Fachbereich 14 - Geowissenschaften
Institut für Planetologie
Planetenphysik

Materialeigenschaften von porösen Stoffen unter Weltraumbedingungen

Part 1

Part of the lander payload for the comet rendezvous mission Rosetta is the thermal probe MUPUS (Multi-Purpose Sensors for Surface and subsurface Science). In this paper we discuss the relationship of the expected MUPUS data to structural and textural parameters of the near-surface layers of the cometary nucleus. Such properties could be crucial parameters concerning the formation and evolution of the nucleus. Thus, we calculate the thermal conductivity of a porous material in terms of microstructural parameters, using a geometrical model with a solid matrix, a surrounding pore space and a distinct contact area between different particles. We include the possibility that a significant amount of heat may be transported by pore filling vapour in addition to heat conducted via the matrix. Furthermore, we consider that the heat is transmitted through only a fraction of the grains and these are organized into a chain-like structure. These chains - and not the single grains - should be regarded as the basic unit of structure. Applying our model to measured thermal conductivities of porous water ice, we interpret the material in terms of microparameters and estimate the effective size of the contact area and the effective pore radius. The results are in good agreement with our knowledge of the prepared samples. Contrary, we can also show that popular models used in cometary reseach do not fit with laboratory data at all.

It is generally accepted that comets are made of frozen volatiles and dust forming a very low-density and high-porosity body. While the porosity of the material is certainly an important parameter affecting the mechanical and thermal behaviour, it is not always a reliable measure. For example, thermal conductivity and thermal diffusivity are strongly influenced by the microstructure of the material, i.e. the size, shape and spatial arrangement of particles and pores as well as the connection and cohesion between neighbouring particles. Especially in the case of frozen volatiles, the critical parameter controlling thermal conductivity is rather bonding--not so much porosity. This fact is well-known in glaciology and snow research, but often ignored in many thermal models describing the evolution of comets. Therefore it is our aim (1) to identify the important textural parameters determining the macroscopic behaviour of a porous material, namely the thermal conductivity; (2) to establish appropriate relationships and (3) to show the applicability of the derived formulae for the analysis and interpretation of the future MUPUS data. For this purpose, we calculate the thermal conductivity by means of a simple geometrical model and apply it to porous water ice samples, for which the thermal conductivity was measured in laboratory experiments. In order to be applicable to such volatile materials, the original model (Keller et al, 1999) has to be modified and extended, as described in the following sections. In particular within such porous volatiles heat transport by vapour in the pores caused by sublimation and condensation processes has to be incorporated into the model.

We could show that a thermal probe, like MUPUS-Pen for the comet rendezvous mission Rosetta, should be able to answer some important questions concerning the near-surface layers of a cometary nucleus. It may be used to estimate, at least roughly, structural and textural parameters by comparing the data outcome of the experiment ensemble mounted on the Rosetta lander with the results of microstructural models, as the one described here. Since the main purpose of the Rosetta mission is the question of formation and evolution of the nucleus, microstructural parameters are probably crucial properties.

Note, however, that clear conceptions of the material in question are essential. We discussed some basic ideas concerning a particulate porous medium, e.g. particles with variable texture, heat transfer across a restricted contact area between individual grains, and a chain-like particle structure which might be expected from a low-density material as snow. Of course, applying all these aspects to the interpretation of the forthcoming MUPUS data we must always have in mind that we limited ourselves to single-component porous water ice so far and our conclusions are only applicable to it.

Due to solar radiation, the upper part of the nucleus should be layered and differentiated, but the deeper interior is likely to be unchanged since the comet's formation and is probably a mixture of different ices - H₂O, CO₂, CO, maybe in an amorphous state - and dust grains, being both silicatic and organic. They may behave in a very complex way and differently from pure water ice. For simplicity, however, we focused ourselves to a single-component material because there is no concise knowledge yet about the appropriate modelling of a cometary nucleus and the relationship between material parameters as porosity and physical properties as thermal conductivity at all. We can only speculate at the time, taking the meagre results of laboratory experiments performed so far. It seems necessary to understand pure water ice first, before arguing about an ice/dust-mixture. Even in the case of a single-component material, we need better models as well as more sophisticated laboratory research. Any future research, in the laboratory or in situ, must include a closer look into the structure of the material in question (e.g. thin sections) to opt for alternative model approaches and improve our understanding.

Penetrators in general have gained interest as powerful yet cheap devices for planetary exploration. Penetrometry is already planned for the Netlander mission to Mars (experiment SPICE) and for the BepiColombo mission to Mercury. Even more interesting targets for a thermal probe would be the Galilean satellites. On Earth, penetrometry has been used for many years for soil science, civil engineering, and studies of snow and ice. Therefore, this could be another very promising application for a MUPUS-type probe.

Part 2

Heat conduction in porous media is - whenever gases or vapor are involved (e.g. in comets, on Mars) - a function of the pore size. Larger pores lead to a higher thermal conductivity than smaller pores. Natural loose granular materials like snow, regolith, soil and probably cometary ice is composed of grains of any size, from fractions of a micrometer to several cm large. The size distribution typically follows a power low: grains of each size interval contribute an equal fraction to the total volume. In such media, the overall thermal conductivity is closer to the thermal conductivity of a material composed of the smallest particles rather than the largest particles. Many thermal models about heat transfer and thermal evolution of comets use a uniform pore size of 100 micrometer to 1 mm, and, therefore, overestimate the heat transport by gas grossly. If a pore size spectrum with a power low size distribution is assumed, heat transport by gas or vapour is almost insignificant for the thermal evolution of comets.

The thermal conductivity in granular, porous media is a strong function of the size of the contacts between single grains (see part 1). If grains are connected with each other, either by sinter necks or by another material that cements grains together, like ice, salts or sediment minerals, the overall thermal conductivity as well as the hardness of the material are increased. Though this is theoretically well known, experimental evidence was scarce so far. Artificially produced samples of rice grains, cemented by wax, allow to study the cementation effect systematically in the laboratory. Samples with increasing wax content reveal - as expected - increasing hardness and thermal conductivity, if and only if the added wax is stirred into the rice at high temperatures, that allow the fluid wax to move to the contact points between single rice grains and attain a shape that minimizes surface energy: a nice sinter neck forms. If the wax is added as a solid powder at cool temperatures, there is no significant effect. A series of measurements with different samples shows furthermore that all samples with a different degree of cementation have very similar bulk densities, while the thermal conductivity varies significantly. This result is not unexpected, but in contrast to the frequently used assumption that the thermal conductiviy would increase with density (or decrease with porosity).

Beteiligte Wissenschaftler:

Prof. Dr. Tilman Spohn, Dipl. Geophys. Tom Keller, Dr. Karsten Seiferlin

Veröffentlichungen:

Seiferlin, K., Kömle, N. I., Kargl, G. and Spohn, T.: Line Heat-Source Measurements of the Thermal Conductivity of Porous H2O Ice, CO2 Ice and Mineral Powders under Space Conditions. Planet. Space Sci. 44(7), 691-704, 1996.

Seiferlin, K., M. Banaskiewicz, T. Spohn, N. Kömle, And G. Kargl: Line heat source measurements of the thermal conductivity of comet analogue material: Revisited. COSPAR 31st Assembly Abstracts, 63, 1996.

Seiferlin, K., M. Banaskiewicz, T. Spohn, N. Kömle, And G. Kargl: Measurement of the thermal properties of comet analogue material. Bull. Am. Astr. Soc. 28, 1087, 1996.

Seiferlin, K., T. Spohn, G. Kargl, N. Kömle, And M. Banaskiewicz: The thermal conductivity of comet analogue material. ACM 96 Abstract Book, 67, 1996.

Banaszkiewicz, M., Seiferlin, K., Spohn, T., Kargl, G. and Kömle, N.: A New Method for the Determination of Thermal Conductivity and Thermal Diffusivity from Linear Heat Source Measurements. Rev. Sci. Instrum. 68(11), 4184-4190, 1997.

KELLER, T., U. MOTSCHMANN, and L. ENGELHARD, 1999: Modelling the poroelasticity of rocks and ice. Geophysical Prospecting 47, 509-526.

SEIFERLIN, K., T. SPOHN, and A. HAGERMANN, 1999: Pore Size Effects on Heat Transport in Comets. Bull. Am. Astr. Soc. 31(4), 1096-1097.

Seiferlin, K., Spohn, T. and Hagermann, A.: The Influence of Grain Size Distributions on the Thermal Conductivity of Comet Nuclei. Presented at COSPAR 2000, Warsaw, 16-23 July 2000. Abstract in COSPAR 2000 Abstracts Volume.

KARGL, G., T. KELLER, and N. I. KÖMLE, 2001: Interpretation of Penetrometry Experiments. In: Kömle, Kargl, Ball, Lorenz (eds). Penetrometry in the Solar System. Österreichische Akademie der Wissenschaften Wien, 151-160.

KELLER, T. and T. SPOHN, 2002: Theoretical aspects and interpretation of thermal measurements concerning the subsurface investigation of a cometary nucleus, Planetary and Space Science, in press.

SEIFERLIN, K., T. SPOHN, and A. HAGERMANN, 2000: Thermal conductivity of comet nuclei derived from grain size distribution. Geophysical Research Abstracts (on CDROM), 2, PS7.02.

KELLER, T., K. SEIFERLIN, and T. SPOHN, 2001: Microstructural Modelling and Cross-Property Analysis of Porous Materials. Geophysical Research Abstracts (on CDROM), 3, PS10.

Seiferlin, K., Kargl, G., Kömle, N., 2003: The Effect of Cementation on the Thermal Conductivity of Porous Media, Abstract EAE03-A-10748 in Geophys. Res. Abstracts 5, 2003. (EGS/AUG/EUG 2003)