Enhanced Modeling for Analysis of Fine Particulate Interactions with Coated Surfaces

Abstract

The adhesion of Martian surface dust to solar panels has been a longstanding challenge for Mars mission researchers. Anti-dust coatings have been developed to deter the adsorption of dust particles onto these solar panels. However, current ground testing methods struggle to accurately verify and assess the coating’s ability to inhibit dust particle adsorption. Consequently, this paper introduces a computational model capable of calculating the contact force between fine particles and the coated surface. This model, grounded in the classical adhesive elastic interactions paradigm, establishes a normal force solution by approximating the pressure distribution on the contact area between the sphere and the coating, subsequently computing the composite force acting on the particle. Utilizing the API module of the EDEM simulation platform, we conducted simulations of the motion of fine particles on both smooth and coated plates. The results reveal that van der Waals forces are more prominent for light-mass particles, and the application of the coating can diminish the pull of these forces, facilitating easier detachment of dust particles from the plate surface.

1. Introduction

Surface dust on Mars has persistently posed a significant challenge to Martian exploration efforts, with observable effects including wear and tear on equipment, adsorption, and electromagnetic interference. The accumulation of fine dust particles on solar panels substantially reduces the energy provision for Mars exploration apparatus, posing a severe threat to the operational lifespan of rovers [1]. Consequently, dust management for Mars rovers remains a pressing priority. This holds true even for the meticulously designed solar panels of NASA’s Mars rovers [2,3], as well as China’s Zhurong rover [4], all of which have had to contend with Martian dust.

The advent of dust removal technology has become a necessary precursor to Mars exploration. A variety of such technologies have been developed [5], including the wind cleaning method [1], anti-dust coating method [6], mechanical wiping method [7], and electrodynamic screen method [8]. The anti-dust coating method [9] is usually chosen as one of the main dust removal strategies for Mars rovers due to its high reliability. Xu et al. [6] advanced this field by developing nano-crystalline composite coatings that provide effective dust protection for solar panels. By employing an ultra-thin solar film in conjunction with a specialized anti-dust coating, the Zhurong rover managed to achieve dust removal efficiency exceeding 86% [10].

Laboratory testing for dust removal efficiency serves as the primary method of evaluating coatings. Zhang et al. [11] conducted performance tests on coatings with varying hydrolysate-silica sol mass ratios, but did not elaborate on the size distribution of the particles involved. Dogra et al. [12] examined the wetting behavior and transmittance of hydrophobic coatings prepared using zirconium nanoparticles and hexamethyldisilazane (HMDS). However, investigations into these coatings’ effectiveness in removing specific dust types from the Martian surface remain unexplored. Conducting laboratory research on the effectiveness of anti-dust coatings for Martian dust removal poses considerable challenges. Replicating the exact environment of the Martian surface within a lab setting is not only costly; the accuracy of simulating certain environmental parameters (e.g., gravitational conditions) also remains questionable. Furthermore, while dust removal tests on coatings have shown promising results with larger particles (e.g., those measuring millimeters in diameter [9]), their effectiveness on finer particles, particularly those with diameters in the tens of micrometers range, is yet to be definitively established. Perko et al. [13] compiled insights from various research studies on Martian surface dust. As gleaned from the literature, dust particles typically found on surfaces are usually smaller than 100 μm. Fine particles with sizes ranging from 5 μm to 100 μm can be swept up during dust storms, while particles smaller than 10 μm might potentially remain suspended indefinitely within the Martian atmosphere. In the force analysis of such fine particles, van der Waals forces should not be overlooked as they may play a significant role in causing fine particles to adhere to surfaces [14]. Nevertheless, carrying out dust removal tests for these fine particles presents numerous challenges. Accurate measurement and observation stand as primary difficulties, while accurately simulating the environmental conditions and the behavior of fine particles poses another formidable hurdle.

The discrete element method (DEM) [15] is an increasingly prominent particle simulation approach suitable for studies that are challenging to conduct within a laboratory setting. This technique breaks down the research object (be it particle or geometric) into independent units, conducts an analysis of interactions among these units, and proceeds to iteratively calculate force and displacement at each time step based on Newton’s laws of motion. EDEM, notably the first modeling and simulation software developed using the DEM [16], has proven successful in various fields. Examples of its application include characterizing material movement in loader shovels [17], analyzing particle trajectories in mixers [18], and understanding the crushing process of gold-bearing ore in a jaw crusher [19]. The built-in JKR model [20] within EDEM is a cohesive contact model, taking into account the influence of van der Waals forces within the contact zone. This allows users to simulate highly adhesive systems. However, this model struggles to accurately capture the dynamics of fine particles interacting with the coating surface. One reason for this is the disparity in scale—several orders of magnitude—between the surface resolution of the coating and the size of the particles, which complicates geometry design. Additionally, EDEM^TM 2022.1 software identifies contact based solely on coordinate distance [21], disregarding the surface properties of the coating. Therefore, accurately characterizing the force interactions between fine particles and coatings is crucial for analyzing the dust removal capabilities of these coatings and conducting dynamic simulations of fine particles.

Drawing from the Hertz contact theory that offers a comprehensive analysis and derivation of elastic contact, this study aims to conduct an analysis of interactions between fine particles and coating surfaces. The central purpose is to develop a computational model that can accurately portray the contact between particles and coatings. Through an in-depth analysis of the coating’s structural intricacies, we construct a simplified equation for estimating the pressure distribution at the interface between the particle and the coating surface. Consequently, this allows us to deduce the normal force acting upon the particle at the coating surface. The model introduced in this study, synergizing with the dynamic simulation capacities of EDEM software, serves as an efficient simulation tool for prospective dust removal tests for coatings. Moreover, it lays a foundation for simulating and evaluating surface dust removal capabilities of future Mars rovers.

This paper is organized as follows. In Section 2, the theoretical model is provided. Numerical simulations and discussions are carried out in Section 3. Section 4 draws the conclusions.

2. Theoretical Model

This paper primarily investigates fine particles, smaller than 100 microns, adhering to solar panel surfaces. To facilitate a comprehensive analysis of force characteristics related to particulate matter, we used an idealized uniform sphere as a representative physical model. Considering the thin atmospheric conditions on Mars, for fine particles, the Knudsen number—pertaining to the airflow circulating around these particles—generally exceeds 0.01. This suggests that the interaction pattern between the airflow and these microscopic entities is largely discontinuous [22]. Additionally, our study primarily focuses on the adsorption characteristics of these fine particles; thus, interactions between these particles and the surrounding discontinuous airflow are not taken into account.

The computation of normal forces for particles relies on the Hertzian contact theory, while tangential force calculations are founded on the Mindlin–Deresiewicz work. Both types of forces incorporate damping components. The tangential friction force adheres to the Coulomb law of friction model, and rolling friction is executed under the context-independent directional constant torque model. These force calculations are all consolidated within the Hertz–Mindlin (no slip) physics module of the EDEM software.

For particles with small size, van der Waals forces become significant and they tend to stich to each other. The calculation of the normal force, whether between particle–particle or particle–geometry interactions, differs from that in the Hertz–Mindlin (no slip) physics module. The JKR model is developed for this kind of adhesive and elastic interactions.

According to the theory of Hertz [23,24], the normal pressure distribution acting over the small circular contact area (shown in Figure 1) of radius a is expressed as:

$$p\left(r\right)=p_0{\left[1-{\left(\frac{r}{a}\right)}^2\right]}^{\frac{1}{2}},$$

(1)

where r($r\in [0,a)$) is the distance from the point to the center point of the contact area, and $p_0$ is the pressure at the center of the contact area. In Figure 1, the dashed arc contour delineates the shape of the two particles prior to contact, while the solid arc contour depicts their shape following the contact. The maximum radius of the contact surface is denoted as ‘a’ in Figure 1. The α_1,2 in Figure 1 are the deformations of the two spheres in the normal direction due to contact, respectively. Additionally, the relative approach of the centroids of the two spheres in the normal direction is defined by:

$$\alpha ={\alpha }_1+{\alpha }_2,$$

(2)

The total normal force is the integral of the pressure on the contact area:

$$F_n={\int }_0^{a}p\left(r\right)2\pi rdr,$$

(3)

Considering the van der Waals force, the normal contact pressure distribution is written as [23]:

$$p\left(r\right)=p_{def}\left(r\right)-p_{van}\left(r\right)=\left(\frac{2E^{*}a}{\pi R^{*}}\right){\left[1-{\left(\frac{r}{a}\right)}^2\right]}^{\frac{1}{2}}-{\left(\frac{2E^{*}\Gamma }{\pi a}\right)}^{\frac{1}{2}}{\left[1-{\left(\frac{r}{a}\right)}^2\right]}^{-\frac{1}{2}},$$

(4)

where $E^{*}$ is the relative contact compliance, $R^{*}$ is the relative curvature of the surface, and $\Gamma$ is the work of adhesion. The first term of this equation $p_{def}\left(r\right)$ signifies the pressure attributed to deformation, while the second term $p_{van}\left(r\right)$ corresponds to the pressure induced by the van der Waals force. The formulae for these three variables above are shown in Formulas (5)~(7):

$$E^{*}=\frac{1}{\frac{1-{\nu }_1^2}{E_1}+\frac{1-{\nu }_2^2}{E_2}},$$

(5)

$$R^{*}=\frac{1}{\frac{1}{R_1}+\frac{1}{R_2}},$$

(6)

$$\Gamma ={\gamma }_1+{\gamma }_2-{\gamma }_{\mathrm{1,2}},$$

(7)

where $E_i\left(i=\mathrm{1,2}\right)$ and ${\nu }_i\left(i=\mathrm{1,2}\right)$ are the Young’s modulus and the Poisson’s ratio for the two spheres, respectively, $R_i\left(i=\mathrm{1,2}\right)$ are the radii of the two spheres, ${\gamma }_i\left(i=\mathrm{1,2}\right)$ are the surface energies of the two solids, and the ${\gamma }_{\mathrm{1,2}}$ is the interface energy.

The normal force is obtained from Equations (3) and (4):

$$F_n=\frac{4E^{*}{a}^3}{3R^{*}}-{\left(8\pi \Gamma E^{*}{a}^3\right)}^{\frac{1}{2}},$$

(8)

The corresponding relative approach is given by:

$$\alpha =\frac{a^2}{R^{*}}-{\left(\frac{2\pi \Gamma a}{E^{*}}\right)}^{1/2},$$

(9)

Equations (8) and (9) show the revised JKR model used to calculate the normal contact force on a sphere particle considering the van der Walls force.

Consider a surface coating with a structure of uniformly distributed cylindrical crystals of equal height [6], as shown in Figure 2: the actual contact area between a particle and the coating corresponds to the base areas of these cylinders. For a circular region with a radius of R^c, whose area is $A^c=\pi {R^c}^2$, the surface area of the top of the crystal is described as:

$$A^{cr}=n\pi {r^{cr}}^2,$$

(10)

where $r^{cr}$ is the radius of the base of the cylinder, and n is the number of the crystals in this region.

The aim of using this particular coating structure is to minimize the actual contact area between the particles and the coating surface, thus reducing the influence of van der Waals forces. When a spherical particle comes into contact with this surface, the actual contact area comprises the combined areas of multiple crystal bottoms, as depicted in Figure 3. Assuming a uniform variation in pressure from the center of the circle along the radius during this kind of contact, we simplify the reduction of contact area as a decrease in pressure along the radial direction to facilitate calculations. As such, the pressure distribution of the spherical particle on the coating surface can be approximately expressed in the following form:

$$p^c\left(r\right)=p_{def}^c\left(r\right)-p_{van}^c\left(r\right)=\left(\frac{2E^{*}{a}^c}{\pi R^{*}}\right){\left[1-{\left(\frac{r}{a^c}\right)}^2\right]}^{\frac{1}{2}}-{\left(\frac{2E^{*}{\Gamma }^c}{\pi a^c}\right)}^{\frac{1}{2}}{\left[1-{\left(\frac{n^{\frac{1}{2}}\frac{r^{cr}}{R^c}r}{a^c}\right)}^2\right]}^{-\frac{1}{2}},$$

(11)

Analogous to Equation (4), the two terms in Equation (11) denote pressure induced by deformation and the van der Waals force, respectively. However, it is crucial to note that the work of adhesion ${\Gamma }^c$ in Equation (11) does not equate to $\Gamma$ in Equation (4), as the actual contact area diminishes the adhesive effect.

Define a parameter of equivalent area ratio for the coating to describe the ratio of the actual contact area to the projected area of the contact surface:

$$k=\frac{A^{cr}}{A^c}=n{\left(\frac{r^{cr}}{R^c}\right)}^2,0<k\le 1,$$

(12)

Then, Equation (11) can be reformulated as the follow equation:

$$p^c\left(r\right)=p_{def}^c\left(r\right)-p_{van}^c\left(r\right)=\left(\frac{2E^{*}{a}^c}{\pi R^{*}}\right){\left[1-{\left(\frac{r}{a^c}\right)}^2\right]}^{\frac{1}{2}}-{\left(\frac{2E^{*}{\Gamma }^c}{\pi a^c}\right)}^{\frac{1}{2}}{\left[1-{\left(\frac{k^{\frac{1}{2}}r}{a^c}\right)}^2\right]}^{-\frac{1}{2}},$$

(13)

Hence, by integrating the pressure over the contact area, we derive the applied normal contact force taking into account the coating:

$$\begin{gathered} F_n^c={\int }_0^{a^c}{p}_{def}^c\left(r\right)2\pi rdr-{\int }_0^{a^c}{p}_{van}^c\left(r\right)2\pi rdr \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=\frac{4E^{*}{a^c}^3}{3R^{*}}-\frac{\left(1-{\left(1-k\right)}^{1/2}\right)}{k}{\left(8\pi \Gamma E^{*}{a^c}^3\right)}^{1/2}, \end{gathered}$$

(14)

Similarly, the corresponding relative approach is:

$${\alpha }^c={\alpha }_c^1+{\alpha }_c^2=\frac{{a^c}^2}{R^{*}}-{\left(\frac{2\pi {\Gamma }^c{a}^c}{E^{*}}\right)}^{1/2},$$

(15)

Equations (14) and (15) are used to calculate the normal force of a spherical particle when contacting a surface with a coating.

This model presupposes that the interaction between the particle and the coating does not alter the deformation characteristics of the contact surface, and that the distribution of pressure resulting from the deformation varies uniformly across the contact surface. The normal forces derived from the solution of this computational model serve as inputs for subsequent computations. These further calculations determine the damping components, along with forces such as tangential and frictional forces.

While performing the DEM simulation, the following iterative calculation steps are adopted:

(1)

Compute the positions of the particles and geometry at the current time step;

(2)

Based on the position data of each unit, determine the relative approach between particle-to-particle or particle-to-geometry interactions;

(3)

Use the relative approach to calculate the normal force exerted on the particles, utilizing the contact model proposed in this paper;

(4)

Compute the other forces acting on the particles based on the revised normal force;

(5)

Update the motion and position of the particles according to these calculated forces;

(6)

Repeat step one until the iteration process reaches completion.

Leverage the API tool to transform the model described above into a plug-in, facilitating its invocation within the EDEM software.

3. Simulations and Discussions

To demonstrate the model presented in this paper, simulations of spherical particles dumping on smooth and coated plates were carried out respectively, based on the Altair EDEM^TM 2022.1 software. It is worth noting that we selected the ideal sphere as the physical model for our simulation, primarily to ease the execution of theoretical analysis. While irregular particles might offer a more realistic simulation, analyzing the force and motion of an ideal sphere is considerably more convenient and straightforward, thereby simplifying the derivation of universal laws. Consequently, we opted for the ideal sphere as our physical model to augment our capability to analyze the impact of the two surfaces on fine particles.

3.1. 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 μm and a standard deviation of 0.4. The particle size range was between 10 μm and 110 μm. Each particle consisted of grid cells arranged in a 30 × 30 × 30 (X × Y × 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 JKR V2, and the friction model employed was standard rolling friction. Gravity was set at 3.71 m/s².

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 × 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_min). While the EDEM’s recommended setting for cell size typically ranged from 3 to 6 times the R_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_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°, a portion of the particles initiated rolling, except for the SiO₂ particles which remained relatively stationary, showcased in Figure 4c. At the point when Ang reached 22.3°, the SiO₂ particles started skidding along with other particles, portrayed in Figure 4d. Yet, some SiO₂ particles persisted on the plate, providing support for Fe₃O₄ particles and preventing them from rolling off. When Ang = 28.3°, all residual particles began their roll off the plate, as captured in Figure 4e. Finally, an SiO₂ particle located comparatively near the top also rolled off the plate, as demonstrated in Figure 4f.

In order to illustrate the interactions of van der Waals forces between the particles and the plate, the five particles depicted in Figure 4e are numerically labeled as shown in Figure 5.

The details of these particles are shown in

Table 1. Details of the five particles on the plate.

No.	Material	Diameter (μm)	Mass (×10−7 g)
1	SiO2	32.6	0.44
2	SiO2	56.5	2.28
3	SiO2	97.4	11.64
4	Fe3O4	62.4	6.59
5	Fe3O4	80.0	13.90

.

Since the mass of different particles varies considerably, define the parameter F_nm to describe the normal force per unit mass:

$$F_{nm}=\frac{F_n}{m},$$

(16)

where m represents the mass of a particle.

Utilizing the post-processing tools of EDEM, we obtained the normal force experienced by each particle at each sampling interval. By further dividing these forces by the respective mass of each particle, we derived the changes in F_nm over time. Then, extracting the Ang value at each sampling interval, we plotted the curves representing the changes in each particle’s F_nm with respect to variations in Ang. The curve representing $F_{nm}$ for angles ranging from Ang = 22.7° to Ang = 30.7° is plotted in Figure 6. From this figure, it becomes evident that an increase in mass for SiO₂ particles corresponds with a decrease in $F_{nm}$. In contrast, the slight difference in mass for Fe₃O₄ particles does not result in a significant variation in $F_{nm}$ values. Initially, particle No. 2 supported particle No. 5 as depicted in Figure 4e. However, as these particles rolled off, particle No. 2 was no longer compressed by particle No. 5, resulting in an $F_{nm}$ value approximately around 750 dyn/g.

3.2. 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 microstructure 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°, certain particles started rolling downward, as portrayed in Figure 7b. The SiO₂ particles remained static, and some Fe₂O₃ and Fe₃O₄ particles ceased their downward roll due to their reliance on the SiO₂ particles, as illustrated in Figure 7c. It was not until the plate was rotated to Ang = 23.4° that SiO₂ particles initiated their downward roll, as captured in Figure 7d. Consequently, the Fe₂O₃ and Fe₃O₄ particles commenced their descent due to the loss of support from the SiO₂ particles. All particles collectively rolled down off the plate, as demonstrated in Figure 7e. Eventually, the smallest SiO₂ 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 SiO₂ particles, one interacting with other particles and the other solely making contact with the plate’s coating. Number 8 represents a Fe₂O₃ particle, and number 9 denotes a Fe₃O₄ particle.

The details of these particles are shown in

Table 2. Details of the four particles on the coated plate.

No.	Material	Diameter (μm)	Mass (×10−7 g)
6	SiO2	55.8	2.19
7	SiO2	18.7	0.08
8	Fe2O3	39.8	1.73
9	Fe3O4	92.0	21.11

.

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 Figure 6 and Figure 9, it is evident that the F_nm value of particle No. 6 exceeded that of particle No. 2 during the downward rolling progress. This discrepancy can likely be attributed to the coating’s mitigation effect on van der Waals forces.

Particle No. 3 in Figure 6 and particle No. 7 in Figure 9, both composed of the same material, remained intact during the rolling down process. The F_nm values for these two particles were close to each other, but the value of particle No. 7 (~330 dyn/g) was marginally higher than that of particle No. 3 (~300 dyn/g) throughout the rolling process. In addition, upon comparing Figure 4c and Figure 7b, it becomes evident that the initiation angle of the particles diminished from 7.00° to 6.75°, a change attributable to the presence of the coating. Consequently, it is markedly evident that the presence of the coating increased the normal force exerted on the fine particles, thereby facilitating the ease with which particles rolled off the plate. Nevertheless, as observed from particle No. 1 in Figure 4 and particle No. 6 in Figure 7, irrespective of the coating’s presence or absence, some particles remained adhered to the plate surface, consequently preventing other particles from rolling off the plate. Moreover, there were differences in the adsorption of particles composed of diverse materials on the plate. As can be seen in both Figure 4 and Figure 7, SiO₂ spherical particles appeared to adhere more readily to the SiO₂ plate compared to their iron oxide counterparts. This phenomenon could potentially be attributed to the inherent material properties of the particles or the interactive properties exhibited during its contact with the plate.

Based on the above simulation cases, we can find that:

• The adherence of minuscule particles to the plate acted as a barrier, preventing larger particles from rolling off the plate;
• The presence of the coating weakened the van der Waals force, resulting in an increase in the normal force;
• Owing to the impact of the coating, tilting the plate facilitated easier rolling off of particles.

It is important to note that the primary objective of this study was to propose a novel computational model and associated method for researchers to investigate the dust removal capabilities of coatings. Consequently, our focus lay in assessing the feasibility of this method by analyzing particle force and motion. To facilitate the analysis, we established an ideal sphere model for the rolling simulation, while not performing simulations with plates tilted at 90°, as compared to common tilting tests. Furthermore, factors such as air humidity, particle shape, and surface roughness greatly influenced particle adhesion to the plate. The numerical simulation of large quantities of fine particles tilting proved to be both time-consuming and complex. Therefore, this research did not undertake comprehensive particle dumping simulations for comparison with relevant experiments. Future research can explore the effects of particle shape on adsorption properties by introducing irregularly shaped particles into the dump.

4. Conclusions

This paper addresses the issue of fine particulate adsorption on solar panels in Mars’s environment. A model was developed to calculate the contact force between the fine particles and the coated surface, utilizing an approximate equivalent pressure measure. We executed the motion simulation of fine particles through the API module of EDEM software. By simulating the movements of particles on a smooth plate and a coated plate, we compared the differences in solution results between the JKRV2 model and our proposed model.

The outcomes of our simulation underscore that the adherence of minuscule particles to a plate acts as a deterrent, impeding other particles from rolling off. The coating attenuates the adsorption of particles, but does not completely eliminate the adsorption of particles.

Future work will concentrate on exploring the agglomeration effects of particles and studying the adsorption of complex-shaped particles on plates.