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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115, E07004, doi:10.1029/2009JE003483, 2010

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Thermal conductivity measurements of particulate materials: 5. Effect of bulk density and particle shape Marsha A. Presley1 and Philip R. Christensen1 Received 3 August 2009; revised 2 February 2010; accepted 17 February 2010; published 7 July 2010.

[1] Thermal conductivities were measured with a line‐heat source for three particulate

materials with different particle shapes under low pressures of a carbon dioxide atmosphere and various bulk densities. Less than 2 mm kaolinite exhibited a general decrease in thermal conductivity with increasing bulk density. For the range of atmospheric pressures appropriate for Mars, a reduction in porosity of 24% decreased the thermal conductivity by 24%. Kaolinite manifests considerable anisotropy with respect to thermal conductivity. As the particles align the bulk thermal conductivity measured increasingly reflects the thermal conductivity of the short axis. When kyanite is crushed, it forms blady particles that will also tend to align with increasing bulk density. Without any intrinsic anisotropy, however, kyanite particles, like other particulates exhibit an increase in thermal conductivity with increasing bulk density. Under Martian atmospheric pressures, a reduction in porosity of 30% produces a 30% increase in thermal conductivity. Diatomaceous earth maintains a very low bulk density due to the highly irregular shape of the individual particles. A decrease in porosity of 17% produces an increase in thermal conductivity of 27%. The trends in thermal conductivity with bulk density, whether increasing or decreasing, are often not smooth. Whether oscillations in the trends presented in this paper and elsewhere have any physical significance or whether they are merely artifacts of the precision error is unclear. Clarification of this question may not be possible without higher‐precision measurements from future laboratories and further development of theoretical modeling. Citation: Presley, M. A., and P. R. Christensen (2010), Thermal conductivity measurements of particulate materials: 5. Effect of bulk density and particle shape, J. Geophys. Res., 115, E07004, doi:10.1029/2009JE003483.

1. Introduction [2] Prior thermal conductivity measurements (Paper 2 of this series: Presley and Christensen [1997b]) demonstrated that thermal conductivity exhibits a strong dependence on particle size over a wide range of atmospheric pressures (sp. 1–100 torr). Under a carbon dioxide atmosphere, this relationship can be expressed empirically as   ¼ C  P 0:6 d  0:11log ðP=K Þ

ð1Þ

where  is the thermal conductivity in W m−1K−1, P is atmospheric pressure in torr, d is the particle diameter in mm, and C and K are constants. When these units are used, C ≈ 0.0015 and K ≈ 8.1 × 104. [3] The size of particles comprising surficial materials on Mars may be estimated by using equation (1) in conjunction with thermal inertia derivations from the brightness temperatures obtained from either the Mars Odyssey Thermal Emission Imaging Spectrometer (THEMIS) [Fergason and 1 Mars Space Flight Facility, School of Earth and Space Exploration, Arizona State University, Tempe, Arizona, USA.

Copyright 2010 by the American Geophysical Union. 0148‐0227/10/2009JE003483

Christensen, 2003; Putzig et al., 2004; Fergason et al., 2006b], the Mars Global Surveyor Thermal Emission Spectrometer (TES) [Mellon et al., 2000; Putzig et al., 2005; Putzig and Mellon, 2007], the Viking Infrared Thermal Mapper [Kieffer et al., 1977; Christensen and Malin, 1988; Haberle and Jakosky, 1991], the Mariner 9 Infrared Radiometer [Kieffer et al., 1973], or the Miniature Thermal Emission Spectrometer (Mini TES) aboard both of the Mars Exploration Rovers (MER), Spirit and Opportunity [Fergason et al., 2006a]. These particle size estimates can then be used to facilitate interpretation of the depositional history and origin of surficial deposits [e.g., Kieffer et al., 1981; Presley and Arvidson, 1988; Edgett and Christensen, 1991; Christensen and Moore, 1992; Merényi et al., 1996; Mellon et al., 2000; Putzig et al., 2005; Fergason et al., 2006b]. [4] Particle sizes estimated in this manner agree well with particle sizes determined by other methods [Presley and Christensen 1997b; Fergason et al., 2006a]. Nevertheless, equation (1) was determined using spherical particles divided into very narrow particle size ranges, and other physical properties of surficial materials that control pore size and shape may also affect the thermal conductivity. These additional properties include mixtures of different particle sizes, bulk density, particle shape and cementation within the pores either by salt or by ice.

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1.1. Experiment Series [5] Paper 1 [Presley and Christensen, 1997a] reviewed the theory of thermal flux in particulate materials, reviewed various methods used to measure thermal conductivity, and compared and evaluated thermal conductivity measurements under Martian atmospheric conditions obtained by previous experimenters. The effect of particle size was investigated in Paper 2. Paper 3 of this series [Presley and Craddock, 2006] addressed the effect of mixtures of different particle sizes. The effect of bulk density in samples composed of spherical and rounded (granular) particles was addressed in Paper 4 [Presley and Christensen, 2010]. Granular particles tend to exhibit a small, linear increase in thermal conductivity with increasing bulk density. However, this increase is not always steady, and the study appeared to duplicate an undulation in the thermal conductivity versus bulk density data for highly porous material previously measured by Fountain and West [1970] under a vacuum. Everest et al. [1963] also showed distinct minima in thermal conductivity versus bulk density measurements. Highly porous perlite and colloidal silica both exhibited a decrease in thermal conductivity with decreasing porosity to a minimum around 95–96% porosity, followed by a subsequent increase [Everest et al., 1963]. Whether these localized minima in the thermal conductivity versus bulk density data are merely an artifact of measurement error, the result of competing thermal mechanisms, or due to shifting packing geometries, is unclear. Theoretical models currently do not adequately address the thermal properties of highly porous materials, particularly under the low atmospheric pressures appropriate for the Martian surface [e.g., Piqueux and Christensen, 2009]. [6] Particles that have not been rounded can form significantly different packing structures than rounded particles. In light of the results presented in Paper 4, this paper presents the results of a preliminary study that examined three distinctly different particle shapes for the purpose of examining further the thermal nature of highly porous materials and to identify trends worthy of further analysis. 1.2. Units [7] Thermal conductivity 1 W m1 K1 ¼ 2:390  103 cal cm1 s1 K1

[8] Pressure 1 torr ¼ 1:333  103 bar ¼ 1:316  103 atm ¼ 133:3 Pa

2. Experimental Procedure 2.1. Experimental Apparatus [9] A line‐heat source method was selected for this project due to its relative simplicity and proven reliability (see discussion in Paper 1). The sample holder employed in this laboratory follows Cremers’s [1971] design, with a rectangular 50 mm × 25 mm × 25 mm recess in the Teflon for holding the sample. A 0.003″ (40 AWG) platinum wire was suspended at the middle height of the sample holder, 7.5 mm above the floor of the cavity, and one millimeter off middle width, or 11.5 mm in from the edge of the cavity. Platinum leads were spot welded to the heating wire at either end of the

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cavity so that the resistance change over the length of the wire during each run could be measured. The resistivity dependence on temperature is well documented for platinum [e.g., McGee, 1988]. In this manner, the platinum wire is used both to heat the sample and to measure the resultant temperature rise. The experimental apparatus is described in detail in Paper 4. 2.2. Samples [10] Three samples were selected from minerals already available through the mineral library of Arizona State University’s Mars Space Flight Facility. The samples were chosen solely based on their unique shapes and not because they are expected to be present on the Martian surface. The three samples are (1) a disordered, poorly crystallized kaolinite, (KGa‐2) purchased from the Clay Minerals Society (origin: Warren County, Georgia; specific gravity ∼ 2.2; characteristics available at http://www.agry.purdue.edu/cjohnston/ sourceclays/PDF/KGa‐2.pdf). Eighty percent of the clay particles are less than 2 mm [Moll, 2001], and the average particle thickness is 42 nm [Sutheimer et al., 1999]; (2) a < 125 mm particle size fraction of crushed kyanite, purchased from Ward’s Natural Science (origin: Prince Edward’s County, Virginia; specific gravity ∼ 3.6 [Deer et al., 1982]); and (3) diatomaceous earth, purchased from KemTek. The specific gravity is ∼ 2.3, and 90% of the silica particles are between 20 and 70 mm in diameter. [11] The kyanite was crushed into small particle sizes in a Jaw Crusher. The resulting sample was sorted through brass sieves. The size fraction used in this study was the portion less than 125 mm. The kaolinite and the diatomaceous earth were examined “as is” from the manufacturer, with no further sample preparation. [12] Thermal conductivities of the kaolinite sample were measured at eight different bulk densities. The thermal conductivity of the < 125 mm kyanite sample was measured at seven different bulk densities. And thermal conductivities of the diatomaceous earth were measured at five different bulk densities. Table 1 lists each of the different bulk densities examined for each of the samples as well as the corresponding apparent porosities calculated from the specific gravity of each mineral and the respective bulk densities. Each of these samples formed highly porous sediments even in their most compact state. [13] In each case, the sample is sifted gently into the cavity of the sample holder from a height typically less than 1 cm above the cavity. The top of the sample is carefully leveled so that the volume of the sample can be equated to that of the cavity. The leveling will slightly increase the packing density at the very top of the sample, but will not affect the value of the overall bulk density within ∼20 kg m−3 or so, and also should not affect the packing of the sample in the vicinity of the heating wire, 1.75 cm below the surface of the sample. Inhomogeneities in the packing of the sample, where the sample is in contact with the heating wire, are expected to average out over the length of the wire. The sample holder is weighed before and after addition of the sample to determine the mass. The sample’s bulk density is then computed from the volume of the cavity (Paper 4). [14] Subsequent densities are prepared by dropping the sample holder from an approximate height of 1 cm. This is repeated until significant compaction is observed and addi-

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Table 1. Bulk Densities and Apparent Porosities of the Samples Used in This Study Samples

Particle Size Rangea,b (mm)

Bulk Density (kg m−3)

Apparent Porosityc

Kaolinite