# Enhanced Modeling for Analysis of Fine Particulate Interactions with Coated Surfaces
## 3 Simulations and Discussions
### Particles Rolling on a Coated Plate  
We applied the modified normal force calculation model to the case just discussed, aiming to compute the interaction between particulate matter and the coating. The mi  
Figure 5: Numbering of particles on the plate. 1, 2 and 3: SiO\({}_{2}\) particles; 4, 5: Fe\({}_{3}\)O\({}_{4}\) particles. Figure 6: Normal force per unit mass of each particle on the plate. crostructure of the coating could not be represented in the EDEM software. Additionally, the EDEM software identifies contact based solely on coordinate distance and ignores surface properties. Hence, we made no additional adjustments for the coating during EDEM processing. In the previous section, we introduced the equivalent area ratio (\(k\)) as a parameter to characterize the surface properties of the coating. In this simulation case, we set the value of \(k\) in advance for the new plugin to invoke. Setting the equivalent area ratio at \(k=0.5\), we then analyzed the resulting simulation outcomes. We introduced the normal force model proposed in this study into the EDEM file location as an API plug-in, enabling the calculation of contact forces between particles and a coated plate. We retained the settings from the previous simulation case. The resultant simulation outcomes are represented in Figure 7. Similar to Figure 4, each subplot in Figure 7 also illustrates a distinct time node during the movement of these particles. To clearly denote the coating on the surface of the plate, we depicted the plate in Figure 7 with a color distinct from that in Figure 4, while maintaining the color consistency of particles with those in the preceding simulation case. Before the rotation of the plate began, particles of three different materials were randomly dispersed on it, as displayed in Figure 7a. Once these particles settled into a relatively stationary state, the rotation of the plate initiated. When the plate was rotated to \(Ang=6.75^{\circ}\), certain particles started rolling downward, as portrayed in Figure 7b. The SiO\({}_{2}\) particles remained static, and some Fe\({}_{2}\)O\({}_{3}\) and Fe\({}_{3}\)O\({}_{4}\) particles ceased their downward roll due to their reliance on the SiO\({}_{2}\) particles, as illustrated in Figure 7c. It was not until the plate was rotated to \(Ang=23.4^{\circ}\) that SiO\({}_{2}\) particles initiated their downward roll, as captured in Figure 7d. Consequently, the Fe\({}_{2}\)O\({}_{3}\) and Fe\({}_{3}\)O\({}_{4}\) particles commenced their descent due to the loss of support from the SiO\({}_{2}\) particles. All particles collectively rolled down off the plate, as demonstrated in Figure 7e. Eventually, the smallest SiO\({}_{2}\) particle became the last one to roll off the plate, as shown in Figure 7f. Analogously, a few representative particles found in Figure 7d were selected and numerically labeled as demonstrated in Figure 8. Numbers 6 and 7 refer to two SiO\({}_{2}\) particles, one interacting with other particles and the other solely making contact with the plate's coating. Number 8 represents a Fe\({}_{2}\)O\({}_{3}\) particle, and number 9 denotes a Fe\({}_{3}\)O\({}_{4}\) particle. The details of these particles are shown in Table 2.  
The variations in the normal force per unit mass of these particles are depicted in Figure 9. Given that particle No. 6 supported several particles above it, it experienced substantial pressure, thereby resulting in a high \(F_{nm}\) value. For particles No. 7 and No. 8, their \(F_{nm}\) values were roughly similar. It is plausible that the smaller mass of particle No. 7 led to it having a slightly larger \(F_{nm}\) value than that of particle No. 8. Despite having the largest mass, particle No. 9 exhibited the smallest \(F_{nm}\) value compared to the others. The mass of particle No. 6 was akin to that of particle No. 2. Upon comparing Figures 6 and 9, it is evident that the \(F_{nm}\) value of particle No. 6 exceeded that of particle No. 2 during the downward rolling progress.