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Thermal and mechanical properties of evacuated powders
lYlmmal
and Mechanical
of Evacuated Powi!erS+:
Properties
A. E. WECHSLER
(Received
SUMMARY This paper swnmarkes the e$ects of enviromnentul and intrinsic powder parameters on the thermal and mechanical properties of euaczated powders. Thermal wnaktkity and d.iiuskCty are controlled primarily by the residual gas pressure, temperature, particle size and shah and mechanical load_ Bearing strength is less dependent on temperature and gas pressure but is strongly inzuenced by density, particle size and shape_
INTRODUCl-ION
The practical implications of the information on thermal and mechanical properties of evacuated powders are significant in many technical areas: heat transfer at high and low temperatures, insulation development, food processing, chemical processing, particle separation, etc. The objectives of this paper are to summ arixethefactorsresponsible for the thermal and mechanical behavior of evacuated powders, to describe the effects of environmental and intrinsic powder parameters on thermal and mechanical properties, and to show the relationships between thermal and mechanical properties of evacuated powders. The forthcoming manned lunar landing and the recent Surveyor experiments have created the desire within the scientik community to have a better understanding of the thermal and mechanical properties of evacuated powders. Wesselink’ was one ofthe lirst to demonstrate that the temperature variation of the lunar surface, as measured from the earth by inkared radiation, could be related to the thermal properties of the surface material_ Subsequently. many investigators2~3 have used experimental data on lunar surface temperature
June
IO, 1969)
variation and laboratory data on the thermal properties of evacuated particulate materials to estimate the nature of the lunar surface. ie-, the particle size, distribution and even composition. The prediction based upon thermal analyses, that the lunar surface layer is composed of somewhat cohesive particles in the size range of 5 to 100 microns, seems to be confirmed by the photographs and mechanical experiments of the Slurveyor spacecraft The bearing strength of the iunar surface layer was also of great interest to the spacecraft designer. Studies have been conductedJ*s of the mechanical properties and the similarities between thermal and mechanical behavior of particulate materials in a vacuum environment. Much of the data obtained in these programs have also been confirmed by experimental measurements on the moon. This impetus provided by the space program has been instrumental in forwarding our understanding of the behavior of powders. THERMALPROPERTiEs
OF EVACUATED
F’OW~ERS
Mechanisms of heat transfZr There are three basic mechanisms of heat transfer in an evacuated powderanduction by the residual gas in the powder, solid conduction witbin particles and across the interpanicle contact areas, and thermal radiation within particles, across the void spaces between particle surfaces, and between void spaces themselVeS
Gas condrrction.In a powder at room temperature and atmospheric pressure, most of the heat is transferred by conduction within rhe gas filling the void spaces between the particles. The effects of gas pressure on gaseous conduction within a powder are well known6-’ Over a wide range of pressures, the thermal conductivity of the gas (and hence the powder) is independent of pressure because the mean free path varies inve-rsely with the pressure andthegasdensityvariesdirectIywiththepressure; the product of mean free path and density deter-
163
A.EWECHSLEft
mines the gas conductivity_When the gas pressure is reduced to the point where the mean free path within the gas is greater than the interparticle spacing, further reduction in gas pressure does not change the effective free path of the gas. Then the thermal conductivity of the gas and the powder is directly proportional to gas pressure.The pressure at which thermal conductivity becomes proportional to the gas pressure (sometimes called the breakaway pressure) increases as the oarticle size decreases Equations giving the relationship between gas pressure,particlesize, and thermal conductivity are available in the literature8-g.For powders with particle size from 1 to 200 k gas conduction within the powder becomes a negligible heat transfer mechanism below about 10-r torr, Solid conduction. In an evacuated powder, solid conduction becomes an important but not well understood heat transfer mechanism Heat is transferredwithintheindividual particlesby phonon conduction, electron conduction, or by thermal radiation, depending upon the powder type These processes are the same as in the bulk solid and can be explained and examined by conventional heat transfer theory and measurements. Heat transfer at the particle interfaces across contact points is difficult to explain and to examine analytically or experimentally. The particle size, shape, composition, density or degree of compaction, and mechanical loading affect the number and the nature of the contact points. Although studies of contact conduction acrass macroscopic contacts have been very successful, it has been difficult to apply these results to a complex powder system. The effects of interparticle for ces-electrostatic, Vsn der Waals, or chemical adhesion-on interparticle contact area may exceed those due to particle shape or mechanical loading. Empirical equations describing contact conduction in the literature4*ro may be valid only for certain selected materials_ As a result it is not possible to predict adequately the heat transfer by solid conduction in powders. However, several general conclusions concerning solid conduction heat transfer can be made: (1) The solid conduction heat transfer in powders composed of inherently high conductivity materials (e-g., metals) will be only slightly higher than in powders composed of low conductivity materials (e-g_, glasses). It is well confirmed by experiment that evacuated powders of many types have nearly the same thermal conductivity at comparable temperature conditions6. (2) The greater the density or
mechanical loading of the powder the greater the solid conduction contribution to heat transfer.This is caused by increased number and area of contacts_ (3) Under high vacuum conditions, where clean surfaces exist, there does not appear to be a great increasein solid conduction in non-metallic powders due tc vacuum adhesion ; in metals vacuum adhesion can result in higher contact conduction. Only few experimental measurements have been made which demonstrate these results. Thennalrudiation.Thermalradiationisthesecond important heat transfer mechanism in evacuated powders. If the materialscomprising the powder are opaque to thermal radiation in the wavelength region of interest (usually 1 to 50 microns for powders at temperatures between 100 and lObOoK), radiation transport within the individual grains will be small. However, radiation between particle surfaces will stilI be important The more dense the powder, and the smaller the void spaces, the smaller the radiation heat transfer between particles_ The presence of radiation reflecting Oi scattering particles also reduces the radiation heat transfer contribution. Empirical and theoretical relations have been derived to predict radiative thermal transport in powders’ 1*8.12_ In general, radiation heat transfer in an evacuated powder increaseswith temperature, normally with the third power of the absolute temperature. The magnitude of the radiation contribution can often be. predicted to within a factor of two if the particle size, composition, and optical properties are known_ The eflects of environmental and powder parameters on thermal proper&s Several examples are given below to demonstrate
the effectsof environmental and powder parameters on thermal properties of evacuated powders. Figure 1 shows the effect of gas pressure on the thermal conductivity of pumice powder”_ At pressuresbelow 10m2 torr the thermal conductivity is independent of gas pressure. The powder with largersize particleshas a lower break-away pressure than the smaller size powder. There is little effect of particle size on thermal conductivity at low gas pressures. This may be caused by the variation in solid conduction and radiation contributions as described below. Figure 2 shows the effect of temperature on the thermal conductivity of evacuated glass beads_ The measurements were performed at gas pressures less than 10e4 torr so that gas conduction is negligible.
PROPERTIES
OF EVACUATED
rial made of amorphous parkks
sire range A
0-44~
0
44-104
0
l---i49
p P Gas
10-G
Fig
m-exxn-e
10-2
1. Thermal conductSty
Ctorr>
1
10’
760
of pumice po=dcr-(Wcchsla
and
Glascr”). Tke thermal conductivity of each material increases
with temperature_ The equations of the lines representing the data have the form: k=A+BT3
(1)
where k is the effective thermal conductivity, A represents the solid conduction term and BT3 represents the contribution of thermal radiation. Table 1 shows the values of these terms for the glass beads and other materials. At low temperatures for most non-metallic materia!s solid wnduction is the most important heat transfer mechanism; at h’gh temperatures radiation is most important- As the particle size increases the solid conduction term decreases and the radiation term increases. The solid conduction term is higher in a material which is composed of crystalline particles such as quartz (high thermal conductivity in bulk) than in a mate-
150
200
165
F’OWDERS
250 Temperature
300
350
400
(‘IO
Fig_ 2 Efktive thermal conductivity of glass beds and quartz powder_ 0. MicroLsxds 44-62 jt. p= 1.42 gkm’ (Wechslu and Simon”); A, quartzpowder < 10 /.a,p= LOO s/cm3 (Wechskr and Sin”).
such as glass. The
radiation contribution to heat transfer is greater m a more transparent powder, &g_, glass or quartz, than in an opaque powder such as basalt From a comparison of the results for spherical glass powders and irregularly shaped pumice or basalt powders, the solid conduction contribution does riot seem to be greatly affected by particle sha? The density and porosity of the materials described in Table 1 varied from 0.82 to 1.6 g/cm3 and O-40 to 0.70 respectively_ No definitive trends of thermal conductivity with density or porosity have been found. However, for consolidated materials, such as sandstone or fused foams, thermal conductivity is often directly proportional to the fraction of solid present. Figure 3 shows the effects of mechanical load on thermal conductivity of evacuated microbeads14_ Measurements were made using 177-210 p diameter glass beads at 5.5 x lo-’ torr ,m pressure and room temperature The thermal conductivity increases with the s power of the applied load Empirical equations based on Hetian loading of orderly spheres4 indicated a 3 power relationship should be obtained if solid conduction were the only heat transfer mechanism_ Little data are available in the literature on the effects of loading; however, a significant variation of heat conduction with depth in a packed bed can occur_ MECFSAMCAL
PROPERTIES
OF EVACUATED
POWDERS
The requirements for soft landing the Surveyor and future manned spacecraft on the moon have provided the impetus for experimental and analytical studies of the static and dynamic properties of evacuated powders_ Principal emphasis has been placed upon estimating or measuring static bearing
-
5
091
! 1
. . . . . . ..
. . ..
10
..I.
.
100 Pen
*
.
-
.
I 1000
rPsig1
Fig_ 3_ Vacuum conductivity variation x=&.I cxrcmal loading. 70/80 mesh microbeads; 0. pressure increasing; l . pressure dsrcasing
166
SOM condvcrion c0ntnbut10n lmicro w/cm ‘C )
Radmtice cont~mion hjcm YI x 10’3 x I-3)
Rk-f:
300°K
400°K
i-8 1.7 13 72 37.0
42 4.1 3.1 17-O 880
10 I1 10 10 10
GIass beads <37 is-73 Ss-I25 250-350
Quartz < 10
63 3.0 34 85 13.0
95
47 7-O 3’ 095
44-62
052
051 039 21 II.0
pander
Pumice poader lo-37 44-74 Basalt pmder lo-37 4+74
3.0 42
0 10
33.5
0.10
033 035
077 OS0
11 10
51 25
31 36
O-49 1.1
1.7 38
39 9.1
11 11
0.58 21
005
0.15
028
O-94
0.34 22
11 11
50
as-74
i ‘l-l.6 61
x 103/T
stren,g@, establishing the effects of vacuum on bearing strength and evaluating methods of failure for powder systems. Mechanisms for mechanical failure The mechanical properties of evacuated powders, with specific application to the lunar environment, have been examined in terms of classical soil
mechanisms15*16 and in terms of models depicting very low-density high-porosity cohesive soils4_ The bearing strength of a particulate material denends upon the particIe cohesion and the internal friction between the particle grains Most particu!ate materiak of low porosity under atmospheric pressure conditions fail predominantly in lateral shear, in which intergramuar friction along the failure plane provides the major resistance against the applied stresses For such a cohesiveless material the bearing strength is proportional to the density of the particulate material, or the packing factor, the characteristic dimension of the applied load, and the at&e of internal friction of the particles. In a hign vacuum environment it may be anticipated that the intergranuk friction wouId increase and also that the particles may be cohesive, thus significantly increasing the bearing strength. In a lowdensity, high-porosity particulate material, the failure mode may be characterized by collapse and compression of the material directly beneath the load and the failure is caused by local or vertical
shear- The bearing strength for such a material is provided by the force necessaq to shear the material in the vertical plane around the load perimeter as well as the force n ecessaq to compact the underlying material. An analysis of low density materials4 rest&s in a relation between bearing strength, initial and compressed porosity of the material, and the interparticle adhesion forces. The bearing strength is dependent on porosity, the characteristic dimension of the Ioad, and the amount of compression, and is strongly influenced by the inter-particle adhesion. Laboratory
measuremenls
Laboratory measurements of bearing strength of particulate materials, primarily silicates, have provided data which seem to be dependent upon the particle tYPe, vacuum treatmenf method of preparation, and test procedure. Efict of gas pressure Laboratory measurements have been made at atmospheric pressure, under high vacuum (1O-5-1O-6 torr) and ultra-high vacuum (10-9-lo-‘c torr). Bemett ef CL” examined the bearing strength of basalt powders of various particle sizes in air at atmospheric pressure and at 10m5 tom They found only minor cliffcrcnccs between resuhs at vacuum and atmospheric pressure. At low packing factors the powders in air had bearing strengths 50% less than in vacuum and at high packing factors bearing strengths were slightly higherinair@aninvacuumBearingstrength
PROPERTIES OF EVACUATED POWDERS
values range frcm about 0.1 to 9 kg/cm2 (l-4-130 psi.) depending upon the packing factor_ Measurements d the bearing strength of freshly sifted silica and alumina in air’ resulted in bearing capacity of from 2 to 30 g/cm’ (0.03-O-4 p.s.i.). Thcsc materials were of very low density_ The cohesion estimated from these measurements was about 500 dynes/cm’. Salisbury et CZI_‘~and Vey and Nelson’g report cohesion of from 750 to 20,000 dynes/cm’ for finely divided silica and silicate powders at pressures of lo-lo tom It must be surmised that these powders are well outgassed and have clean surfaces resulting in greater cohesion Such a material could have a bearing strength of 2500 g/cm2 (30 psi.) on the basis of cohesion effects alone, even if internal friction did not increase in vacuum Thus, the existing data indicate that for fine powders at low densities and Packing factors, ultra-high vacuum increases bearing capacity, but at higher densities ultra-high vacuum has less of an effect on bearing strength_ Many qualitative measurements have been made on the cohesion of particles prepared and treated in high vacuum; more quantitative measures of static and dynamic mechanical properties are needed. EBct of dswity or packing factor_ Most studies of the static bearing have shown increasing static bearing strength with increasing density. Figure 4 presents some results for powders in air and vacuum as well as characteristic curves based upon theoretical analyses and calculations. Curves 1 and 2 are~best fit curves obtained by Halajia# using the fluff (low density) and cohesionless soil models. There is some region of overlap or transition at solid fractions near 040. Region 3 is the range of data obtained by Bemett et uL” for a variety of sizes of basalt at both atmospheric pressure and at lo-’ torr. It is interesting to note that the data obtained from the landing of Surveyor V agrees well with terrestrial laboratory datazO. Also, the photographic data fromRanger 7,8, and 9 have produced lower bo-ur& ofsurface bearing strength from about 10 to 55X) g/cm2. depending upon bearing width, and densities of 06-l g/cm3 near the surfaa~?~_ This region is in general agreement with the data presented in Fig 4. Thus, the static bearing strength is a strong function of the density or packing factor of the particulate material. A change of over 100 in the bearing strength is not uncommon when the fraction of solid is changed from 0.2 to 0.6. Other fizctors 4ffecting beakg strength In addition to gas pressure and density- factors such as temperature, particle shape, and size distribution
167
Fig 4. Mass be&g suen_mhof pouderx I. Best iit 10% densir? fluff,compression depth equal plate dtamcta (HalajzmL): : bcsr finsouls, 3 in_ plate diaxn @hk+ni); 3, basalt pondc;. 154)zci 35 mesh, in air and vacuum (Bemett ez ~2~“) 4. siha ponder m air (Jaff~e’~); 5. Surxqor I_ interpretation(ChrisrexxenETnl_=q; data’9 . Survq or V simulation
may affect bearing strength There are no definitive data on the effect of temperature on bearing strength of evacuated powders. It is known that the bulk moduli of many non-metallic materials vary m-ith temperature and it is possible that the interparticle friction could change at low temperatures_ However_ more laboratory data arc needed to establish these effects Particle shape and size distribution may hare a significaut effect on bearing strength_ Particle interlocking, especially for higher density materials, may greatly enhance interparticle friction and cohesion resulting in increased bearing strength Most theories and correlations of particle strength are based on relatively uniform round particles and are not valid for platelets or elongated grains Little effort has been devoted to the study of the behavior of irregularly shaped particles in vacuum Perhaps. as a better understanding of thebehavior of particulates in air is evolved, extrapolation to vacuum conditions can be made_
168
A.EWECHSLER
RELATlON
Tl-mwAL
BEnvEEN PFtOPERm
AND
OF EVACUA~
MECHANICAL
P0WDERS
At first thought_ it might be expected that a strong correlation would be found between the thermal properties (e-97 thermal conductivity) and mechanical properties (e_g_beariug strength)of evacuated particulatematerials Unfortunately, thiscorrelation is not
observed,
as illustrated
below.
A change in gas pressure in a powder from atmospheric to 10S4 torr may yield a decrease in thermal conductivity of from 20 to ?GO; a similar change in gas pressure will produce only a small change in static bearing strength_ In the pressure range from 10m4 to lo- lo torr, only small changes in thermal wnductivity are observed experimentally whereas significant increases in cohesion lead to similar changes in bearing strength. The thermal conductivity of many evacuatednonmetallic powders is independent of density or packing factor, as shown in Table 2 Figure 4 shows a variation of over lOCKI in bearing strength for the corresponding density or solid fraction range The difference in the thermal and mechanical behavior may be attributable to sever-a! factors: thermal conduction of evacuated powders is caused by radiative and solid conduction mechanisms Although the solid conduction contribution to heartransferinereaseswithinereasingdensity,the radiation contribution decreases with increasing density- The net effect is the independence of conductivity on density. The beariug strength is attributable to interparticle friction and cohesion, each of which cnn be expected to increase withan increase in den&y or packing factor. Despite the apparent lack of correlation between thermal and meehanieal properties of evacuated powders, it is not surprisingthat for a wnsohdated TABLE
2:
m
Ml?&Y&Z
CoUoidd siha PerI& Pnmiapoader Quartzpoh Basalt powder GlaSSbeads
Glaabcads Basalt powder
coxDucnvrry PowDensity
OF SVERAL
EVACUATED
Themaltxmhaidy at 3ooOK (won/cm OC x 10-5)
Refe
@/an’)
(106 (LO8 Q8 LO 1.3-1.4 1.42 l-4-1.7 Ll-1-8
1.8 21 12-I-4 32-35 l.Ch1.8 12 1.5 154
7 7 11 11 11 11 10 21
or siuteredevaccted material such as pumice, sandstone or sintered bea& it is observed that both the thermal conductivity and bearing or crushing strength increase with increased density. For these materials, the thermal conduction as well as the mechanical strength are related to the average area of the solid phase in the plane perpendicularto the heat flow or load. The results of the work described above illustrate the needs for and benefits to be derived from interdisciplinary studies of powders Thermal property measurementswhenwmbinedwithmechanicalproperty measurementscan lead to greaterinsight of-he behavior of powders under marrydifferenteuvironmental conditions. REFERENCES 1 A.J.W
-a~, Hat condnctlvity and nature of the lsurface matuial, E&L hrror~_ I=r. Nefh_. 10 (1948) 35L 2 J. C. Jm The smfaa tanpaature of the moon. AusfraIian J. Physv, 6 (1953) 10. 3 V. D. KROTIKOV AHD V. S. T~O~ISKII, Thermal conductivity ofhmarmataialfivmpr&semcasnrem mts of 1radioemission, &v&z Artron-AI, 7 (1963) 119_ 4 J. D. HAURAN, Con-elation of mazhanhl and thermal propatia of cxnata~cstrial materials. Fmal ZZepon, NASA Conrrpcr NASi?-20084. 1967. S L D. JAFFE. Bearing strength o: “Fairy castk” strndurrs. J. Gcophys Re, 70 (l%S) 62686 M. Slaox.ucnows~~, Sur la conductibihti cabrisque da corps pulvais&, wrll. ht. de rAaadcmie des Scide Cmcor;ie. A (1910) 129. on the thcr7 A.E\xxEY& P. E. Gwen AX= A. E W~cnea, mal condnctiv&y of powder insulations. XI Inrem. Congr. Rejiigerarkm. Avgust 1963. 8 W. ,w Thermal conductivity of packed beds. Am Insf_ Chem_ Ehgrs_ J, 6 (1960) 63. 9 R. G. Dmsrrr AFZVC S. EIAN, NACA Rrvmrh M-raw don RME 52cOS. 1952 10 K. Wxrsox~. Thermal condmtivity of selected silicate powden in vacuum from lSO-3XPK. Zhsis. CalX Iast ofTechnology. 1964. AhD 1. SIMON. Tbamd ccmd naivityand 11 A.E.Wm didatric constant of silicate mate&k, Frz Report under NASA tZmrracf NAS&m6.1966. 12J.C(3iw~S_W_Cm~~cnt~s_Radianthcattransfain pa&d beds, Am. Inrr. Cknx. hgrs_ J.. 9 (1963) 35. i3 kW_ ANDP.~PRSSUKC effecbonposmlated hmar mataials, z-, 4 (1965) 335. 14 J. ?SR, PasonaY Commmkation, Gulf Rcscazh and Dcvclopmalt Corp.. 1966. 15 I.. D_ Jm Stra& of lunar dust, J. Gwphys: iZa_, 70 (1%5) 6139. 16 L. D. JAFFE, L-surface strength. I-, 6 (1967) 7515. 17 EC~,R.S.SCOTT,L.D.JAFFE,EP.FRINKAND H.EMunqBearingc&pacityofsim~lmurnafacn in vm, AlAA Jcxmwl, 2 (1964) 93. 18 J_W.S~~~~~.P_EG~RA_~ANDB_V~.
PROPERTIESOF
169
EVACUA-IEDFOXVDERS
Adhcrivcbchaviorofsiligtcpowdminuluahigh~acuum. J. Gcoph>s. Rex., 69 (1964) 235. 19 EV~~~~~J.D.N~~~~~.Enginmingpropcrriesofsimulated lunar soils. Soil Me&. Fd. ASCE Pl(1965) 25. 20 Jet Propulsion Laboraroxy, Stxrve_vor V misson repot-t. F’artII:Scienarcsnlts, TcchnicaIRcporr32-124646.1967.p. 87.
21 ECBERKEIT_ H. I_. WOOD. I_ D. JAFFE AXD H_ E_ MARTEXS. Thd properties of simulated lunar material AIAA Journal. I (i963) 1402_ 22 E- M. cHRnre;ns e al_, Lunar surfaa mechamcal properties-Surveyor 1. J. Geoph>s. Rex, 2 (1967) 801.
Powder Technol. 3 (1%9/70)
163-169
and Mechanical
of Evacuated Powi!erS+:
Properties
A. E. WECHSLER
(Received
SUMMARY This paper swnmarkes the e$ects of enviromnentul and intrinsic powder parameters on the thermal and mechanical properties of euaczated powders. Thermal wnaktkity and d.iiuskCty are controlled primarily by the residual gas pressure, temperature, particle size and shah and mechanical load_ Bearing strength is less dependent on temperature and gas pressure but is strongly inzuenced by density, particle size and shape_
INTRODUCl-ION
The practical implications of the information on thermal and mechanical properties of evacuated powders are significant in many technical areas: heat transfer at high and low temperatures, insulation development, food processing, chemical processing, particle separation, etc. The objectives of this paper are to summ arixethefactorsresponsible for the thermal and mechanical behavior of evacuated powders, to describe the effects of environmental and intrinsic powder parameters on thermal and mechanical properties, and to show the relationships between thermal and mechanical properties of evacuated powders. The forthcoming manned lunar landing and the recent Surveyor experiments have created the desire within the scientik community to have a better understanding of the thermal and mechanical properties of evacuated powders. Wesselink’ was one ofthe lirst to demonstrate that the temperature variation of the lunar surface, as measured from the earth by inkared radiation, could be related to the thermal properties of the surface material_ Subsequently. many investigators2~3 have used experimental data on lunar surface temperature
June
IO, 1969)
variation and laboratory data on the thermal properties of evacuated particulate materials to estimate the nature of the lunar surface. ie-, the particle size, distribution and even composition. The prediction based upon thermal analyses, that the lunar surface layer is composed of somewhat cohesive particles in the size range of 5 to 100 microns, seems to be confirmed by the photographs and mechanical experiments of the Slurveyor spacecraft The bearing strength of the iunar surface layer was also of great interest to the spacecraft designer. Studies have been conductedJ*s of the mechanical properties and the similarities between thermal and mechanical behavior of particulate materials in a vacuum environment. Much of the data obtained in these programs have also been confirmed by experimental measurements on the moon. This impetus provided by the space program has been instrumental in forwarding our understanding of the behavior of powders. THERMALPROPERTiEs
OF EVACUATED
F’OW~ERS
Mechanisms of heat transfZr There are three basic mechanisms of heat transfer in an evacuated powderanduction by the residual gas in the powder, solid conduction witbin particles and across the interpanicle contact areas, and thermal radiation within particles, across the void spaces between particle surfaces, and between void spaces themselVeS
Gas condrrction.In a powder at room temperature and atmospheric pressure, most of the heat is transferred by conduction within rhe gas filling the void spaces between the particles. The effects of gas pressure on gaseous conduction within a powder are well known6-’ Over a wide range of pressures, the thermal conductivity of the gas (and hence the powder) is independent of pressure because the mean free path varies inve-rsely with the pressure andthegasdensityvariesdirectIywiththepressure; the product of mean free path and density deter-
163
A.EWECHSLEft
mines the gas conductivity_When the gas pressure is reduced to the point where the mean free path within the gas is greater than the interparticle spacing, further reduction in gas pressure does not change the effective free path of the gas. Then the thermal conductivity of the gas and the powder is directly proportional to gas pressure.The pressure at which thermal conductivity becomes proportional to the gas pressure (sometimes called the breakaway pressure) increases as the oarticle size decreases Equations giving the relationship between gas pressure,particlesize, and thermal conductivity are available in the literature8-g.For powders with particle size from 1 to 200 k gas conduction within the powder becomes a negligible heat transfer mechanism below about 10-r torr, Solid conduction. In an evacuated powder, solid conduction becomes an important but not well understood heat transfer mechanism Heat is transferredwithintheindividual particlesby phonon conduction, electron conduction, or by thermal radiation, depending upon the powder type These processes are the same as in the bulk solid and can be explained and examined by conventional heat transfer theory and measurements. Heat transfer at the particle interfaces across contact points is difficult to explain and to examine analytically or experimentally. The particle size, shape, composition, density or degree of compaction, and mechanical loading affect the number and the nature of the contact points. Although studies of contact conduction acrass macroscopic contacts have been very successful, it has been difficult to apply these results to a complex powder system. The effects of interparticle for ces-electrostatic, Vsn der Waals, or chemical adhesion-on interparticle contact area may exceed those due to particle shape or mechanical loading. Empirical equations describing contact conduction in the literature4*ro may be valid only for certain selected materials_ As a result it is not possible to predict adequately the heat transfer by solid conduction in powders. However, several general conclusions concerning solid conduction heat transfer can be made: (1) The solid conduction heat transfer in powders composed of inherently high conductivity materials (e-g., metals) will be only slightly higher than in powders composed of low conductivity materials (e-g_, glasses). It is well confirmed by experiment that evacuated powders of many types have nearly the same thermal conductivity at comparable temperature conditions6. (2) The greater the density or
mechanical loading of the powder the greater the solid conduction contribution to heat transfer.This is caused by increased number and area of contacts_ (3) Under high vacuum conditions, where clean surfaces exist, there does not appear to be a great increasein solid conduction in non-metallic powders due tc vacuum adhesion ; in metals vacuum adhesion can result in higher contact conduction. Only few experimental measurements have been made which demonstrate these results. Thennalrudiation.Thermalradiationisthesecond important heat transfer mechanism in evacuated powders. If the materialscomprising the powder are opaque to thermal radiation in the wavelength region of interest (usually 1 to 50 microns for powders at temperatures between 100 and lObOoK), radiation transport within the individual grains will be small. However, radiation between particle surfaces will stilI be important The more dense the powder, and the smaller the void spaces, the smaller the radiation heat transfer between particles_ The presence of radiation reflecting Oi scattering particles also reduces the radiation heat transfer contribution. Empirical and theoretical relations have been derived to predict radiative thermal transport in powders’ 1*8.12_ In general, radiation heat transfer in an evacuated powder increaseswith temperature, normally with the third power of the absolute temperature. The magnitude of the radiation contribution can often be. predicted to within a factor of two if the particle size, composition, and optical properties are known_ The eflects of environmental and powder parameters on thermal proper&s Several examples are given below to demonstrate
the effectsof environmental and powder parameters on thermal properties of evacuated powders. Figure 1 shows the effect of gas pressure on the thermal conductivity of pumice powder”_ At pressuresbelow 10m2 torr the thermal conductivity is independent of gas pressure. The powder with largersize particleshas a lower break-away pressure than the smaller size powder. There is little effect of particle size on thermal conductivity at low gas pressures. This may be caused by the variation in solid conduction and radiation contributions as described below. Figure 2 shows the effect of temperature on the thermal conductivity of evacuated glass beads_ The measurements were performed at gas pressures less than 10e4 torr so that gas conduction is negligible.
PROPERTIES
OF EVACUATED
rial made of amorphous parkks
sire range A
0-44~
0
44-104
0
l---i49
p P Gas
10-G
Fig
m-exxn-e
10-2
1. Thermal conductSty
Ctorr>
1
10’
760
of pumice po=dcr-(Wcchsla
and
Glascr”). Tke thermal conductivity of each material increases
with temperature_ The equations of the lines representing the data have the form: k=A+BT3
(1)
where k is the effective thermal conductivity, A represents the solid conduction term and BT3 represents the contribution of thermal radiation. Table 1 shows the values of these terms for the glass beads and other materials. At low temperatures for most non-metallic materia!s solid wnduction is the most important heat transfer mechanism; at h’gh temperatures radiation is most important- As the particle size increases the solid conduction term decreases and the radiation term increases. The solid conduction term is higher in a material which is composed of crystalline particles such as quartz (high thermal conductivity in bulk) than in a mate-
150
200
165
F’OWDERS
250 Temperature
300
350
400
(‘IO
Fig_ 2 Efktive thermal conductivity of glass beds and quartz powder_ 0. MicroLsxds 44-62 jt. p= 1.42 gkm’ (Wechslu and Simon”); A, quartzpowder < 10 /.a,p= LOO s/cm3 (Wechskr and Sin”).
such as glass. The
radiation contribution to heat transfer is greater m a more transparent powder, &g_, glass or quartz, than in an opaque powder such as basalt From a comparison of the results for spherical glass powders and irregularly shaped pumice or basalt powders, the solid conduction contribution does riot seem to be greatly affected by particle sha? The density and porosity of the materials described in Table 1 varied from 0.82 to 1.6 g/cm3 and O-40 to 0.70 respectively_ No definitive trends of thermal conductivity with density or porosity have been found. However, for consolidated materials, such as sandstone or fused foams, thermal conductivity is often directly proportional to the fraction of solid present. Figure 3 shows the effects of mechanical load on thermal conductivity of evacuated microbeads14_ Measurements were made using 177-210 p diameter glass beads at 5.5 x lo-’ torr ,m pressure and room temperature The thermal conductivity increases with the s power of the applied load Empirical equations based on Hetian loading of orderly spheres4 indicated a 3 power relationship should be obtained if solid conduction were the only heat transfer mechanism_ Little data are available in the literature on the effects of loading; however, a significant variation of heat conduction with depth in a packed bed can occur_ MECFSAMCAL
PROPERTIES
OF EVACUATED
POWDERS
The requirements for soft landing the Surveyor and future manned spacecraft on the moon have provided the impetus for experimental and analytical studies of the static and dynamic properties of evacuated powders_ Principal emphasis has been placed upon estimating or measuring static bearing
-
5
091
! 1
. . . . . . ..
. . ..
10
..I.
.
100 Pen
*
.
-
.
I 1000
rPsig1
Fig_ 3_ Vacuum conductivity variation x=&.I cxrcmal loading. 70/80 mesh microbeads; 0. pressure increasing; l . pressure dsrcasing
166
SOM condvcrion c0ntnbut10n lmicro w/cm ‘C )
Radmtice cont~mion hjcm YI x 10’3 x I-3)
Rk-f:
300°K
400°K
i-8 1.7 13 72 37.0
42 4.1 3.1 17-O 880
10 I1 10 10 10
GIass beads <37 is-73 Ss-I25 250-350
Quartz < 10
63 3.0 34 85 13.0
95
47 7-O 3’ 095
44-62
052
051 039 21 II.0
pander
Pumice poader lo-37 44-74 Basalt pmder lo-37 4+74
3.0 42
0 10
33.5
0.10
033 035
077 OS0
11 10
51 25
31 36
O-49 1.1
1.7 38
39 9.1
11 11
0.58 21
005
0.15
028
O-94
0.34 22
11 11
50
as-74
i ‘l-l.6 61
x 103/T
stren,g@, establishing the effects of vacuum on bearing strength and evaluating methods of failure for powder systems. Mechanisms for mechanical failure The mechanical properties of evacuated powders, with specific application to the lunar environment, have been examined in terms of classical soil
mechanisms15*16 and in terms of models depicting very low-density high-porosity cohesive soils4_ The bearing strength of a particulate material denends upon the particIe cohesion and the internal friction between the particle grains Most particu!ate materiak of low porosity under atmospheric pressure conditions fail predominantly in lateral shear, in which intergramuar friction along the failure plane provides the major resistance against the applied stresses For such a cohesiveless material the bearing strength is proportional to the density of the particulate material, or the packing factor, the characteristic dimension of the applied load, and the at&e of internal friction of the particles. In a hign vacuum environment it may be anticipated that the intergranuk friction wouId increase and also that the particles may be cohesive, thus significantly increasing the bearing strength. In a lowdensity, high-porosity particulate material, the failure mode may be characterized by collapse and compression of the material directly beneath the load and the failure is caused by local or vertical
shear- The bearing strength for such a material is provided by the force necessaq to shear the material in the vertical plane around the load perimeter as well as the force n ecessaq to compact the underlying material. An analysis of low density materials4 rest&s in a relation between bearing strength, initial and compressed porosity of the material, and the interparticle adhesion forces. The bearing strength is dependent on porosity, the characteristic dimension of the Ioad, and the amount of compression, and is strongly influenced by the inter-particle adhesion. Laboratory
measuremenls
Laboratory measurements of bearing strength of particulate materials, primarily silicates, have provided data which seem to be dependent upon the particle tYPe, vacuum treatmenf method of preparation, and test procedure. Efict of gas pressure Laboratory measurements have been made at atmospheric pressure, under high vacuum (1O-5-1O-6 torr) and ultra-high vacuum (10-9-lo-‘c torr). Bemett ef CL” examined the bearing strength of basalt powders of various particle sizes in air at atmospheric pressure and at 10m5 tom They found only minor cliffcrcnccs between resuhs at vacuum and atmospheric pressure. At low packing factors the powders in air had bearing strengths 50% less than in vacuum and at high packing factors bearing strengths were slightly higherinair@aninvacuumBearingstrength
PROPERTIES OF EVACUATED POWDERS
values range frcm about 0.1 to 9 kg/cm2 (l-4-130 psi.) depending upon the packing factor_ Measurements d the bearing strength of freshly sifted silica and alumina in air’ resulted in bearing capacity of from 2 to 30 g/cm’ (0.03-O-4 p.s.i.). Thcsc materials were of very low density_ The cohesion estimated from these measurements was about 500 dynes/cm’. Salisbury et CZI_‘~and Vey and Nelson’g report cohesion of from 750 to 20,000 dynes/cm’ for finely divided silica and silicate powders at pressures of lo-lo tom It must be surmised that these powders are well outgassed and have clean surfaces resulting in greater cohesion Such a material could have a bearing strength of 2500 g/cm2 (30 psi.) on the basis of cohesion effects alone, even if internal friction did not increase in vacuum Thus, the existing data indicate that for fine powders at low densities and Packing factors, ultra-high vacuum increases bearing capacity, but at higher densities ultra-high vacuum has less of an effect on bearing strength_ Many qualitative measurements have been made on the cohesion of particles prepared and treated in high vacuum; more quantitative measures of static and dynamic mechanical properties are needed. EBct of dswity or packing factor_ Most studies of the static bearing have shown increasing static bearing strength with increasing density. Figure 4 presents some results for powders in air and vacuum as well as characteristic curves based upon theoretical analyses and calculations. Curves 1 and 2 are~best fit curves obtained by Halajia# using the fluff (low density) and cohesionless soil models. There is some region of overlap or transition at solid fractions near 040. Region 3 is the range of data obtained by Bemett et uL” for a variety of sizes of basalt at both atmospheric pressure and at lo-’ torr. It is interesting to note that the data obtained from the landing of Surveyor V agrees well with terrestrial laboratory datazO. Also, the photographic data fromRanger 7,8, and 9 have produced lower bo-ur& ofsurface bearing strength from about 10 to 55X) g/cm2. depending upon bearing width, and densities of 06-l g/cm3 near the surfaa~?~_ This region is in general agreement with the data presented in Fig 4. Thus, the static bearing strength is a strong function of the density or packing factor of the particulate material. A change of over 100 in the bearing strength is not uncommon when the fraction of solid is changed from 0.2 to 0.6. Other fizctors 4ffecting beakg strength In addition to gas pressure and density- factors such as temperature, particle shape, and size distribution
167
Fig 4. Mass be&g suen_mhof pouderx I. Best iit 10% densir? fluff,compression depth equal plate dtamcta (HalajzmL): : bcsr finsouls, 3 in_ plate diaxn @hk+ni); 3, basalt pondc;. 154)zci 35 mesh, in air and vacuum (Bemett ez ~2~“) 4. siha ponder m air (Jaff~e’~); 5. Surxqor I_ interpretation(ChrisrexxenETnl_=q; data’9 . Survq or V simulation
may affect bearing strength There are no definitive data on the effect of temperature on bearing strength of evacuated powders. It is known that the bulk moduli of many non-metallic materials vary m-ith temperature and it is possible that the interparticle friction could change at low temperatures_ However_ more laboratory data arc needed to establish these effects Particle shape and size distribution may hare a significaut effect on bearing strength_ Particle interlocking, especially for higher density materials, may greatly enhance interparticle friction and cohesion resulting in increased bearing strength Most theories and correlations of particle strength are based on relatively uniform round particles and are not valid for platelets or elongated grains Little effort has been devoted to the study of the behavior of irregularly shaped particles in vacuum Perhaps. as a better understanding of thebehavior of particulates in air is evolved, extrapolation to vacuum conditions can be made_
168
A.EWECHSLER
RELATlON
Tl-mwAL
BEnvEEN PFtOPERm
AND
OF EVACUA~
MECHANICAL
P0WDERS
At first thought_ it might be expected that a strong correlation would be found between the thermal properties (e-97 thermal conductivity) and mechanical properties (e_g_beariug strength)of evacuated particulatematerials Unfortunately, thiscorrelation is not
observed,
as illustrated
below.
A change in gas pressure in a powder from atmospheric to 10S4 torr may yield a decrease in thermal conductivity of from 20 to ?GO; a similar change in gas pressure will produce only a small change in static bearing strength_ In the pressure range from 10m4 to lo- lo torr, only small changes in thermal wnductivity are observed experimentally whereas significant increases in cohesion lead to similar changes in bearing strength. The thermal conductivity of many evacuatednonmetallic powders is independent of density or packing factor, as shown in Table 2 Figure 4 shows a variation of over lOCKI in bearing strength for the corresponding density or solid fraction range The difference in the thermal and mechanical behavior may be attributable to sever-a! factors: thermal conduction of evacuated powders is caused by radiative and solid conduction mechanisms Although the solid conduction contribution to heartransferinereaseswithinereasingdensity,the radiation contribution decreases with increasing density- The net effect is the independence of conductivity on density. The beariug strength is attributable to interparticle friction and cohesion, each of which cnn be expected to increase withan increase in den&y or packing factor. Despite the apparent lack of correlation between thermal and meehanieal properties of evacuated powders, it is not surprisingthat for a wnsohdated TABLE
2:
m
Ml?&Y&Z
CoUoidd siha PerI& Pnmiapoader Quartzpoh Basalt powder GlaSSbeads
Glaabcads Basalt powder
coxDucnvrry PowDensity
OF SVERAL
EVACUATED
Themaltxmhaidy at 3ooOK (won/cm OC x 10-5)
Refe
@/an’)
(106 (LO8 Q8 LO 1.3-1.4 1.42 l-4-1.7 Ll-1-8
1.8 21 12-I-4 32-35 l.Ch1.8 12 1.5 154
7 7 11 11 11 11 10 21
or siuteredevaccted material such as pumice, sandstone or sintered bea& it is observed that both the thermal conductivity and bearing or crushing strength increase with increased density. For these materials, the thermal conduction as well as the mechanical strength are related to the average area of the solid phase in the plane perpendicularto the heat flow or load. The results of the work described above illustrate the needs for and benefits to be derived from interdisciplinary studies of powders Thermal property measurementswhenwmbinedwithmechanicalproperty measurementscan lead to greaterinsight of-he behavior of powders under marrydifferenteuvironmental conditions. REFERENCES 1 A.J.W
-a~, Hat condnctlvity and nature of the lsurface matuial, E&L hrror~_ I=r. Nefh_. 10 (1948) 35L 2 J. C. Jm The smfaa tanpaature of the moon. AusfraIian J. Physv, 6 (1953) 10. 3 V. D. KROTIKOV AHD V. S. T~O~ISKII, Thermal conductivity ofhmarmataialfivmpr&semcasnrem mts of 1radioemission, &v&z Artron-AI, 7 (1963) 119_ 4 J. D. HAURAN, Con-elation of mazhanhl and thermal propatia of cxnata~cstrial materials. Fmal ZZepon, NASA Conrrpcr NASi?-20084. 1967. S L D. JAFFE. Bearing strength o: “Fairy castk” strndurrs. J. Gcophys Re, 70 (l%S) 62686 M. Slaox.ucnows~~, Sur la conductibihti cabrisque da corps pulvais&, wrll. ht. de rAaadcmie des Scide Cmcor;ie. A (1910) 129. on the thcr7 A.E\xxEY& P. E. Gwen AX= A. E W~cnea, mal condnctiv&y of powder insulations. XI Inrem. Congr. Rejiigerarkm. Avgust 1963. 8 W. ,w Thermal conductivity of packed beds. Am Insf_ Chem_ Ehgrs_ J, 6 (1960) 63. 9 R. G. Dmsrrr AFZVC S. EIAN, NACA Rrvmrh M-raw don RME 52cOS. 1952 10 K. Wxrsox~. Thermal condmtivity of selected silicate powden in vacuum from lSO-3XPK. Zhsis. CalX Iast ofTechnology. 1964. AhD 1. SIMON. Tbamd ccmd naivityand 11 A.E.Wm didatric constant of silicate mate&k, Frz Report under NASA tZmrracf NAS&m6.1966. 12J.C(3iw~S_W_Cm~~cnt~s_Radianthcattransfain pa&d beds, Am. Inrr. Cknx. hgrs_ J.. 9 (1963) 35. i3 kW_ ANDP.~PRSSUKC effecbonposmlated hmar mataials, z-, 4 (1965) 335. 14 J. ?SR, PasonaY Commmkation, Gulf Rcscazh and Dcvclopmalt Corp.. 1966. 15 I.. D_ Jm Stra& of lunar dust, J. Gwphys: iZa_, 70 (1%5) 6139. 16 L. D. JAFFE, L-surface strength. I-, 6 (1967) 7515. 17 EC~,R.S.SCOTT,L.D.JAFFE,EP.FRINKAND H.EMunqBearingc&pacityofsim~lmurnafacn in vm, AlAA Jcxmwl, 2 (1964) 93. 18 J_W.S~~~~~.P_EG~RA_~ANDB_V~.
PROPERTIESOF
169
EVACUA-IEDFOXVDERS
Adhcrivcbchaviorofsiligtcpowdminuluahigh~acuum. J. Gcoph>s. Rex., 69 (1964) 235. 19 EV~~~~~J.D.N~~~~~.Enginmingpropcrriesofsimulated lunar soils. Soil Me&. Fd. ASCE Pl(1965) 25. 20 Jet Propulsion Laboraroxy, Stxrve_vor V misson repot-t. F’artII:Scienarcsnlts, TcchnicaIRcporr32-124646.1967.p. 87.
21 ECBERKEIT_ H. I_. WOOD. I_ D. JAFFE AXD H_ E_ MARTEXS. Thd properties of simulated lunar material AIAA Journal. I (i963) 1402_ 22 E- M. cHRnre;ns e al_, Lunar surfaa mechamcal properties-Surveyor 1. J. Geoph>s. Rex, 2 (1967) 801.
Powder Technol. 3 (1%9/70)
163-169