# Enhanced Modeling for Analysis of Fine Particulate Interactions with Coated Surfaces
## 3 Simulations and Discussions
### Particles Rolling on a Smooth Plate  
Three kind of bulk materials, SiO2, Fe2O3, Fe3O4, were created to characterize the motion of different types of particles on a surface. The primary motivation for choosing these materials was their prevalence on the Martian surface, where silicon oxides and iron oxides are among the most commonly found constituents. The reason for selecting two different types of iron oxide materials was to compare the differences that may arise between these two iron oxide particulates during simulated rolling. For comparative data analysis, all particles were designed as ideal spheres. The size distribution was set to follow a standard normal distribution with a mean value of 60 \(\upmu\)m and a standard deviation of 0.4. The particle size range was between 10 \(\upmu\)m and 110 \(\upmu\)m. Each particle consisted of grid cells arranged in a 30 \(\times\) 30 \(\times\) 30 (X \(\times\) Y \(\times\) Z) configuration. The plate material was chosen to be SiO2. Indeed, the protective materials used on the surface of solar panels were meticulously designed to endure the harsh conditions of a Mars exploration mission. However, in the context of this study, our primary focus was on the normalization of the plate relative to fine particles. As such, we opted for silica as the plate material, due primarily to its readily available and well-documented material properties. Three types of particles were deposited onto the horizontal plane via particle factories, with each type represented by 10 particles. After the particles had been dispensed and their relative motion had ceased, the plate was rotated along the \(y\)-axis at a constant speed until the particles rolled off the plate. The base contact model used was Hertz-Mindlin with IKR V2, and the friction model employed was standard rolling friction. Gravity was set at 3.71 m/s\({}^{2}\). To maintain numerical stability and precision throughout the particle dynamics simulation, the time step was configured to be 40% of the Riley time step, equating to \(8.74\times 10^{-10}\) s. This was determined by taking into account the recommended setting (20-40%) of the EDEM software as well as the iteration speed. Moreover, given that the physical models discussed in this paper did not encompass any additional elements (such as bonds), there was no explicit necessity to shorten the iteration step with the aim of enhancing simulation stability and precision. The cell size was determined to be 2.5 times the minimum particle radius (\(R_{\text{min}}\)). While the EDEM's recommended setting for cell size typically ranged from 3 to 6 times the \(R_{\text{min}}\), we took into account the diminutive particle size of our physical model in this study. To guarantee solution accuracy, we adjusted the cell size to be set at 2.5 times the \(R_{\text{min}}\). Considering the storage space and the continuity of data changes, the time interval for data saving was set to 0.005 s.  
The simulation results are shown in Figure 4. Each subplot in Figure 4 depicts a unique time node in the movement of these particles, marking critical instances such as the onset or conclusion of motion. We introduced the variable \(Ang\) to denote the angle between the smooth plate and the horizontal plane, as depicted in Figure 4a. Initially, the plate was maintained in a horizontal position and particles of the three materials were randomly spread on the plate, as illustrated in Figure 4b. As the rotation of the plate commences, the particles tended to roll off. When \(Ang=7^{\circ}\), a portion of the particles initiated rolling, except for the SiO\({}_{2}\) particles which remained relatively stationary, showcased in Figure 4c. At the point when \(Ang\) reached 22.3\({}^{\circ}\), the SiO\({}_{2}\) particles started skidding along with other particles, portrayed in Figure 4d. Yet, some SiO\({}_{2}\) particles persisted on the plate, providing support for Fe\({}_{3}\)O\({}_{4}\) particles and preventing them from rolling off.