Characterizing microstructure of refractory porous materials
J M A T E R S C I41(2006)3403–3415
Characterizing microstructure of refractory
porous materials
XIN CHEN,DAYAKAR PENUMADU?
Civil and Environmental Engineering Department,University of Tennessee,223Perkins Hall, Knoxville,TN37996,USA
E-mail:dpenumad@https://www.sodocs.net/doc/946888458.html,
Published online:12April2006
Liquid Expulsion technique was used in this study to quantify the transport properties and microstructure of a refractory coating used in the Lost Foam Casting process.The pore size information obtained from the Liquid Expulsion Method is found to be well correlated with the transport properties of the porous coating material.For manufacturing process control,the viscosity of these coating slurries prior to its application on expanded polystyrene foam is often reduced by dilution with water and/or using a dispersant.In this paper,the effects of diluting or dispersing the slurry on the microstructure and transport properties of the dried refractory coatings are evaluated.Results show that the dilution and dispersion have opposing in?uences on the pore size and transport properties.Adding dispersant was found to reduce the transport properties of the refractory coatings signi?cantly,potentially leading to defects in metal castings.The pore characterization technique developed in this paper is also used to determine the effects of drying methods(oven versus air dry)on the pore size and transport properties.
C 2006Springer Science+Business Media,Inc.
1.Introduction
Microstructure is one of the important factors governing the transport behavior of a porous medium,such as its Darcy coef?cient,and the related properties such as ther-mal conductivity and density.Therefore,it is necessary to understand the microstructure of porous media such as the pore size and distribution.A number of experimental tech-niques and commercial instruments are available for de-termining pore size distribution,such as:Scanning Elec-tron Microscopy(SEM),Mercury Intrusion Porosimetry (MIP),the Bubble pressure and gas transport method,Gas Absorption,and the Liquid Displacement Method(LDM) [1–3].In a porous medium that originates from drying of slurries,voids exist as the spaces between the particles. Some of them are connected to each other,forming the channels for the air/liquid to pass through,which are con-sidered effective pores.Some voids are isolated and not open to the atmosphere and are considered ineffective pores.For a porous medium,the transport properties are particularly related to the effective pores in the porous structure.Therefore,the effective pore size and pore size distribution are important for understanding the physical behavior of a porous medium.
?Author to whom all correspondence should be addressed.
In this paper,a technique known as water-expulsion porosimetry,also called the Liquid Expulsion method, proposed by Gelinas and Angers[4],was used to charac-terize the microstructure information of ceramic coatings. The results from this study are compared with those ob-tained using the mercury intrusion method.The major purpose of this paper was to investigate the applicability of such a technique for refractory porous materials used in foundry industries.The relationship between the exper-imentally determined pore size information and the cor-responding transport properties of these refractory porous materials was also investigated.In addition,this paper also studied the in?uences of dilution/dispersion and different drying procedures(oven and air)on the microstructure and transport properties of lost foam casting coatings. 2.Background
In this work,the applicability of the Liquid Expulsion Method was investigated to evaluate the microstructure of refractory coatings used in a relatively new metal cast-ing technique called Lost Foam Casting(LFC).LFC,also known as Expandable Polystyrene Casting(EPC),is a
0022-2461C 2006Springer Science+Business Media,Inc.
DOI:10.1007/s10853-005-5342-93403
popular casting method being used as a replacement for the conventional casting techniques to obtain near net-shape metal castings.The casting products are produced by pouring molten metal into a foam pattern that is coated with refractory material,which is then surrounded and compacted by unbonded sand through vibration.The foam pattern degrades into gas and vents into the loose sand af-ter the molten metal is introduced,and the metal then?lls the foam pattern to get the?nal product.In order to ensure the adequate thermal properties of?lling molten metal and the venting of pyrolysis products,the EPS foam pattern is coated with refractory slurry.The refractory coating has to be strong enough to resist the pressure to avoid metal pen-etration defects.At the same time it should have adequate transport properties to allow the escape of the degraded materials(styrene gas predominantly)to avoid defects in the metal casting,such as mis-runs,folds,and porosity [5–14].These refractory coatings are initially applied to the polystyrene foam patterns in a slurry stage and are allowed to dry.The microstructure of these porous mate-rials is complex and affects the mechanical strength and transport properties of the refractory coating.Therefore, the characterization of pore size and pore size distribution is important for developing new and novel coatings and also for manufacturing process control in LFC foundries.
3.Experiments
Mercury Intrusion Porosimetry has been widely used in the past as a technique to characterize the microstructure of porous media[15–18].Thus,this paper includes com-parison results from the Mercury intrusion method and the Liquid Expulsion Method developed in this study. Non-wetting material such as mercury is used in the Mercury Intrusion Method.As a non-wetting material, mercury will not spontaneously wet most surfaces or en-ter the pores in a solid because of its high surface ten-sion.In order to?ll the pores with mercury,external pressure is needed to force mercury into the pores.If a cylindrical pore model is assumed,the relationship be-tween pressure and pore size is given by the Washburn equation[20].Because the sizes of the pores that can be?lled with mercury are inversely proportional to the applied pressure,mercury intrudes the bigger pore?rst and,successively,the smaller ones with in-creasing pressures.Thus,the pore size distribution can be determined by monitoring the volume of intruded mercury as a function of increasing applied pressure [19].In this study,the pore size analysis was eval-uated by a Poromaster60(Quantachrome Corpora-tion),which can generate a maximum intrusion pres-sure of413.7Mpa for pore size analysis from approx-imately950microns to0.0036microns equivalent pore diameter.
According to Hernandez et al.[21],Bechhold et al.
[22]were the?rst to use the Liquid Expulsion Method to evaluate pore size by measuring the pressure to blow air through water-?lled https://www.sodocs.net/doc/946888458.html,tely,the Liquid Expulsion Method has been modi?ed in several ways and adopted by ASTM and British Standards Institu-tion for determining pore size characteristics of porous materials[23–25].The Liquid Expulsion Method uses a wetting liquid instead of a non-wetting liquid to mea-sure pore size.The wetting liquids will spontaneously ?ow into pores in the solid,and work is required to re-move the wetting liquid from the pores.A relationship between the applied pressure,the?ow rate of the air through saturated porous materials,and pore size can be used to estimate the pore size distribution of porour materials.
In this work,the pore size analysis was investigated by a Capillary Flow Porometer(Porous Material Inc.)
[26]and a portable automated porometry system de-veloped at the University of Tennessee[27],which can generate pressure to 3.45MPa for pore size analy-sis from over500micron to0.013micron pore di-ameter.The sample was soaked in a wetting liquid (Galwick)of low surface tension(γ=0.0156N/m),low vapour pressure and low reactivity.The saturated sample was then subjected to increasing pressure.As the pres-sure increases,it will reach a point where applied pressure overcomes the surface tension of the liquid in the largest pores and will push the liquid out.This minimum pres-sure required to push the liquid out from largest effective pore and make the?rst detectable?ow is called“bub-ble pressure,”which is used to calculate the“bubble pore size”—the maximum pore size.Continuing to increase the pressure further allows the air to empty smaller pores.By testing the sample both in the dry condition and the satu-rated(wet)condition,it is possible to obtain a plot of?ow rate versus applied pressure,as illustrated in Fig.1.When the applied pressure empties all of the pores saturated with Galwick,the?ow rate vs.pressure curve(?ow-pressure curve)will return to the?ow-pressure curve of the dry sample.By comparing the gas?ow rate of both a wet and dry sample at the same pressure,the percentage of the?ow passing through the sample caused by the
pores Figure1Typical?ow rate versus applied pressure for wet and dry samples.
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larger than or equal to the speci?ed size can be calculated as:
%Filter Flow Percentage =
wet ?ow rate
dry ?ow rate
×100(1)
The ?ow caused by the pore size in a certain range between d1and d2can also be calculated as
%Filter Flow Percentage (d 2?d 1)
= Q w 2Q d 2?Q w 1Q d 1
×100
(2)
The mean ?ow pore size is determined by the inter-section of a wet ?ow-pressure curve and a half dry ?ow-pressure curve,where the ?ow rate through the wet sample
is one half of the ?ow rate through the dry sample at the same pressure.The corresponding pressure is called the mean ?ow pressure.
3.1.Evaluation of transport properties
Transport properties of porous materials are generally characterized using their permeability coef?cients.In this work,Forchheimer’s equation [28]is used to calculate the permeability coef?cient of the refractory LFC coatings.Forchheimer’s equation has proven to be more appropri-ate for estimating the transport properties of the refractory LFC coating in a relatively wide range of applied pres-sures [27],since it includes parabolic parts in the equation by considering the in?uence of inertia and turbulence.Forchheimer’s equation can be written as
P 2i ?P 2
02P L =μk 1νs +ρk 2
ν2
s .
(3)
where ρis the ?uid density;constant k 1and k 2are the Darcian (viscous)permeability and non-Darcian (inertia)permeability coef?cients,respectively;νs is the ?uid ve-locity,calculated by dividing the exit volumetric ?ow rate Q by the cross-sectional area A .μis the viscosity of the ?uid.P i is the pressure at the sample entrance;P o is the pressure at the sample exit;and P is the ?uid pressure at which Q and μare measured or calculated.In gen-eral,P equals to P o .L is the coating thickness.In this research,permeability coef?cients were obtained by ?t-ting experimental data through the least squares method to Equation 3.
The term “?ow factor”as de?ned in Equation 4was developed in this study for transport property comparison purposes for coating materials of differing composition.It not only considers the effect of the material’s microstruc-ture (for example,Darcian permeability coef?cient)but also considers another key factor controlling the coating’s transport properties,its average thickness.This “?ow fac-tor”can be used to compare different types of coatings’
transport properties at the same differential pressure.A large “?ow factor”indicates high transport capability.
Flow Factor =
k 1L
(4)
3.2.Sample preparation
In this work,fourteen different types of Lost Foam Casting refractory coating have been investigated.These slurries were produced for two major automotive Powertrain LFC foundries by three commercial suppliers.These coating slurries were used for different parts,such as an engine block or a cylinder head.These water-based coatings con-sist of silica,mica,binding clay,synthetic ceramic parti-cles,and some latex binders with solids percentages of 40to 62%.
In order to investigate the dilution and dispersion ef-fects,5%of water by volume was added to the synthetic coating H to obtain the diluted synthetic coating H.Simi-larly,1%of dispersant (CALGON)by weight was added to the synthetic coating H to obtain the dispersed synthetic coating H.In addition,some data collected from a man-ufacturing facility dealing with casting 4cylinder blocks and head are also included in this study.
The coating samples were obtained by dipping a 100×100stainless steel mesh disc of 6.51cm diame-ter into the coating slurries,whose rheological properties were well controlled and studied.The steel mesh has very high permeability,which will not affect the measuring results for the coating permeability.The dipped coating discs were then dried at room temperature.After drying,the thickness of each coating was measured by using a 0–2.54cm micrometer (with a resolution of 0.00254mm).In order to investigate the oven-dry effects on the coating permeability,samples of coatings B and H that were dried at room temperature (25?C)and in an oven at 60?C were individually prepared for comparison purposes.
4.Results and discussion
https://www.sodocs.net/doc/946888458.html,parison of the Mercury Intrusion
Method and the Liquid Expulsion method Fig.2compares the pore side distributions measured by the Mercury Intrusion Method and Liquid Expulsion Method for coatings B and H.It shows that a major-ity of the intruded mercury (87%)volume for coating H correspond pores with a diameter of 5um or higher (up to 150um);while for coating B the pores with a diameter larger than 5um correspond to only 45%in-trusion of volume.This indicates that the pore diameters of coating B are smaller compared to the pore diameters of coating H.Based on theory discussed earlier,the ?l-ter ?ow percentage can be calculated as shown in Fig.2according to Equation 1,which shows that the detectable effective pores were smaller than 15um for both coat-ings B and H.It also shows that the pores of coating B are ?ner than those of coating H.Fig.3shows the ?ow
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Figure 2Comparison of pore size distributions determined by Mercury Intrusion Method and Liquid Expulsion
Method.
Figure 3Flow rate against applied pressure curves for coating B and H.
rate versus applied pressure curves obtained by the Liq-uid Expulsion Method for these two coatings (B and H).The air ?ow rate versus differential pressure data clearly show that coating H is more permeable than coating B.It can also be seen that the ?ow rate of the wet sample increases with increasing pressure as pores saturated ini-tially with Galwick are being emptied with higher gas pressure.In this study,considering the strength of coat-ing samples,the maximum pressure applied on the sam-ples was set at 76kpa.Although 76kPa was not high enough to expel Galwick from the wet sample pores completely,it was suf?cient to obtain the bubble pore
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size and the mean pore size information,with the mea-sured pressure range being identical for both coatings. Table I lists the comparison of pore size determined by the Mercury Intrusion Method and the Liquid Expulsion Method.It can be seen that the?ow factor is a valuable indicator to evaluate the transport properties of the re-fractory coatings.There are differences in microstructure information(pore size)determined by the Mercury Intru-sion Method and the Liquid Expulsion Method,in that the Mercury Intrusion Method shows relatively larger pores than those detected by the Liquid Expulsion Method.
It is not surprising that the results from the Mer-cury Intrusion Method and the Liquid Expulsion Method are not in quantitative agreement.In the Mercury In-trusion Method,when pressure increases,the mercury will intrude the bigger pores?rst and then the smaller pores,which does not take into consideration whether the pores are permeable to liquid or not.Therefore, the non-effective(blind)pores may be detected in the Mercury Intrusion Method,thereby contributing to the calculation of the pore size distribution.However,the Liq-uid Expulsion Method only measures the effective pores, which means the pore size distribution obtained by the Liquid Expulsion Method only accounts for the perme-able pores.For this reason,the Liquid Expulsion Method will be more suitable for the study of materials’transport properties,which is critical for refractory coating mate-rials used in LFC foundries.In reality,most of the pores in a porous medium will not be made of straight tubes of varying diameters.The typical pore channel shapes for a given coating are qualitatively illustrated in Fig.4.Pore type d shown in Fig.4is a blind pore,which will not contribute to the transport properties;however,the Mer-cury Intrusion Method will still measure it.The Liquid Expulsion Method only detects those pores which are to-tally open through the coating thickness;therefore,pores a–c in Fig.4will be detected only if the pressure reaches a certain point to push the liquid out through the con-stricted portion of the pore channels.Thus,the pore size measured by the Liquid Expulsion Method is the smallest diameter of the whole pore channel.However,the Mer-cury Intrusion Method may consider such a pore as several different-sized pores.For example,pore a and b will be individually considered as3pores of different sizes.Pore c might be detected as dozens of pores varying in size. In order to analyze small pores,very high pressure is applied in the Mercury Intrusion Method,which may dis-tort the microstructure of tested samples[21].The high pressure may deform some pores and even make them collapse.In addition,the Mercury Intrusion Method has a relatively low resolution at larger pore sizes[29].Mea-surements of the maximum pore size(bubble pore size) by the Mercury Intrusion Method will not be as accurate as those obtained from the Liquid Expulsion Method.The differences mentioned above explain the reasons that the Mercury Intrusion Method might give relatively larger size ranges for pores than those detected by the Liquid Expulsion Method.
Although differences exist between the Mercury In-trusion Method and the Liquid Expulsion Method,both methods tend to indicate that coating H had relatively larger pores than coating B,which is also con?rmed by images obtained from the Scanning Electron Microscope. Comparing Figs5and6,it can be seen that the surface of coating B is fairly smooth,while the surface of coating H is particularly rough.It is reasonable to assume that particle shape is one of the factors in?uencing pore size distribution.Coating B is mainly based on mica,which is?aky;while the majority of particles in coating H are silica,which is bulky.Bulky particles might more easily tend to construct voids between particles,which form tun-nels for gas/liquid to pass through.Since any porous mate-rial may contain both?ow-through pores and blind-pores, the maximum of the PSD obtained from liquid-expulsion porometry is usually shifted toward smaller pores as com-pared with mercury intrusion technique[30].
4.2.Pore shape factor
From Figs5and6,it can also be seen that most of the pores do not have cross-section that mimics a circle,an implicit assumption for interpretation.Therefore,a pore shape factor is often proposed to consider the non-circular cross section.If the pore section is considered to be ellip-
T A B L E I Comparison of pore size determined by Mercury intrusion method and liquid expulsion method
Thickness Bubble
pressure(KPa)
Permeability
coef?cient Flow factor Bubble pore size(um)Mean pore size(um)
Sample(mm)LEM LEM MIP LEM MIP(Darcy)(Darcy/mm) Coating B0.559 5.7411.15149.00 1.06 4.410.0130.022
Coating H0.503 3.8616.59146.00 2.0118.900.027
0.053
Figure4In?uences of pore channel shape on pore size determination.
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Figure 5Surface microstructures image of coating
B.
Figure 6Surface microstructure image of coating H.
tical with minor axis d and major axis nd ,the following relationship exists:
d S
dV
=
1d ·8·(1+n )n 2
(5)
The pore shape factor can be de?ned as
λ=d D
=
1+n 2·n (6)
Some typical values of the pore shape factor are listed
in Table II .In the following part of this paper,all the pore sizes have been assumed to have n value of 7,and thus the results based on cylindrical pore shape are multiplied using a pore shape factor of 0.715.
4.3.Correlation between bubble pore size,
mean pore size and ?ow factor
In this work,it was found that useful relationships exist between bubble pore size,mean pore size and ?ow fac-tor.As shown in Fig.7,the mean pore size increases as
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T A B L E I I Pore shape factor
Pore cross section
n
Shape factor λ(d =λD
)
1
12
0.7914
0.7297
0.714
Figure 7Bubble pore size vs.mean pore size for coating B and H.
the bubble pore size increases for coating B and H.The data collected at a manufacturing facility using the liquid expulsion technique described in this paper for coatings I,LB,LH and T are shown in Fig.8.These data show that mean pore size increases with the increased bub-ble pore size.However,coating LH did not demonstrate this trend signi?cantly,which might be attributed to the bulky-shaped particles in coating LH.The majority of the particles in coating I,LB and T were ?aky-shaped particles,mica.During the dipping and drying process,the ?aky-shaped particles might demonstrate relatively organized orientations,which might cause the consistent trend between bubble pore sizes and mean pore sizes.However,coating LH mainly consisted of bulky-shaped particles,silica.During the dipping and drying process,these bulky-shaped particles might have all kinds of ori-entations,which might disrupt the trend between bubble pore sizes and mean pore sizes.
A strong relationship was also observed between ?ow factor,bubble pore size and mean pore size as shown in Fig.9through Fig.13,which indicates that it is possible to predict the transport properties (?ow factor in this study)by measuring the microstructure information (pore size in this study)of refractory LFC coatings.As shown in Fig.11,linear regression gives R 2=0.81for an assumed linear relationship between ?ow factor and mean pore size for coatings
B and H,which suggests that 81%of the changes in ?ow factor can be explained by the changes of mean pore size for the samples prepared and studied in the laboratory of the authors.In contrast,the data col-lected at a manufacturing process control facility for 8types of commercial refractory LF
C coatings as shown in Fig.12seem to ?t two linear trends,both of which demon-strate fairly good linearity (R 2≥0.81).In addition,the linear regression equations obtained for 8types of com-mercial refractory LFC coatings seem to work fairly well for coating I,LB,LH and T,which are the refractory LFC coatings currently used at this metal casting facility.Although R 2=0.32is relatively poor for coating LH,the variations between the predicted ?ow factor using the
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Figure 8Bubble pore size vs.mean pore size for coating I,LB,LH and
T.
Figure 9Flow factor vs.bubble pore size for coating B and H.
linear equation in Fig.12and the measured ?ow factor are within ±30%,as shown in Fig.14.The reason for the inconsistent behavior for coating LH is not clear yet;however,the overall results do imply that the linear re-lationship between ?ow factor and mean pore size does exist but might not be able to be predicted by a unique
equation that is universal to coating component varia-tions.The analysis of the bubble pore size and mean pore size data provides valuable insight for understanding a relationship between the microstructure and the transport properties of these complex multi-component refractory LFC coatings.
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Figure 10Flow factor vs.bubble pore size for coating I,LB,LH and
T.
Figure 11Flow factor vs.mean pore size for coating B and H.
4.4.Effect of dilution and dispersion
In LFC foundries,the coating slurries shipped from suppliers are normally concentrated,and have a viscosity higher than what is used for actual coating purposes.
Generally,operators in LFC foundries will add water and/or dispersant to these concentrated slurries to obtain desirable rheological data (?ows well,does not drip,and levels without sagging).Therefore,it is essential
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Figure12Flow factor vs.mean pore size for various coatings.
to investigate the effects of dilution and dispersion on the transport properties of refractory coatings.In this study,5%of water by volume was added to the synthetic coating H to obtain diluted synthetic coating H.Similarly,1%of dispersant(CALGON)by weight was added to the synthetic coating H to obtain the dispersed synthetic coating H.Results shown in Table III suggest that adding dispersant may reduce the bubble pore size
as
Figure13Flow factor vs.mean pore size for coating I,LB,LH and T.
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Figure14Percent variance of predicted?ow factor for coating LH.
well as mean pore size;correspondingly,the?ow factor declines.In contrast,adding only water tends to increase the bubble pore size and mean pore size,which simul-taneously raises the?ow factor.This study suggests that adding dispersant will reduce the pore size and transport properties although adding dispersant might get similar rheological performance(viscosity values at a target rpm)as can be obtained by simply diluting with water.
4.5.Effect of drying process
Generally,oven and air drying are two practical ap-proaches used in LFC foundries.Table IV shows the comparison data for two drying techniques for the two coatings B and H.Oven drying at60?C slightly increases the bubble pore size as well as the mean pore size;however,it does not signi?cantly affect the transport properties(?ow factor).Therefore,it is reasonable to con-clude that oven versus air drying processes do not have substantial differences on the pore size and transport prop-erties.It will be interesting to perform similar studies for other drying techniques such as freeze and critical point drying.This could shed new light on obtaining desirable properties by varying the drying process.The equipment and procedures developed in this study will be valuable for generating such data.
5.Conclusion
In this study,the applicability of the Liquid Expulsion Method was investigated for refractory LFC coatings.The results have shown that the Liquid Expulsion Method is more suitable to characterize the“effective pore”https://www.sodocs.net/doc/946888458.html,pared to the Mercury Intrusion Method,the Liquid Expulsion Method has the following advantages: (1)No toxic liquid(Mercury)is used;(2)It is a non-destructive test;the sample is not damaged or contam-inated;(3)Only effective pores are detected;therefore, this technique is more appropriate to characterize the mi-crostructure of porous material for transport behavior. Results from this study have also suggested that useful relationships can be derived between?ow factor,bubble pore size and mean pore size.This has implications for using fewer variables such as a bubble pore size and mean pore size as good indicators to understand the relationship between the microstructure and the transport properties of refractory LFC coatings.The present study also found that the dilution and dispersion have opposing in?uences on the pore size and permeability.The dispersant should be used cautiously in LFC foundries because it might reduce the transport properties of the refractory coatings.No sig-ni?cant differences between oven and air dry processes were found for interpreted and measured parameters us-ing Liquid Expulsion Method for refractory coatings used in Lost Foam Casting.
SYMBOLS LIST
d1pore diameter corresponding to applied pressure P1
d2pore diameter corresponding to applied pressure P2
Q w1?ow rate measured for wet sample corresponding to applied pressure P1
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T A B L E I I I Dilution and dispersion effects on pore structure
Sample Thickness
(mm)
Bubble pore size
(um)
Mean pore size
(um)
Permeability
coef?cient(Darcy)
Flow factor
(Darcy/mm)
Coating H diluted0.43216.23 1.510.0280.065 Coating H dispersed0.30110.570.830.0100.035 Coating H original0.43611.10 1.320.0200.047 T A B L E I V Comparison of oven-dry and room-dry process results
Sample Thickness
(mm)
Bubble pore size
(um)
Mean pore size
(um)
Permeability
coef?cient(Darcy)
Flow factor
(Darcy/mm)
Oven-dry coating B0.4808.750.850.0160.033 Room-dry coating B0.4798.270.750.0160.033 Oven-dry coating H0.50210.55 1.190.0240.048 Room-dry coating H0.4949.71 1.100.0200.040
Q w2?ow rate measured for wet sample corresponding to applied pressure P2
Q d1?ow rate measured for dry sample corresponding to applied pressure P1
Q d2?ow rate measured for dry sample corresponding to applied pressure P2
P1applied pressure at point1
P2applied pressure at point2
ρ?uid density
k1Darcian(viscous)permeability coef?cient
k2non-Darcian(inertia)permeability coef?cient
ν?uid velocity
Q volumetric?ow rate
A sample cross-sectional area
μthe viscosity of the?uid
P i the pressure at the sample entrance
P o the pressure at the sample exit
P the?uid pressure at which Q andμare measured or calculated
L sample thickness
dS differential of pore area
dV differential of pore volume
d minor axis of elliptical or por
e diameter
n the ratio of major axis to minor axis
λPore Shape Factor
Acknowledgments
The authors gratefully acknowledge the?nancial sup-port received from the US Department of Energy and New York State Energy Research Development Author-ity(NYSERDA)under the project NICEEE(DE-FG41-01R110926),and help from General Motors Powertrain. The authors would also like to gratefully acknowledge the involvement,support and encouragement from the project team members:Mr.Ross M.Johnson,Dr.Calvin C.John-son,Mrs.Joanna Jenack,Mr.Mahboob Murshed,and Mr. Mark Hoover.The authors would also like to thank the lost foam coating suppliers for providing the refractory coatings,Dr.Xiaohu Tang for assistance with the Scan-ning Electron Microscope and Dr.Jingyao Cao for sharing some valuable opinions.The opinions expressed in this paper are only those of listed authors and do not re?ect the opinions of the acknowledged team members or project sponsors
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Received3November2004
and accepted7July2005
3415
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萧楚女 11、人的一生可能燃烧也可能腐朽，我不能腐朽，我愿意燃烧起来！——奥斯特洛夫斯基 12、风前有恨梅千点，沙上无人月一痕。——谭知柔《晚醉口占》 13、我给我母亲添了不少乱，但是我认为她对此颇为享受。——马克·吐温 14、恨芳菲世界，游人未赏，都付与，莺和燕。——陈亮 15、在孩子们的口头心里，母亲就是上帝的名字。——萨克雷 16、欣赏，这就是为着一件事物本身而爱好它，不为旁的理由。——达·芬奇 17、你若要喜爱你自己的价值，你就得给世界创造价值。——歌德 18、我们往往只欣赏自然，很少考虑与自然共生存。——王尔德 19、人生就象弈棋，一步失误，全盘皆输，这是令人悲哀之事；而且人生还不如弈棋，不可能再来一局，也不能悔棋。人生就是跋涉，人生就是开拓，人生就是与苦难争斗角逐；假如因我们承受苦难，能使后代免于受苦，那就是我们无上的幸福。 20、世界上的一切光荣和骄傲，都来自母亲。——高尔基 21、我之所有，我之所能，都归功于我天使般的母亲。——林肯
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