Due to the unique conditions of the space environment and abundant resources, the field investigation and study of the Moon, Earth's sole natural satellite, represent a crucial milestone in China's forthcoming deep space endeavors. The successful collection of lunar soil by the Chang'E-5 mission signifies the next phase of the lunar exploration program, which aims to establish a preliminary research station on the lunar south pole. Highly adhesive fine dust particles with an adhesion strength of 0.1 to 1.0 kN/m2, which originate from the regolith, disperse throughout the lunar surface. These particles exhibit a lasting attraction and subsequent persistent adhesion to the surface of spacecraft or spacesuits. The accumulation of highly adhesive dust on spacecraft presents a serious issue to hinder long-term extravehicular activity and the establishment of a permanent station on lunar surface. In contrast to the immediate physical damage caused by hypervelocity (> 1.0 km/s) impacts, this adhesion observed at low- velocity (0.01 to 100 m/s) collisions can more unobtrusively and mortally degenerate the performance of equipment. In recent years, many interaction models have been developed to forecast the adhesion and ejection dynamics of lunar dust on various surfaces. Most researches on the electrostatic force applied on dust particles near the surface use point-charge approximation. Although this simplification makes the simulation easier, the error can be large due to the polarization of dust induced by the image charge. In a research article recently published in Space: Science & Technology, scholars from Beijing Institute of Technology, China Academy of Space Technology, and Chinese Academy of Sciences together propose a theoretical model aimed at comprehensively analyzing the dynamics of adhesion and escape phenomena occurring during low-velocity impacts between charged dust particles and spacecrafts enveloped by a plasma sheath which serves as a crucial step toward understanding the mechanism of lunar dust pollution.
First, the model of electrostatic force is demonstrated. As depicted in Fig. 1, dominated by the photoelectron effect induced by solar ultraviolet and x-ray radiation, the spacecraft and lunar regolith on lunar dayside typically charge positive. As a result, a photoelectron sheath forms above the surface. On the nightside, the spacecraft and regolith usually are negatively charged since the collection of plasma electrons. Due to the higher average thermal velocity of electrons compared to ions, a Debye sheath consequently forms around the vehicle. Besides, the exposure to the solar wind, the lunar plasma wake, and plasma in the magnetotail lobes and plasma sheet also electrically charges the spacecraft and regolith. This study only focuses on the interaction between charged particles and spacecraft within the confines of the plasma sheath, while the interaction between dust with plasma can be safely neglected. Considering the significant difference in size between the vehicle and the dust particle, the vehicle can be assumed as an infinite conducting plane coated with a dielectric layer, as depicted in Fig. 2. A dielectric dust particle, characterized by its radius Rp, uniform surface charge density σp, and permittivity εp, is positioned at a distance d above the surface. The distance between the surface of the coating and the shell is triple the Debye length (Rd) of plasma sheath. The potential of the shell is denoted by κ and is usually defined as the reference potential. The decay of potential in the sheath follows an exponential pattern. Hence, the distribution of the electric potential field within the plasma sheath can be expressed as: φ0 = κ exp[-(z-3Rd)/Rd], E0 = κ/Rd·exp[-(z-3Rd)/Rd], 0 ≤ z ≤ 3Rd. The electrostatic force FE is composed of 3 components: electric field force FEF, dielectrophoretic force FD, and image force FI, i.e., FE = FEF + FD + FI. The expression for FEF can be given by E0 with x = 0, y = 0, z = d + Rp multiplying the free charge Qp carried by the particle. FD is expressed using dyadic tensor notation. The multipole image force FI that acts on the induced multipole moments can be mathematically expressed considering the distance between the source point and the field point.
Then, the model of adhesive–elastic–plastic collision is demonstrated. In the present study, although lunar dust particles have extremely small size, irregular shape, and high hardness, they can be equivalently simplified to a spherical particle according to the conservation of normal contact force. The spacecraft coating consists of a Kapton layer. According to a dimensionless discriminant parameter μT, the commonly acknowledged JKR model which is useful for the analysis of collisions involving soft materials characterized by high interface energy can be utilized to describe the adhesive behavior of dust particles in this study. Additionally, in the context of low-velocity collisions, it is crucial to consider the energy dissipation caused by the plastic deformation of the coating. Based on the Thornton's adhesive–elastic–plastic model, in which the adhesive energy dissipation is described by the JKR model, the process of low-speed collision can be divided into 3 distinct stages: the adhesive–elastic loading stage, the adhesive–elastic–plastic loading stage, and the adhesive–elastic unloading stage. Figure 3 depicts the distribution of contact stress between the dust and coating, referred to as p(r), throughout the various stages. In the adhesive–elastic loading stage (see Fig. 3A), the relationship between the JKR pressure distribution p(r), the relative compression δ, and the contact force P1 in the first stage can be mathematically expressed as
As illustrated in Fig. 3B, during the adhesive–elastic–plastic loading stage, the normal contact force P2 is formulated and simplified as
In the unloading stage (see Fig. 3C), the correlation between the contact force P3 and the contact radius a continues to closely adhere to the JKR model with an irrecoverable displacement δp:
Finally, results and discussion are presented. As for electrostatic force, that a dielectric coating with a high thickness and low permittivity can effectively reduce the electrostatic force between charged dust and spacecraft can be inferred from the variation in the electrostatic force FE between the charged particle and the coated ground plane. Figure 5 illustrates the variation in the theoretical and simulated electrostatic force between the charged particle and the coated ground plane, considering various important parameters of the particle. It can be summarized that for dimensionless distance d/Rp ≥ 1 the electrostatic force between a charged particle and a coated ground plane can be approximated as F ≈ K Rp2 σp2 / (1 + d/Rp)2. Besides, results also show that the surface charge density plays a more significant role than the spacecraft potential. In the context of low-velocity collisions, a larger size of particle results in a higher maximum coefficient of restitution. The adhesive van der Waals force rather than electrostatic attraction force predominantly influences the adhesion of lunar dust during the low-velocity collision process, if the surface charge density σp is below 0.1 mC/m2. It can be inferred that the low-interface-energy coating, which can be created by employing low-surface-energy material and increasing the surface roughness, is effective to decrease the difficulty of dust removal. When it comes to the interaction between low-velocity charged particle and spacecraft, it is important to acknowledge that the final adhesion of particles to the spacecraft is not solely determined by the initial collision. Adhesion to the surface occurs only when the initial velocity of a negatively charged particle is within the range of the critical adhesion and escape velocities. At last, the conclusion is drawn that the theory presented in this study offers a framework for investigating various issues pertaining to the accumulation of charged dust particles. It can be applied to analyze phenomena such as dust deposition in electrostatic precipitators and the adhesion of energetic powder to mixer walls and serves as a basis for predicting and mitigating dust adhesion. Future research will focus on the integration of irregular shapes of dust, the plasma environment, and solar radiation effect into the interaction model.
