Mar 25, 1997 - comprehensive suite of measurements of the dependence of thermal conductivity on particle size. The thermal conductivity increases with ...
JOURNAL
OF GEOPHYSICAL
RESEARCH, VOL. 102, NO. E3, PAGES 6551-6566, MARCH 25, 1997
Thermal conductivity measurements of particulate materials 2.
Results
Marsha A. Presley NASA Ames Research Center, Moffett Field, California
Philip R. Christensen Department of Geology, Arizona State University, Tempe
Abstract. A line-heatsourceapparatus wasassembled for thepurposeof measuring thermal conductivitiesof particulatesamplesunder low pressuresof a carbondioxide atmosphere.The primary resultof this projectis the compilationof the first comprehensive suiteof measurements of the dependenceof thermal conductivityon particlesize.The thermalconductivityincreaseswith increasingparticlesizeand atmosphericpressure.In particular,over the rangeof Martian atmosphericpressures, from 1 to 7 torr, the thermal conductivitywas found to be empiricallyrelated to approximatelythe squareroot of the particle diameterand the squareof the cubedroot of the atmosphericpressure.At the averagepressureof the Martian surface(6 torr) the thermal conductivityvariesfrom 0.011 W/m K, for particleslessthan 11/am in diameter, to 0.11 W/m K, for particles900/am in diameter.These resultsdiffer significantlyfrom the
particlesizedependence estimated for Marsfrompreviousmeasurements, exceptfor 200/am particles,whosethermal conductivityis 0.053 W/m K. The thermal conductivitiesof larger particlesare lower than the previousestimate,by 40% at 900/am, and the thermal
conductivities of smallerparticlesare higherthanthe previousestimate,by 60% at 11/am. Thesenewerestimates agreewithotherlinesof evidence fromMartianatmospheric and surficialprocesses and lead to improvedparticlesizeestimatesfor mostof the planet's surface.
1.
atmosphericpressureat a poin.tat a heighth abovethe datum, Po is the atmosphericpressureat the datum, and ß is the scale height,whichis 10.8km at 210 K [Zureket al., 1992].Previous
Introduction
1.1. Background
The particlesizeof surficialdepositscan provideimportant meaõurements of the thermalconductivity of particulatemacluesaboutthe historyof erosion,transport,and depositional terialshave shownthat particle sizehas a significanteffecton processes thatformedthedeposits. Particle sizemayalsobe a thermalconductivityunderthe rangeof atmosphericpressures significantkey in determiningthe originof thosedeposits.On that existsat the Martian surface[e.g., Wechs!er and Glaser, Mars,mostof thesurface iscovered withatleasta thincoasting1965;Wechsleret al., 1972;Smoluchowski, 1910].Thus a mean of depositionalmaterial that tendsto obscuredirect evidence particlediameterfor surficialunitson Mars had been approxof bedrock[e.g.,Kiefferet al., 1977;Amidsonet al., 1989;Chris- imated by applying thermal inei'tiadeterminations fromthe tensenand Moore, 1992]. Thus one of the primary goals of Mariner infrared radiometer and the Viking infrared thermal Martian studiesand exploration[e.g.,Haberle,1993;Albeeet mappertogetherwith the prior thermal conductivitymeasureal., 1992] has been to understandthe nature of the Martian ments[Kiefferet al., 1973,1981].•Severalstudies[e.g.,Kiefferet surficialmaterialsand to deciphertheir relationships with bed- al., 1981;Presley andAmidson, 1988;Edgett andChristensen, rock geology.The purposeof this project is to improve the 1991]havethenusedthisapproximation in orderto characabilityto determinethe particlesizesthat comprisethe surfi- terize the Martian surficial materials and infer their nature and cial unitsof Mars by providingthe first comprehensive set of possibleorigin. measurementsof the dependenceof thermal conductivityon A derived correspondenceof thermal inertia to a mean particlesizeunder a simulatedMartian atmosphere. particle diameterimpliesa certain homogeneityin the mateMartian atmosphericpressuresat the surfacevary signifi- rials analyzed.Yet the samplesusedin previousthermalconcantlywith elevation,season,and time of day. The range of ductivity measurements [Wechsle) andG!aser, 1965] werecharpressures on the surfacevariesfrom lessthan 1 torr on the top acterizedby wide rangesof particlesizeswith little information of OlympusMons,whichis 27 km abovethe datum,to approxaboutthe distributionof sizeswithin thoseranges.Interpretaimately 7 torr at the bottom of Hellas Basin,which is 4 km tion of thermal data in termsof particle sizeis further limited below the datum. The datum is defined as the elevation at by the lack of data on other propertiesthat affectthe thermal which the averagepressureis 4.6 torr (6.1 mbar) and the conductivity,suchas mixturesof differentparticlesizes,parti-
atmospheric pressure scalesasP = Poe-h/* whereP is the Copyright1997by the AmericanGeophysicalUnion.
Paper number 96JE03303. 0148-0227/97/96JE-03303509.00
cleshape, packing, andformation df saltprecipitates between grains. • To addresstheselimitationsand to providea more comprehensiveset of measurementsof thermal conductivitiesversus
6551
6552
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THERMAL
CONDUCTIVITY
MEASUREMENTS
Figure 1. The sampleholder.Within the sampleholderare the thermocouple(on the left) and the heating wire (on the right). Also picturedare the connectionsto each end of the thermocouple,to each end of the heatingwire, and to each heatingwire lead.
particlesize,a linear-heatsourceapparatuswas assembledto providesa summaryand overviewof the project and offers provide a means of measuringthe thermal conductivityof suggestions for future endeavors. particulatesamples.The first paper of this duo (Presleyand 1.2. Units Christensen[this issue],hereinafter referred to as Paper 1) Thermal conductivity providesthe backgroundfor this study.It reviewsthe various methods available for the measurement of thermal conductiv1 W/m K = 2.390 x 10-3 cal/cm s K ity, discusses the theoryof thermaltransferin particulatemaThermal inertia terials,andpresents,compares,and evaluatespreviousthermal conductivitymeasurements obtainedby other experimenters. 1 J/m2 S1/2K (IU) = 2.390x 10-5 cal/cm 2 S1/2K Section2 of this paper describesthe method used in this Pressure studyto determinethermal conductivityvalues.As discussed in Paper 1, severalpreviousinvestigatorsobtaineddata that did 1 torr = 1.333 x 10-3 bar = 1.316 x 10 -3 atm = 133.3 Pa not appearconsistentwith data obtainedby other investigators. Without more detailedknowledgeof their experimental setup,better evaluationof their data is difficult.With that in 2. Experimental Procedure mind, the technique,experimentalapparatus,samplepreparaThis sectiondescribesthe experimentaldesignand procetion, and data analysisusedin this projectare all discussed in duresthat were appliedin this project In the first part of this detail. The data are then presentedin section3. Section 4 sectionthe setupof the experimentalapparatusis described. reportsthe resultsof this studyand comparesthesenew data The secondpart of this sectiondescribesthe samplepreparato those obtainedpreviously.The implicationsof these new tion, and the third part describesthe procedurefor the data measurementsare discussedin section 5. Finally, section 6 analysis.
PRESLEY
2.1.
AND
CHRISTENSEN:
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MEASUREMENTS
6553
Experimental Apparatus
2.1.1. Sampleholder. As discussed in Paper 1, Cremers's [1970, 1971; Cremersand Birkebak, 1971; Cremersand Hsia, 1974] line-heat sourcemethod appearsto be a simple yet accurateprocedure,so a decisionwas made to emulate his experiments.Accordingly,the sampleholder (Figure 1) was designedlike that of Cremers[1971], and was also fabricated from Teflon, as Teflon is a goodthermal insulator.The cavity in which the samplewas placed is a rectangularhole with dimensions
Bell
•Jar
Sample Chamber
50 mm x 25 mm x 25 mm.
The heating wire diameter was selectedto be as small as possibleto minimize errors due to deviationfrom an "ideal" line-heat source(Paper 1). Wire of 0.001 inch (0.025 mm, 50 AWG) diameter is not ductile and tends to break easily.A 0.003-inch(0.075 mm, 40 AWG) diameter wire, however,is ductileenoughto manipulateand hasshownsufficientstrength to permit prolongedusage.
f-- •'amp'•e 'h
I
Electrical
Baseplate
,'11 II
I
II II
Feedthrough • • • To
The time restrictions for each run, based on the wire and
sample dimensions,have been discussedin Paper 1 and are illustrated in Figure 2. Calculationsindicate that a 90 s run time is sufficient,for the range of conductivitiesexpected,to reachthe very long-timeregime,without significanterror from either axialheat lossor sampleboundaryeffects.Theserestrictions on the length of a run are examinedfurther in the dis-
!
Vacuum
LN2 CO2
Figure 3. Schematicview of the experimentalapparatus.
by potential movementof the wire when it expands,the wire was springloaded at one end. Leadswere spotwelded to the heating wire at either end of the cavity in order to allow cussion of the data in section 3.3. measurement of the resistancechangeover the length of the The heatingwire wasstrungat the midheightof the sample holder, 7.5 mm above the floor of the cavity, and 1 mm off wire during each run. A copper-constantan (typeT) thermocoupleis setparallelto midwidth,or 11.5mm in from the edgeof the cavity.Platinum the heating wire at a distance of 2 mm. Originally,a differenwasselectedasthe compositionof the heatingwire becauseits tiated line-heat source method [Merrill,1968;Paper 1] wasalso resistivitychangewith temperatureis well documented[e.g., McGee, 1988].As is discussed in section3.2, the error due to goingto be employedand evaluated.Owingto technicalprobthe resistancechangeover the duration of a run is generally lems, however,this techniquehas not yet been set up. The retainedin the originalposition lessthan 10%. With very low conductivesamples,as encoun- thermocouplewasnonetheless tered in near vacuum conditions,the error becomesintolerable and was usedto verify that the sampleswere in thermal equi-
(muchgreaterthan 10%). Currentwasfed througheachendof the wire from a LambdaLQ413 constantcurrentpowersupply. Platinum has a thermal expansioncoefficientof 9 p•m/møC, at 25øC.Over a 10øCincreasein temperature,the wire would be expectedto expandby about4.5 p•m.To avoiderror caused
librium
before the start of each run and to measure the initial
temperaturesof the samples.At 2-mm distance,and only0.003 inch(0.075mm) diameter,the thermocouplewasnot expected to affectthe measurements from the heatingwire by more than a few percent[Merrill,!968]. 2.1.2. Samplechamber. The samplechamber(Figure 3) wasmachinedout of copper.The walls are hollow,asis the lid, to allow for flow of cold fluid. The bottom is insulated from the
I
I
I
I
I
I I I [
I
I
I
I
I
I I ,
104
).... 103
- --...'"
Sample boundary .......
Axial loss ßheat 1%
-.
' -- - /
effectsß 1%
' - - ... .
90 s run time
102 101 100 10'1 0.001
Long-time regime •• minimum
,
, , , l,,,[
,
, , , ,,,,
0.01
0.1
Thermal Conductivity(W/m K)
Figure 2. Illustration of the restrictionson experimentrun time with respect to thermal conductivity.The bottom line indicatesthe minimum time necessaryto reach the very long time regime.The top two linesindicatewhen the axialheat loss and the sampleboundaryeffects,respectively,will causeerrors greaterthan 1% in the thermal conductivitycalculation.
vacuumchamberbaseplate by three legs,1 inch (25 mm) in height, capped with Teflon feet. The sample chamber was designed to allow regulation of the sample temperature througheither the flow of cold fluid or the heat from heating tapes.The intent is to eventuallytake some of the measurements at an averageMartian temperature (-30øC), and to repeat the thermal conductivityversustemperaturemeasurementsof Fountainand West[1970]. 2.1.3. Vacuum chamber. The base plate of the vacuum chamber(Figure 3) is machinedout of 1 inch (25 mm) thick stainlesssteel. It is 18 inches(460 mm) in diameter and contains a concentric,19-mm-wide,2-mm-deepgrooveto accommodatethe neoprenegasketfitted to a 12 inch (305 mm outer diameter) x 12 inch(305 mm height)Nalgenevacuumjar. The base plate is fitted with five feedthroughs:(1) a Huntington IF-051 eight-tube feedthrough,through which the electrical wires are fed; the wires are those that connect to each end of
the heatingwire, to each of the two leads from the heating wire, and to eachend of the thermocouple,aswell asthe wires that connecteach end of the heatingtape to a variable transformer power supply;the wires are sealedin the tubesusinga
6554
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2.SK
THERMAL
+12V
CONDUCTIVITY
MEASUREMENTS
5OOK
_1 ADC1
J- 1.5K lOOK DACl
4.99K
+12V
lOOK
-
383
/
=
J-
I
lOOK -12V
49
ADCO
½•
DACO
7.5K
Figure 4. Schematicview of the electroniccircuitsthat composethe signalconditionerand voltageconverter. The voltagesare amplifiedand then offsetby an amountspecifiedby the operator,in order to take advantageof the full 10-V rangeof the analogto digitalconverter(ADC) board.The offsetrequestis made throughthe computer,andis sentthroughthe digitalto analogconverter(DAC) channels. The thermocouple is connectedto channel0, and the heatingwire is connectedto channel1. The voltagesare then sentto the ADC board through the DAC channels.
putty-likehigh-vacuum sealant;(2) a HuntingtonFT-189 dualconductorliquid nitrogenfeedthrough;(3) a port leadingto a pressurecontrol system;(4) a port leadingto a Varian type 0532/801thermocouplevacuumgaugefor the measurementof pressurevaluesbelow 0.1 torr; and (5) a port leading to a SargentWelch 1400 duo-sealvacuumpump. The baseplate sitson a square"ring" standconstructedout of 1 inch x 1 inch (25 x 25 mm) aluminumstruts.The ring stand,in turn, sitson four dampingpads to minimize the vibrationaleffectsof the vacuum pump on the packing of the sample. For safety, a vacuum guard is placed over the vacuum chamberwhen the chamberis holdinga vacuumor at low-pressureatmosphere. The air pumpedout of the chamberpassesthrougha HuntingtonCT-073 coaxialforelinetrap to removeanyparticulates before they are drawn into the vacuumpump and to curtail backstreamingof oil from the pump into the system.The exhaustport of the pump is fitted with a Balstontype 9955-12 filter to remove oil fumes.
A MKS Baratron type 122A absolutepressuretransducer measuresthe pressureto an accuracyof +_0.03torr within the vacuumchamberand transmitsthe informationto a MKS type 250C pressurecontroller.The pressurecontrollermanagesthe chamberpressurewith a MKS type 248A controlvalve,which regulatesthe flow of CO2 into the chamber. The flow rate balancesany leak rate and keeps the pressuresteadywithin _+0.1torr. When a vacuum is desired, the controller is shut off,
and only the valve to the vacuumpump is open. Leaks in the
systemlimit the vacuumachievable to only 10-2 torr. The Varian thermocouple vacuum gauge was calibrated on an
ultrahigh(10-8 torr) vacuumline andusedto setthe zero point on the pressurecontroller.
2.1.4. Electronics. The voltagesput out by the thermocoupleand the heatingwire are fed througha National InstrumentsLab-SE analogto digital(A/D) circuitboard,developed for usewith the MacintoshSE computer.Sincethe voltagesare very small, they are initially fed through a signalconditioner, which amplifiesand offsetsthe voltage signalsto take advantageof the full 10 V range(-5 V to 4.96 V) of the A/D board. Figure 4 is a schematicof the signalconditionercircuitry.The A/D board provides8-bit, or 0.039 V, resolution. 2.2.
Sample Preparation
Thermal conductivitymeasurements were performedon the sampleslisted in Table 1. Glassbeads,obtained from Jaygo, Inc., were usedin this first suiteof comprehensive studiesto
Table 1. ParticleSizesof GlassBeadsUsed in This Study Size Range,
Density,
vm
kg/m3
710-900 500-520 250-275 160-180 149-160 125-130 90-100 70-75 25-30 15.6-20 11-15.6 25 Ixm. The glassbeadswere initially separatedinto wide particlesizerangesusing8 inch(200 mm) Gilsonbrassmeshsieves.The differentsizefractionswere then collectedand separatedinto smallersize fractionsusing 12-mm nylon meshsieves.The nylon meshwas held in place betweentwo concentricplasticframes.So that looseparticles do not getbetweenthe two frames,a stripof electricaltapewas placed over the top where they come together.Initially, the nylonmeshwouldwear out quicklyowingto the impacton the edgesof the meshwhen the framesseparate,howeverslightly, and are slammedback togetherduring the Roto-Tap process. Duct tape was then usedto hold the entire stackof no more than four sievestogetherin order to minimize the impact on the nylon mesh.A woodenadapterwas constructedto fit the smallerplasticframesonto the Roto-Tap. After sieving,the glassbeadswere coatedwith smallerparticlesand dustpickedup throughoutthe preparationprocess. The sampleswere washedin one of two ways to remove as manycontaminants asreasonablypossible.For the largestpar-
CONDUCTIVITY
MEASUREMENTS
6555
Table 2. Compositionof GlassBeads Composition
wt %
SiO2 AI203 K20
67 1 7
BaO
6
B203
2
CaO
5
Na20 MgO
10 1
Compositionin weightpercent,as suppliedby Jaygo,Inc.
arate from the supernatantfluid. The height of thesesettling columns
is 0.16 m at the 50-mL
mark.
The graduatedcylinderswere thoroughlywashedwith soap and water, then rinsed with acetone before each use. The
acetoneremoveshardwater depositsand reducesthe tendency of the sample to adhere to the inside wall of the settling columns.The cylinderswere then allowed to air dry. If the cylindersare not completelydry before the sampleis initially ticlesizesandthesmallest particlesizes, 2-5 cm3of thesample added,the samplewill adhereto the insidewall of the settling were washed at a time by rinsingwith deionizedwater for column, even after water is added and vigorousshakingis 10-15 min on the appropriatesievefor the particlesizeof the applied.With careanddiscipline,the settlingprocedurecanbe basis,with 10 cylindersprosample.The samplewasthenovendried.For the intermediate performedon an assembly-line particlesizes, approximately 30-50cm3 at a timewereplaced cessed30 s apart. The three smallestsize fractionslisted in in a large beaker and rinsedvigorouslywith deionizedwater Table 1 were separatedin thismanner.More detailsare given [Hutchinson,1974]. The water was decanted,and the proce- in the work by Presley[1995]. dure repeateduntil the rinsewater was clear.Again, the sam2.3. Data Analysis pleswere ovendried. 2.2.2. Glass beads
(16)
Pressure (torr)
Figure 10. Plot of thermal conductivityversusatmospheric pressurefor (a) the 90- to 100-pom glassbeadscomparedto the sameplotsfor 94-pomquartz [Smoluchowski, 1910] and 44- to 104-pomgranite [Wechslerand Glaser,1965]. (b) The 250- to 275-poreglassbeads compared to the same plot for 254-pore quartz [Smoluchowski, 1910].
where t is time, R is the radial extent of the material, and a is
the diffusivityof the sample.If the time at whichthe instability first becomes visible is substituted for t, and a is assumed to be
2.4 x 10-8 m2/sfor the 25- to 30-pore glassbeadsat 8.0 torr, and 1.4 x 10-7 m2/sat atmospheric pressure, thenR is approximatelyequal to 2-3 mm. This result suggeststhat the
6562
Table
PRESLEY
3.
AND
Power Law Parameters
CHRISTENSEN:
THERMAL
for Particle Size
Dependence
CONDUCTIVITY
4.
4.1. •< = Ad •
Pressure, torr
A
B
0.5 1.0 2.0 3.0 4.0 5.0 6.0 8.0 10.0 12.0 15.0 20.0 30.0 40.0 60.0 80.0 100.0
0.00095 0.0013 0.0021 0.0029 0.0035 0.0042 0.0047 0.0056 0.0065 0.0075 0.0083 0.010 0.012 0.014 0.018 0.020 0.023
0.51 0.52 0.51 0.49 0.48 0.47 0.46 0.45 0.44 0.42 0.42 0.40 0.38 0.37 0.34 0.33 0.31
MEASUREMENTS
Results
Particle Size and Thermal Conductivity
The dependenceof thermalconductivity on particlesizeand pressureis illustratedin Figure 7, where thermal conductivity is plottedagainstpressurefor the variousparticlesizesamples. The relationshipof thermal conductivityand particle size is more clearlyevidentin Figure 8, however,where thermal conductivityis plottedagainstparticlesizefor variousatmospheric pressuresthat are encounteredon the Martian surface(0.5-8 tort). For eachpressurea linear relationshipbetweenthe log of the thermal conductivityg and the log of the particle diameter d is very well defined. This linear relationshipindicates that the dependenceof thermal conductivityon particle size
canbefit to a powerlawcurve,i.e.,g = Ad•, withintheerror of precision. The power law curvesin Figure 8 displaya regular dependenceon pressureaswell. This dependencecan be seenmore clearlywhen the parametersA andB are comparedover the full rangeof pressures studied(0.5-100 tort) (Table 3). These
valuesindicatethat A • 0.0015Pø'6 andB • -0.11 log P/81,000 tort. Thus the thermal conductivitycan be approximatelyrelated to particle diameter and pressureby the rela-
thermocoupledoesaffectthe temperaturebehaviorof the sample and thus contributeserror to the thermal conductivity measurement,despite assurances from Merrill [1968] that it doesnot. For most measurementstaken during the courseof this project, with the exceptionof those taken at ambient atmosphericpressure,and thosewith thermal conductivities higher than ---0.1W/m K, the very long time regime can be easily identified before the thermocoupleeffects are manifested, and the error should be less than 1%.
tion
t( = (Cpø'6)d (-o.•logP/K)
(17)
where ,c is thermal conductivity,P is pressure,d is particle diameter (in micrometers),and C and K are constants.C =
0.0015, andK • 8.1 x 104 torr, whenunitsof W/m K are used for thermal conductivityand the unit torr is used for pressure.Thermal conductivityalsodependson other factors, suchas the bulk densityof the material [Presleyand Christensen,1996a](also M. A. Presleyand P. R. Christensen,The effectof bulk density,particle shape,and sortingon the thermal conductivityof particulatematerialsunder Martian atmosphericpressures,submittedto Journalof GeophysicalResearch,1996;hereinafterreferredto as submittedpaper). This equationis valid for particulatematerialsthat have a medium well-packedbulk density(Table 1). At low pressures(0.5-8 torr), B = 0.5 (Table 3). The thermal conductivityis thereforeroughlyproportionalto the squareroot of the particle diameterat the Martian surface. Thisresultmakessensephysicallybecausethe area overwhich gasconductiontakesplacebetweenparticlesis proportionalto the squareof the particlediameter[Schotte,1960].At higher pressures,collisionsbetween gas moleculesplay an increasingly larger role in the transfer of thermal energy, and the dependenceon particle sizedecreases.
The linear part of the long-timedomain(i.e., the very long time domain)is easilyidentifiedat 0.5 torr (Figure 6c; > 15 s) and 8.0 torr (Figure 6d; 3-70 s) and somewhatdiscernibleat ambientatmosphericpressure(Figure6e; 2-16 s). At 0.01 torr (Figure 6a), however,the long-timedomainis dominatedby a near levelingof the temperature.This levelingoccursfor all samplesat 0.01 torr, and increasingthe lengthof the run does not alleviateit. The long-timedomainat 0.1 torr (Figure6b) is not aslevel asthat at 0.01 torr (Figure6a), but the slopeof the temperatureincreaseappearslower than what would be expected.For many samplesthe slopeat 0.1 torr is often more shallow than the slope at 0.5 torr. One problem that may contributeto this anomalousbehavioris the inabilityto assume constantpower. At very low atmosphericpressuresthe resistanceof the platinumwire nearlydoublesover the period of a run, which nearly doublesthe power.Becausethe assumption of constantpowerwith this experimentalsetupis clearlyinaccurateat thesepressures,and becausethe linear portion of the 4.2. Comparison With Previous Results The thermalconductivity versusparticlesizeat 6.0 mbar (4.5 long-timedomainis often poorlyor not defined,thermalconductivitiesare not presentedfor atmosphericpressuresless torr) previously estimatedbyKiefferet al. [1973,Figure11] has than 0.5 torr. commonlybeen usedto relate thermalconductivityto particle As discussed in Paper 1, the specificbehaviorof the curves size on the Martian surface.In Figure 12 the data for glass in Figure 6 is dependenton the experimentalsetup,aswell as beadsat 5.0 torr, aspresentedherein (Figure 80, is compared the conductivityof the sample,and may not appear the same to that curve.As can be seen,there are significantdifferences for other wires or other probe designsand compositions.For betweenthe two curves.The slopeof the curvederivedfrom the thermal conductivityprobe, which is another line-heat this studyis much shallowerthan that of the previouscurve. sourcemethodfor measuringthermal conductivities(see Pa- The two curves cross at 215 /xm, 0.053 W/m K. At larger per 1) and which has a much higher diameter,for example, particle sizesthe thermal conductivitiesare lower. For examthesedivisionsof the temperatureversusIn time curvetypically ple, for a particle size of 900 /•m the thermal conductivityis occur over minutes or hours, rather than seconds,and a much approximately40% lower than that previouslyestimated.At are higher.For largersampleis necessarily requiredto avoidboundaryeffects. smallerparticlesizesthe thermalconductivities
PRESLEY
AND
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THERMAL
example,for a particle sizeof 11/•m, the thermal conductivity is approximately60% higherthan that previouslyestimated.If (17) is extrapolatedto muchlargerparticlesizes,asillustrated in Figure 14, the thermal conductivitymatchesthat of dense igneousrocks. This correspondenceappearsto support the power law relation. The primary reasonfor the discrepancyat higher thermal conductivitiesis that the previousestimatehad only one measurementabove 250 /•m to extrapolatefrom. This measurementwastakenfrom the data of Woodside andMessmer[1961], which are suspect,as discussedin Paper 1, sincethe thermal conductivities that Woodsideand Messmet[1961]obtainunder vacuumare an order of magnitudehigher than acceptedvalues, and sinceWoodside[1958] acknowlegedthat his thermal conductivityprobe producedvaluesthat are sometimeshigher than those obtained with reliable steadystate methods.The contrastin the lower conductivitypart of the curvesis probably due to the differencesin the particle shapeof the materials tested[Presley and Christensen, 1996a,submittedpaper, 1996]. The previousestimatewasbasedon thermal conductivitiesof crushedmaterial [Wechslerand Glaser, 1965]. The angular shapeof thosegrainswould createa looser,lessdensepacking of the material,and the lower densitywouldlower the thermal conductivity.The data in this study were taken from glass beads,whichtend to form more denselypackedsamples. The differencesbetweenthe two curveshave important implicationsfor the analysisof Martian thermal inertia data. Palluconiand Kieffer[1981]estimatedthat the thermal inertias
for the Martiansurfacerangein valuefrom 60 J/m2 s1/2K (abbreviatedIU for inertia units) to 630 IU, with peak occurrencesat 100 and 270 IU. Thermal conductivityis estimated from thermal inertia by assumingthat the productof density
andspecific heatis 1.0x 106J/m3 K [Neugebauer etal., 1971]. From the previous thermal conductivityversusparticle size estimate[Kiefferet al., 1973],thesevaluescorrespondto 10/•m for 60 IU, 30 /•m for 100 IU, and 295 /•m for 270 IU. The valuesobtainedfrom this study,however,indicatethe correspondenceis
