factors. Mixing efficiency is quantitatively assessed using the Lacey mixing index (LMI), a well-established statistical metric in powder-mixing research. The contribution of this study lies in identifying the conditions under which CGM delivers reliable results while significantly reducing computational costs. The findings offer valuable guidance for optimizing DEM simulations in mixing applications.