Poster Presentation

Relationship between Regolith Particle Size and Porosity on Small Bodies

Masato Kiuchi (Kobe University,Japan) Akiko M. Nakamura (Kobe University,Japan)

Planetary small bodies are covered by a particle layer called regolith. The particle size and porosity of the regolith surface of small bodies are important physical properties. The responses of the surface to solar irradiation are dependent on the particle size and porosity. The particle size and porosity have influences on the dynamic responses of the surface, such as cratering efficiency. In previous studies, these two quantities were measured or estimated by various methods. Here we propose a semi-empirical relationship between the particle size and porosity for small bodies’ surfaces.

An empirical relationship between porosity of granular materials in loose packing state under 1 G and the ratio of the magnitudes of the interparticle force and gravity which acts on a particle was presented in a previous study [1]. In this study, we assume that the van der Waals force Fv is predominant in the interparticle forces and adopt a model formula [2] which is different from that adopted in the previous study [1]:
Fv=(AS^2)/(48Ω^2 ) r (1)
where A is Hamaker constant, r is particulate radius, Ω is diameter of an O^-2 ion, and S is cleanliness ratio which shows the smallness of a number of the adsorbate molecules [2]. It was shown that cleanliness ratio, S, is approximately 0.1 on the Earth, and is almost unity in the interplanetary space. In addition to the data of the several previous studies, our own measurement result of micron-size fly ash particles in atmospheric condition is used in the present analysis. We calculate Fv using Eq.1, and obtain a relationship between porosity and the ratio RF = Fv/Fg, where Fg is gravity. An empirical formula used in the previous study [1],
p=p0+(1-p0 )exp⁡(-mRF^(-n)) (2)
is applied to fit the data, where p is porosity and p0, m and n are constants. We assume that p0 is 0.36. By substituting Eq. 1 to Eq. 2 we obtain
p=p0+(1-p0 )exp⁡{-m((AS^2)/(64πΩ^2 ρgr^2 ))^(-n) } (3)
Where ρ is particle density and g is gravitational acceleration. We found that previous data and our own measurement result were fit successfully by Eq.3 as shown in the left figure.

We then apply Eq. 3 to the conditions of small bodies’ surfaces to derive the relationship between particle radius and porosity for the several objects. For example, in the case of asteroid 25143 Itokawa, the range of porosity is expected between 0.55 and 0.8 for the surface area consisting of mm–cm in size.

References:
[1] Yu, A. B., et al., 2003. Powder Technol. 130. 70-76.
[2] Perko, H. A., et al., 2001. J. Geotech. Geoenviron. Eng. 127, 371-383.