The effect of bulk density and particle size sorting on the thermal ...

JOURNAL

OF GEOPHYSICAL

RESEARCH,

VOL. 102, NO. E4, PAGES 9221-9229, APRIL 25, 1997

The effect of bulk density and particle size sorting on the thermal conductivity of particulate materials under Martian atmospheric pressures Marsha A. Presley NASA Ames Research Center, Moffett Field, California

Philip R. Christensen Departmentof Geology,Arizona State University,Tempe

Abstract. Preliminarymeasurementsof the effectsof bulk densityand particle size sortingon the thermal conductivityof particulatematerialsunder Martian atmospheric pressuresare presentedand discussed. Concoidallyfracturedparticlestend to form more looselypacked,lessdensesedimentarystructures,due to irregularitiesin the shapeof the particles,than thoseformedby sphericalparticlesof similarsize.The lower bulk density of the angular-shaped particlesleadsto a lower thermal conductivityof the sample.If the densitydifferenceis assumedto be the sole factor that controlsthe differencein conductivityin this case,then the thermal conductivityof 25-30/•m sizeparticlesappears to increaselinearly with increasingbulk densityand with the squareroot of the atmosphericpressure.Initial experimentsappearto indicatethat the bulk thermal conductivityof a particulatematerial containinga mixtureof differentparticlesizesis the sameas the thermal conductivitythat a material of similar bulk densitywould have if it were composedentirelyof the largestparticlesizecontainedwithin that material. More studiesare, however,necessaryto confirmthis apparenttrend. 1.

particles and acrossinterparticle contacts,•s; and thermal radiation within the particles,acrossthe void spacesbetween particle surfaces,and between void spaces,•r:

Introduction

Previousexperiments[Presley and Christensen, 1997b](hereafter referred to asPaper 2) haveshownthat over a wide range K : Keff: K•7q- Ksq- Kr (2) of atmospheric pressures (1-100 tort) the thermalconductivity of particulate materials is empirically related to the particle Particle-particlecontactsbehavelike thermal capacitors,which size of the material and the atmosphericpressureof carbon causeheat to build up around the contactsand significantly dioxide by reducethe contribution from •s. Because •a >> •, the compositionof the particlesdoesnot effectthe bulk thermal con•: : (ceo.6)d-O. ll ,og (?/g) (1) ductivity of the particulate sample [Wechsleret al., 1972]. Smoluchowski [1910] and Watson[1964] demonstratedexperwhere • is the thermal conductivityin W/(m K), P is atmoimentally that even under a vacuum the composition of the sphericpressurein torr, d is the particle diameter in/•m, and particlesis not a significantfactor. C and K are constants. When these units are used, C •

0.0015 andK • 8.1 x 104 torr.Equation(1) maybeusedto

The contribution fromradiation,•r, is proportional to T3,

Surveyorthermal emissionspectrometer,the Viking infrared thermalmapper,and the Mariner 9 infraredradiometer[Paper 2; Kiefferet al., 1973].Theseparticlesizeestimatescan then be

atureslessthan300K, however, •a >> •r, evenat atmospheric

estimatethe particle size of surficialunits on Mars through where T is temperature [Watson,1964], and for high temperatures,radiation can becomea significantfactor. For temperthermal inertia determinations obtained from the Mars Global pressuresas low as 1 torr, for most particulate materials. Schotte[1960] establishedthat the radiative factor becomes significantfor 1 mm particles above 400øC, and for 100 /•m used to characterize the surficial units and infer their nature and possibleorigin, as severalstudieshave done with previous particlesabove 1500øC,and relates that theselimits will hold estimates[e.g.,Kiefferet al., 1981;Presleyand Arvidson,1988; for nonsphericalparticle shapes,as well as for sphericalparticles. The transfer of thermal energy due to collisionsof gas Edgettand Christensen, 1991]. molecules, •a, is thereforethe predominant mechanism of Particle size and atmosphericpressureare not the only parameters that can affect the thermal conductivityof Martian thermal conductionin porous sedimentsnot under vacuum surficialdeposits,however.The effectivethermal conductivity [Wechsleret al., 1972]. Table 1 liststhe mean free path of carbon dioxide gasmolof a sampleconsistsof contributionsfrom three primary heat ecules for a few combinationsof Martian atmosphericprestransfermechanisms:conductionby the gaspresentin the void sure, which rangesfrom _

10'4 E

glass beads(1700kg/m3).

o 10-2 O

v

o

ferencesin thermal conductivitiesbetween the quartz, the

25-30/zmglassbeads,andthe 15.6-20/zmglassbeads.However,the bulkdensityof the crushedquartzis alsolowerthan

thatof the 11-15.6/zmglass beads(900kg/m3),andyetthe

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10'3

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i iiiiiii

0.01

i

0.1

Thesecomparisons implythatparticleshapeinfluences the thermalconductivity primarilybyaffecting thebulkdensity and thatsignificant differences in bulkdensity influence thethermal conductivity. A reduction in bulkdensity by nearly50%

, 1,11,11

,

, 1111111

1

10

I

,

I

,

Ill

100

Pressure(torr)

thermalconductivities of the quartz are slightlyhigherthan thoseof the 11-15.6/zm glassbeads.

10'5

b

Figure8. Plot of thermalconductivity versusatmospheric pressure for (a) the90-100/zmglass beadscompared to the sameplotsfor 94/zmquartz[Smoluchowski, 1910]and44-104 /zmgranite[Wechsler and Glaser,1965]and(b) the 250-275 /zmglassbeadscompared to the sameplotfor 254/zmquartz

1910]. will decreasethe thermalconductivityby 16 _+5%. Yet the [Smoluchowski, lowerbulk densityof the 25-30 /zm crushedquartz,as com-

paredto thatof the11-15.6/zmglass beads, indicates thatthe sizeof the particlesis alsoan importantfactor. Theseresultsare expected. A lowerbulkdensityindicatesa

will be reducedbecauseof the longerthermaltransferdistance

between particles. Largerparticles will havea largerthermal transfer area, for similar packing, than smallerparticles,and largerporesizewithinthe sample. The thermalconductivity consequently, the thermalconductivity will be higher.These effectsnecessarilywould compete.

If bulk densityis assumed to be the primaryfactorthat

10ø

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i

i i i iii

I

i

i

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i

controls the differencesin thermal conductivitiesbetween the

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10'a

•, 10-1 .... .•,

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10'4

: •

-

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O •

10.2 10'5

glassbeadsandthecrushed quartzof the sameparticlesize, thena quantitative relationship between thermalconductivity and densitymaybe derived(Figure9). Sucha comparison demonstrates a nearlylinearrelationship of the thermalconductivity withbulkdensity. Thislinearrelationship holdsover

thefullrangeof atmospheric pressures studied(0.5-100torr), notjustthethreepressures illustrated. For25-30/zmparticles, at an averageMartianpressure of 6 torr,thisrelationship can be expressedas

• = 0.01 W/(mK) + [6.4 x 10-6 m4/(s 3K)]p 10'3 0.1

I

I

I I I Illl

I

1

I

I , t t•ll

10

Pressure(torr)

I

I

I I III

(6)

=

100

where • is the thermalconductivity in W/(m K) and p is the

densityof the samplein kg/m 3. More dataobviously are needed to confirm this trend as well as to establish a more

Figure7. Plot of thermalconductivity versusatmospheric betweenthermalconductivity, bulkdenpressure for