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Gaosheng Wei1

School of Energy and Power Engineering,

Key Laboratory of Condition Monitoring

and Control for Power Plant Equipment

of Ministry of Education,

North China Electric Power University,

Beijing 102206, China

e-mail: [email protected]

Yusong LiuEnergy Department of Beijing Sustainable

Development Centre,



Xiaoze DuSchool of Energy and Power Engineering,

Key Laboratory of Condition Monitoring

and Control for Power Plant Equipment

of Ministry of Education,

North China Electric Power University,



Xinxin ZhangDepartment of Thermal Engineering,

University of Science and Technology Beijing,



Gaseous Conductivity Study onSilica Aerogel and Its CompositeInsulation MaterialsThis paper presents a theoretical and experimental study on gaseous conductivity ofsilica aerogel and composite insulation materials. First, the insulation material samples(including silica aerogel, xonotlite-type calcium silicate, xonotlite-aerogel composite,and ceramic fiber-aerogel composite) were prepared. Next, the gaseous conductivities ofthe prepared samples were measured from 0.045 Pa to atmospheric pressure using thetransient hot-strip (THS) method. The gaseous conductivity expressions obtained basedon the kinetic theory were then compared with the experimental results. It is shown thatthe gaseous conductivity of both xonotlite-type calcium silicate and silica aerogeldecreases significantly with decreasing pressure. The gaseous conductivities of xonotlite-type calcium silicate and silica aerogel reach zero at about 100 Pa and 10 4 Pa, respec-tively. The theoretical gaseous conductivity expressions match well with the experimentalresults of xonotlite-type calcium silicate and silica aerogel but not with the experimentalresults for the composite insulation materials. This mismatch indicates that the aerogeldoes not totally fill the original interspace of the xonotlite-type calcium silicate and ce-

ramic fiber in the two kinds of composite insulation materials. [DOI: 10.1115/1.4004170]

Keywords: aerogel, thermal conductivity, thermophysical properties, transient hot-stripmethod, xonotlite-type calcium silicate

Introduction

Silica aerogel is a super insulation material made by solgelchemical processing and supercritical drying technologies. It hasexcellent insulation properties with a thermal conductivity lowerthan still air at ambient temperature because of its nanostructuredSiO2 network and a very high porosity up to 99%. Many argu-ments have been made in recent years for using aerogels as ther-mal insulation material [15]. The major disadvantage of usingmonolithic silica aerogel for thermal insulation is that it is brittleand easily broken. Some researchers are trying to composite silicaaerogel with other tougher materials [68]. Xonotlite-aerogel andceramic fiber-aerogel composite insulation materials are two typi-cal cases. Xonotlite-type calcium silicate (6CaO 6SiO2 H2O) isa synthesized high porosity insulation material created by hydro-thermal processing with quartz powder and limestone as the rawmaterial (with CaO=SiO2 % 1:1). Compared with fire-retardantfiber, xonotlite-type calcium silicate has excellent insulating per-formance, such as low thermal conductivity, environmentallyfriendly, high strength, and a wide application temperature rangeup to 1000 C [9,10]. Better insulation materials with higherstrength are expected by compositing an aerogel with xonotlite-type calcium silicate and ceramic fiber [7,8].

The heat transfer mechanisms in porous insulation materialsinclude solid conduction, gaseous conduction, natural convection,and thermal radiation. Natural convection can always be neglectedif the pore in the material is small (

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surface before rebounding, and some do not reach the temperatureof the solid surface before rebounding. The accommodation coef-ficient is the quotient of heat accommodation between the gasmolecules and the wall, and varies between 0 and 1. For somerepresentative values of the accommodation coefficient betweenvarious surfaces and gases, refer to the literature [17]. If gas mole-cules rebound between two parallel surfaces, the steady net heatflux can be calculated, where the corresponding apparent thermalconductivity is given as

kg k0

gT1 2 2 a

a

2c

c 1

1

PrKn

(2)

where k0gT is the gaseous conductivity related to a temperatureat constant pressure, Kn is Knudsen number defined as

Kn lm=d (3)

d is the characteristic system size and is the distance between twoparallel surfaces. lm is the mean free path of gas molecules in freespace and calculated as

lm 1ffiffiffi2p

ngpd2g kBT

ffiffiffi2p

pd2gp(4)

where ng is the number density of gas molecules, dg is the diameterof a gas molecule (for nitrogen dg = 3.798 1010 m); kB is theBoltzmann constant (kB = 1.38 1023 J=K), and p is the pressure.

For conventional porous insulation material, such as calciumsilicate, foam, etc., the Knudsen number in Eq. (3) is close to zeroat atmospheric pressure. Equation (2) is simplified as kg k0g.While the mean pore diameter of aerogel is in the range of about20 nm, it is apparently less than the mean free path of gas mole-cules (about 70 nm), and Kn > 1. Equation (2) has been adoptedto depict the gaseous conductivity in aerogel by many researchers[1,19,20] and can be simplified as

kg

k0gT

1 2fKn(5)

where, f is a constant, for airf % 2, or Ref. [21]

kg k0gT

1 C=pd (6a)

C 2f kBTffiffiffi2

ppd2g

(6b)

It must be mentioned that Eq. (2) was derived by analyzing the heattransfer problem between two parallel surfaces. Its validity for gas inporous media is questionable, however, especially in aerogel. Thepore dimensions of aerogel are in the nanoscales range, and the solidsurfaces are silica matrix distributed over the entire space. Accord-

ingly, it is questionable to apply temperature slip conditions directly.In addition, Eq. (4) is the mean free path of gas molecules in freespace. The mean free path of gas molecules in nanoporous structuresof aerogel is different because the solid matrix in aerogel restricts thegas molecules free movement greatly. Zeng et al. [22] provide a com-prehensive investigation of the mean free path of gas molecules in po-rous media and give the following mean free path expression

lm 1ffiffiffi2

pngpd2g Sq=/

(7)

where S is the specific surface area of porous media defined assurface area per unit mass (m2=kg), q is the bulk density (kg=m3),

and / is the porosity of the media. For conventional porous insu-lation materials with micron pores, the second part in the denomi-nator of Eq. (7) can be ignored because of their relatively smallervalue of specific surface area, and Eq. (4) still can be used. Butin an aerogel, Sq=/ is comparable to

ffiffiffi2

pngpd

2g for its relative

higher value of S and cannot be simply ignored. Using kinetictheory, and considering the mean free path of Eq. (7), the gaseousconductivity in aerogel was derived by Zeng et al. [22,23] as

kg

60:22 105pT0:5

0:25Sq/1

4:01 109

pT1(8)

Both Eqs. (5) and (8) show that the gaseous conductivity in po-rous media is a function of temperature and pressure for a fixedstructures material. The gaseous conductivity can be evaluatedby measuring the thermal conductivity of porous media at differ-ent pressures. The thermal conductivity measured at vacuum con-dition can be considered the conductivity contribution of solid andthermal radiation. The thermal conductivity measured at a givenpressure minus the value at vacuum condition can be a measure ofgaseous conductivity contribution.

Experimental Investigation

The Material Preparation. Three samples of silica aerogel

with different bulk densities were prepared using a two stepmethod (solgel processes and supercritical evaporation technol-ogy). First, TEOS=EtOH-based polymeric silica sols were pre-pared with tetraethoxysilane (TEOS), EtOH absolute alcohol(C2H5OH), and deionized water with hydrochloric acid (HCl) ascatalysts. The prepared silica sols were modified by ammonia to aneutral or alkaline condition. After stirring for 3 h, the silica solswere poured into a mould until a gel was formed. An absoluteaqueous alcohol solution was then added to the gel for ageing. Af-ter ageing, the resulting SiO2 alcogel was taken out and placedinto an autoclave. The autoclave was heated to exceed the super-critical point of absolute alcohol (243 C, 6.3 MPa) for supercriti-cal evaporation. Finally, the silica aerogel samples were obtained.Samples with different bulk densities can be obtained by adjustingthe molar ratio of the raw material and the technological parame-

ter. For the detailed preparation process and the microstructurefeatures (including the SEM image, pore size distribution, andspecific surface area) of the sample refer to the literature [24]. Thesamples of xonotlite-type calcium silicate were prepared using theconventional hydrothermal process with quartz powder and lime-stone as the raw material (with CaO=SiO2 % 1:1) [9,10,25,26].The samples of xonotlite-aerogel and ceramic fiber-aerogel com-posite insulation materials were prepared using the vacuum dip-ping technology [7,27]. SiO2 sols were first prepared using thesame method mentioned above, then a vacuum chamber contain-ing xonotlite-type calcium silicate or ceramic fiber was vacuu-mized to 0.5 Pa. The prepared SiO2 sols were placed into thechamber, then the vacuum valve was quickly turned off. The vac-uum valve was opened after half an hour, then the floating xonot-lite-type calcium silicate or ceramic fiber would suck into theSiO2 sols, and sink down. The vacuum valve was turned off untilthe gel was formed and then poured into an ethanol solution(water=ethanol = 1=4) for ageing. The composite materials wereplaced in an autoclave for supercritical drying after replacing theethanol solution four times at 12 h intervals. The final correspond-ing samples of xonotlite-aerogel and ceramic fiber-aerogel com-posite insulation materials were obtained. For the detailed micro-structure features (including the SEM image, pore sizedistribution, and specific surface area) of the prepared samplesrefer to the literature [28,29].

Thermal Conductivity Measurement. The transient hot-stripmethod was used to measure the thermal conductivity of aerogel,xonotlite-type calcium silicate, xonotlite-aerogel composite, and

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ceramic fiber-aerogel composite insulation materials with variousbulk densities in the pressure range of 0.045 Pa to atmosphericpressure. Figure 1 gives the schematic illustration of the THSmethod. An electric current is passed through the hot-strip pressedbetween two equal size slabs of the sample and the temperature ofthe strip increases. The rate at which the temperature of the stripincreases depends on the thermal conductivity of the sample.This is the basis for thermal conductivity measurements using theTHS method. For an extensive description of the theory of theTHS method, refer to Gustafsson et al. [30]. The result for thermal

conductivity is calculated as k P0=4p=dTt=d lnt, whereP0 is the power input to the strip, tis the time, and dTt=d lnt isthe slope of temperature versus ln(t) after heating for severalseconds.

A 2.0 mm (width) 0.1 mm (thickness) nickelchrome(Ni80Cr20) strip was used as the heat source. The strip was sand-wiched between two identical samples, each about 150 mm(length) 100 mm (width) 60 mm (thickness). The PA 36-3A=AL type stabilized power source supplies 03 A=036 V directcurrent output. The variations of temperature were detected usingtype K 0.1 mm-diameter thermocouples welded on the center ofthe strip surface. The signals from the thermocouple, togetherwith the voltage signals between two sides of the sample andbetween two sides of the standard resistance, were all digitized bya YOCOGAWA DL-708E type digital oscilloscope before beingprocessed by a computer.

A vacuum system was designed specifically for the THSmethod as shown in Fig. 2, which can provide any vacuum sur-rounding for thermal conductivity measurements in the pressurerange of 103 Pa to atmospheric pressure at ambient temperature.The size of the inner room of the vacuum bell was / 340 400 mm.Three groups, all together 24 electrodes, were set at the bottom ofthe vacuum bell. It was convenient to connect the inner room tothe outer space using a lead. Two 2XZ-4 type direct drive rotaryvane vacuum pumps (mechanical vacuum pump), and a molecularpump was used to control the vacuum condition of the system.Here, the measured thermal conductivity value minus the valuemeasured under a pressure less than 1 Pa was considered as thegaseous conductivity of the material at a fixed pressure. This dif-ference was because the contribution of gas on thermal conductiv-ity was reaching zero when the pressure was less than 1 Pa.

Uncertainty Analysis in Thermal ConductivityMeasurement. The thermal conductivity of the sample is esti-mated as k P0=4p=dTt=d lnt in the THS method by esti-mating the slope of the measured temperature rise versus timeevolution in logarithmical scale over a defined time interval. Themain sources of thermal conductivity uncertainty are connected tothe measurement of temperature, the stability of the power supply,and the satisfaction of the experimental conditions as they areassumed in the theoretical model. Some sources of the nonmea-surement errors may cause differences between the real conditions

and the assumptions of the analytical model. For example, theheating strip has a finite nonzero thickness and a nonzero heatcapacity. There are thermal resistances between the strip and thesample, and between the thermocouple and the strip. The sampleand the strip have finite dimensions, and heat loss on the samplesurface may occur. For a comprehensive discussion of uncertaintyassessments of the THS method, refer to the literature [31].

In order to minimize the effect of the power supply on measure-ment uncertainty, a stabilized, direct current supply was offeredthrough the strip. The heating rate was carefully examined in each

test to guarantee the overall temperature rise was in the range of810 C during the heating time interval of 0500 s. A relativemiddle time interval of 50300 s was adopted to determine thethermal conductivity of the measured samples, which can alsodepress the effects of nonzero heat capacity of the strip and finitedimensions of the samples on thermal conductivity determination.As mentioned in the literature [32,33], the temperature responseDT of the strip in the THS method is a sum of two components:DT A Bfs, where A is a constant representing thermal con-tact resistance effect, and the second component, Bfs, is notinfluenced by any thermal contact resistance. In an actual experi-ment, the transient component B is used to determine thermal con-ductivity of the material. Therefore, the thermal conductivitydetermination is not influenced by any thermal contact resistance.

According to our previous numerical study [34], the nonzero

thickness and the nonzero heat capacity of the heating strip is themain measurement error, especially for materials with relativelylow thermal diffusivities. The thermal diffusivities of the materi-als in this study are all larger than 4.0 107 m2=s. By adopting aminimum time tmin of 50 s, the measurement error caused by thenonzero thickness and the nonzero heat capacity of the heatingstrip can be maintained at less than 2%.

The measurement error caused by the heat loss on thesample surface is governed by the thermal penetration depth:Dp 2 ffiffiffiffiffiffiffiffiffiffiatmaxp [32,33]. It represents the minimum distance fromany part of the heating area of the sensor to the lateral boundaryof the sample, i.e., the available probing depth. By adopting a tmaxof 300 s and a relatively large sample dimension, the measurementerror can be guaranteed to be less than 1% due to the finite dimen-sions of the sample in this study. All of the above uncertainties

are considered to be independent in this study. By consideringuncertainty analysis separately, and using the law of uncertaintypropagation, the combined standard uncertainty of the thermalconductivity determination is sure to be less than 3%.

Results and Discussion

Figures 35 show comparisons of the experimental gaseousthermal conductivity data measured at ambient temperature withthe theoretical heat transfer equation results. In the calculation,the mean pore diameter of the porous media is adopted as thecharacteristic system size of d in Eq. (5), and d = 20 lm areadopted for xonotlite-type calcium silicate according to measuredstructural values in the literature [10,35]. For gaseous thermalFig. 1 Schematic illustration of transient hot strip setup

Fig. 2 Picture of the arrangement of THS apparatus in a vac-uum system

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conductivity estimation using Eq. (8), considering that a depend-ence relationship exists between the specific surface area andthe bulk density of aerogel, the following relation is adopted [15]to estimate the specific surface area of aerogel according tothe measured and simulated results in this study and in literature[3638]

S 324:3=q 5:03 105 (9)

It is shown (Fig. 3) that the theoretical gaseous thermal conductiv-ity from Eq. (5) matches well with experimental data of xonotlite-type calcium silicate when pressure is less than 104 Pa. The gase-ous conductivity decreases significantly with a drop in pressureand reaches zero at about 100 Pa for various bulk densities ofxonotlite-type calcium silicate. Equation (5) does not match wellwith experimental data of xonotlite-type calcium silicate at atmos-pheric pressure, which indicates that one cannot simply use the

experimental measured data at atmospheric pressure minus the ex-perimental thermal conductivity data at vacuum condition to rep-resent the gaseous conductivity contribution to the total thermalconductivity of the material. It is because the coupled process ofgas and solid, as well as radiation, may enlarge the total thermalconductivity at atmospheric pressure. Therefore, if the total heattransfer process is analyzed, Eq. (5) still can be used to depict thegaseous thermal conductivity in the xonotlite-type calcium silicateas mentioned in our previous work [13,39].

Figure 4 indicates a great error when using Eq. (5) (with d = 18nm, which is the mean pore diameter of silica aerogel samples) todepict the gaseous conductivity of aerogel. As mentioned above,Eq. (4) is the mean free path of gas molecules in free space, whichis different from the mean free path of gas molecules in nanopo-rous structures of aerogel. It is because the solid matrix in aerogelgreatly restricts the gas molecules free movement. The resultsshow that Eq. (8) derived by Zeng et al. [22,23] is a perfect depic-tion of gaseous thermal conductivity in aerogel. The gaseous con-ductivity of aerogel decreases greatly with the drop of pressureand reaches zero at about 104 Pa, which decreases dramaticallyfaster than gaseous conductivity in xonotlite-type calcium silicatefor the nanoporous structure features of aerogel.

Figure 5 depicts the pressure dependence of gaseous conductiv-ity in the composite insulation materials, where the experimentalgaseous conductivity data includes both xonotlite-aerogel and ce-ramic fiber-aerogel composite insulation materials. It is shownthat both Eqs. (5) and (8) do not match well with the experimentalresults. Generally, the gaseous conductivity of composite insula-tion materials should have the same trend as aerogel with a varia-tion of pressure if xonotlite-type calcium silicate and ceramic fiberare filled fully with aerogel. Here, it does not meet this variation

because the aerogel does not fill xonotlite-type calcium silicateand ceramic fiber materials entirely, and some micro level poresstill exist in the composite insulation materials. All of the experi-mental data show that the gaseous conductivity decreases dis-tinctly with the drop of pressure for xonotlite-type calcium, aero-gel, and the composite insulation materials. This indicates thatgaseous conductivity still contributes significantly to the totalthermal conductivity of these kinds of insulation materials.

Concluding Remarks

Gaseous conductivity is one of the main contributors to thethermal conductivity of silica aerogel and its composite insulationmaterials, well known for their high porosity (>90%) and open-cell structures, especially at ambient temperature. Many studies

have researched materials preparation, thermal conductivity anal-ysis, and measurement for these kinds of insulation materials dur-ing the past decade. However, the gaseous conductivity in theseinsulation materials is rarely discussed comprehensively. In thisstudy, the gaseous conductivities confined in silica aerogel and itscomposite insulation materials are measured at different pressureswith the THS method. Expressions derived based on the kinetictheory are used to analyze gaseous conductivity and comparethe outcomes to experimental results. It is shown that both thegaseous conductivity of xonotlite-type calcium silicate and silicaaerogel decreases significantly with the drop of pressure. The the-oretical gaseous conductivity expressions match well with the ex-perimental results of xonotlite-type calcium silicate and silicaaerogel, respectively, but do not match with the experimental

Fig. 3 Pressure dependence of gaseous conductivity in xonot-lite-type calcium silicate

Fig. 5 Pressure dependence of gaseous conductivity in thecomposite insulation materials

Fig. 4 Pressure dependence of gaseous conductivity in silicaaerogel

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results for the composite insulation materials. This indicates thatthe aerogel does not completely fill the composite insulation mate-rial samples prepared using the vacuum dipping technology, andsome microlevel pores still exist. The uncertainty analysis showsthat the measurement error of the thermal conductivity determina-tion is less than 3%.

Acknowledgment

The authors wish to express their appreciation to Dr. HailongYang for his help with the materials preparation. This researchwas financially supported by the National Natural Science Foun-dation of China (No. 50806021), the Fundamental Research Fundsfor the Central Universities (No. 10MG22) and the National BasicResearch Program of China (2009CB219804).

Nomenclature

dg diameter of a gas molecule, mkB Boltzmann constant, J=K

Kn Knudsen numberK thermal conductivity, W=(m K)lm mean free path, mng number density of gas moleculesP power, WPr Prandtl numberp pressure, PaS specific surface area, m2=kgT temperature, Kt time, sq density, kg=m3a accommodation coefficientd characteristic system size, mc ratio of gasf constant/ porosity

Subscripts

g gasw wall

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Journal of Heat Transfer APRIL 2012, Vol. 134 / 041301-5
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041301_1