Abstract During the landing of lunar probes on the surface of the Moon, lunar soil particles are lifted and diffused under the action of a plume. This study used three methods to numerically investigate the diffusion of lunar soil particles under a plume in a vacuum environment. First, an analytical solution of Fick's second law is used to obtain the motion results of lunar soil particles under the influence of diffusion in a steady state. Then, Fick's second law of finite-difference solution is used to obtain the motion results under the influence of diffusion. Finally, the discrete solution method of the mass- and energy-conservation equations is used to determine how the particles are affected by the plume in a transient state, including effects such as drag and lift, gravity, and temperature. The results show that lunar soil particles with small diameters diffuse more easily. After considering diffusion, the diffusion speeds of the 10- and 40-μm lunar soil particles are 3.6–4.5 times the speeds of those without diffusion; the spatial distribution range is increased by 1.4–4.5 times. The maximum lifting angle is increased by 1.0°–1.6°. However, lunar soil particles with diameters of 70 and 100 μm are not considerably affected by diffusion. At the same time, the introduction of the energy-loss coefficient showed that the impact of energy loss on the diffusion effect is substantial and that greater energy losses result in more diffusion-weakening trends. Compared with energy loss without considering the energy loss, diffusion speed is reduced by 10.2%–50.6%, occupied space is decreased by 18.3%–48.5%, and lifting angle is decreased by 18.8%–21.8%.Among the three methods, the mass- and energy-conservation method can fully consider the effects of particles and other factors. After considering the diffusion effect, the spatial distribution of lunar soil particles coheres better with the actual landing pictures, confirming that the impact of lunar soil particle diffusion on spatial distribution cannot be ignored.

中文翻译：

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真空环境羽流下月球土壤颗粒扩散现象的数值模拟

摘要 月球探测器着陆月球表面时，月球土壤颗粒在羽流的作用下被提升和扩散。本研究使用三种方法对真空环境中羽流下月球土壤颗粒的扩散进行数值研究。首先，利用菲克第二定律的解析解，得到稳定状态下月壤粒子在扩散影响下的运动结果。然后，利用菲克第二定律有限差分解法得到扩散影响下的运动结果。最后，使用质量守恒和能量守恒方程的离散求解方法来确定粒子在瞬态状态下如何受到羽流的影响，包括阻力和升力、重力和温度等影响。结果表明，直径小的月球土壤颗粒更容易扩散。考虑扩散后，10μm和40μm月球土壤颗粒的扩散速度是没有扩散的月球土壤颗粒的3.6-4.5倍；空间分布范围扩大了1.4-4.5倍。最大提升角度增加1.0°–1.6°。然而，直径为 70 和 100 微米的月球土壤颗粒不受扩散的影响很大。同时，能量损失系数的引入表明，能量损失对扩散效应的影响是显着的，能量损失越大，扩散弱化趋势越大。与不考虑能量损失的能量损失相比，扩散速度降低10.2%～50.6%，占用空间降低18.3%～48.5%，升角降低18%。8%~21.8%。在三种方法中，质量守恒和能量守恒方法可以充分考虑粒子等因素的影响。考虑到扩散效应后，月球土壤颗粒的空间分布与实际着陆画面更加吻合，证实了月球土壤颗粒扩散对空间分布的影响不可忽视。