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Thermal conductivity of porous materials

Published online by Cambridge University Press:  03 July 2013

David S. Smith*
Affiliation:
Groupe d’Etude des Matériaux Hétérogènes (GEMH), ENSCI, Centre Européen de la Céramique, 87068 LIMOGES Cedex, France
Arnaud Alzina
Affiliation:
Groupe d’Etude des Matériaux Hétérogènes (GEMH), ENSCI, Centre Européen de la Céramique, 87068 LIMOGES Cedex, France
Julie Bourret
Affiliation:
Groupe d’Etude des Matériaux Hétérogènes (GEMH), ENSCI, Centre Européen de la Céramique, 87068 LIMOGES Cedex, France
Benoît Nait-Ali
Affiliation:
Groupe d’Etude des Matériaux Hétérogènes (GEMH), ENSCI, Centre Européen de la Céramique, 87068 LIMOGES Cedex, France
Fabienne Pennec
Affiliation:
Groupe d’Etude des Matériaux Hétérogènes (GEMH), ENSCI, Centre Européen de la Céramique, 87068 LIMOGES Cedex, France
Nicolas Tessier-Doyen
Affiliation:
Groupe d’Etude des Matériaux Hétérogènes (GEMH), ENSCI, Centre Européen de la Céramique, 87068 LIMOGES Cedex, France
Kodai Otsu
Affiliation:
Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, Aichi, 466-8555 Japan
Hideaki Matsubara
Affiliation:
Japan Fine Ceramics Center, Atsuta, Nagoya, 456-8587 Japan
Pierre Elser
Affiliation:
De Cavis Ltd., 8093 Zürich, Switzerland
Urs T. Gonzenbach
Affiliation:
De Cavis Ltd., 8093 Zürich, Switzerland
*
a)Address all correspondence to this author. e-mail: david.smith@unilm.fr
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Abstract

Incorporation of porosity into a monolithic material decreases the effective thermal conductivity. Porous ceramics were prepared by different methods to achieve pore volume fractions from 4 to 95%. A toolbox of analytical relations is proposed to describe the effective thermal conductivity as a function of solid phase thermal conductivity, pore thermal conductivity, and pore volume fraction (νp). For νp < 0.65, the Maxwell–Eucken relation for closed porosity and Landauer relation for open porosity give good agreement to experimental data on tin oxide, alumina, and zirconia ceramics. For νp > 0.65, the thermal conductivity of kaolin-based foams and calcium aluminate foams was well described by the Hashin Shtrikman upper bound and Russell’s relation. Finally, numerical simulation on artificially generated microstructures yields accurate predictions of thermal conductivity when fine detail of the spatial distribution of the phases needs to be accounted for, as demonstrated with a bio-aggregate material.

Type
Invited Papers
Copyright
Copyright © Materials Research Society 2013 

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References

REFERENCES

Schulle, W. and Schlegel, E.: Fundamentals and properties of refractory thermal insulating materials (High-temperature insulating materials), in Ceramic Monographs – Handbook of Ceramics, Supplement to Interceram. 40(7), No. 2.6.3, 112 (1991).Google Scholar
Smith, D.S., Fayette, S., Grandjean, S., Martin, C., Telle, R., and Tonessen, T.: Thermal resistance of grain boundaries in alumina ceramics and refractories. J. Am. Ceram. Soc. 86, 105111 (2003).CrossRefGoogle Scholar
Yang, H.S., Bai, G.R., Thompson, L.J., and Eastman, J.A.: Interfacial thermal resistance in nanocrystalline yttria stabilized zirconia. Acta Mater. 50, 23092317 (2002).CrossRefGoogle Scholar
Michot, A., Smith, D.S., Degot, S., and Gault, C.: Thermal conductivity and specific heat of kaolinite: Evolution with thermal treatment. J. Eur. Ceram. Soc. 29, 347353 (2008).Google Scholar
Charvat, F.R. and Kingery, W.D.: Thermal conductivity: XIII, effect of microstructure on conductivity of single-phase ceramics. J. Am. Ceram. Soc. 40, 306315 (1957).CrossRefGoogle Scholar
Bourret, J., Prudhomme, E., Rossignol, S., and Smith, D.S.: Thermal conductivity of geomaterial foams based on silica fume. J. Mater. Sci. 47, 391396 (2012).CrossRefGoogle Scholar
Carslaw, H.S. and Jaeger, J.C.: Conduction of Heat in Solids (Oxford University Press, London, 1959).Google Scholar
Assael, M.J., Dix, M., Gialou, K., Vozar, L., and Wakeham, W.A.: Application of the transient hot-wire technique to the measurement of the thermal conductivity of solids. Int. J. Thermophys. 23(3), 615633 (2002).CrossRefGoogle Scholar
Gustafsson, S.: Transient plane source techniques for thermal conductivity and thermal diffusivity measurements of solid materials. Rev. Sci. Instrum. 62(3), 797804 (1991).CrossRefGoogle Scholar
Degiovanni, A.: Thermal diffusivity and flash method. Rev. Gen. Therm. 185, 420441 (1977).Google Scholar
Parker, W.J., Jenkins, R.J., Butler, C.P., and Abbott, G.L.: Flash method of determining thermal diffusivity, heat capacity, and thermal conductivity. J. Appl. Phys. 32(9), 16791684 (1961).CrossRefGoogle Scholar
Klemens, P.G.: Thermal conductivity and lattice vibrational modes. Solid State Phys. 7, 198 (1958).CrossRefGoogle Scholar
Berman, R.: The thermal conductivity of some polycrystalline solids at low temperatures. Proc. Phys. Soc. London, Sect. A 65, 10291040 (1952).CrossRefGoogle Scholar
Raghavan, S., Wang, H., Dinwiddie, R.B., Porter, W.D., and Mayo, M.J.: The effect of grain size, porosity and yttria content on the thermal conductivity of nanocrystalline zirconia. Scr. Mater. 39, 11191125 (1998).CrossRefGoogle Scholar
Kittel, C.: Interpretation of the thermal conductivity of glasses. Phys. Rev. 75, 972974 (1949).CrossRefGoogle Scholar
Fleig, J. and Maier, J.: A finite element study on the grain boundary impedance of different microstructures. J. Electrochem. Soc. 145, 20812089 (1998).CrossRefGoogle Scholar
Smith, D.S., Grandjean, S., Absi, J., Founyapte Tonyo, S., and Fayette, S.: Grain boundary thermal resistance in polycrystalline oxides: Alumina, tin oxide and magnesia. High Temp. High Press. 3536, 9399 (2004).Google Scholar
Young, D.A. and Maris, H.J.: Lattice-dynamical calculation of the Kapitza resistance between fcc lattices. Phys. Rev. B: Condens. Matter 40, 36853693 (1989).CrossRefGoogle ScholarPubMed
Collishaw, P.G. and Evans, J.R.G.: An assessment of expressions for the apparent thermal conductivity of cellular materials. J. Mater. Sci. 29, 22612273 (1994).CrossRefGoogle Scholar
Loeb, A.L.: Thermal conductivity: VIII, a theory of thermal conductivity of porous materials. J. Am. Ceram. Soc. 37, 9699 (1954).CrossRefGoogle Scholar
Maxwell, J.: A Treatise on Electricity and Magnetism (Clarendon Press, Oxford, 1892).Google Scholar
Hashin, Z. and Shtrikman, S.: A variational approach to the theory of the effective magnetic permeability of multiphase materials. J. Appl. Phys. 33, 31253131 (1962).CrossRefGoogle Scholar
Rayleigh, L.: On the influence of obstacles arranged in rectangular order upon the properties of medium. Philos. Mag. 5(34), 481502 (1892).CrossRefGoogle Scholar
Landauer, R.: The electrical resistance of binary metallic mixtures. J. Appl. Phys. 23, 779784 (1952).CrossRefGoogle Scholar
Ticha, G., Pabst, W., and Smith, D.S.: Predictive model for the thermal conductivity of porous materials with matrix-inclusion type microstructure. J. Mater. Sci. 40, 50455047 (2005).CrossRefGoogle Scholar
Russell, H.: Principles of heat flow in porous insulators. J. Am. Ceram. Soc. 18, 15 (1935).CrossRefGoogle Scholar
Ashby, M.F.: The properties of foams and lattices. Philos. Trans. R. Soc. London, Ser. A 364, 1530 (2006).Google ScholarPubMed
Litovsky, E., Shapiro, M., and Shavit, A.: Gas pressure and temperature dependances of thermal conductivity of porous ceramic materials: Part 2, refractories and ceramics with porosity exceeding 30%. J. Am. Ceram. Soc. 79(5), 13661376 (1996).CrossRefGoogle Scholar
Reichenauer, G., Heinemann, U., and Ebert, H.P.: Relationship between pore size and the gas pressure dependence of the gaseous thermal conductivity. Colloids Surf., A 300, 204210 (2007).CrossRefGoogle Scholar
Zeng, J.S.Q., Stevens, P.C., and Hunt, A.J.: Thin-film-heater thermal conductivity apparatus and measurement of thermal conductivity of silica aerogel. Int. J. Heat Mass Transfer 39(11), 23112317 (1996).CrossRefGoogle Scholar
Baillis, D. and Coquard, R.: Radiative and conductive thermal properties of foams, in Cellular and Porous Materials: Thermal Properties Simulation and Prediction, edited by A. Ochsner, G.E. Murch, and M.J.S. de Lemos (Wiley-VCH, Weinheim, 2008).Google Scholar
Grandjean, S.: Réponse thermique à l’échelle locale dans les matériaux céramiques, effets des pores et des joints de grains. Ph.D. Thesis, University of Limoges, 2002.Google Scholar
Turkes, P., Pluntke, C., and Helbig, R.: Thermal conductivity of SnO2 single crystals. J. Phys. C: Solid State Phys. 13, 49414951 (1980).CrossRefGoogle Scholar
Zivcova, Z., Gregorova, E., Pabst, W., Smith, D.S., Michot, A., and Poulier, C.: Thermal conductivity of porous alumina ceramics prepared using starch as a pore-forming agent. J. Eur. Ceram. Soc. 29, 347353 (2009).CrossRefGoogle Scholar
Nait-Ali, B., Haberko, K., Vesteghem, H., Absi, J., and Smith, D.S.: Thermal conductivity of highly porous zirconia. J. Eur. Ceram. Soc. 26, 35673574 (2006).CrossRefGoogle Scholar
Bourret, J., Tessier-Doyen, N., Nait-Ali, B., Pennec, F., Alzina, A., Peyratout, C.S., and Smith, D.S.: Effect of pore volume fraction on the thermal conductivity and mechanical properties of kaolin based foams. J. Eur. Ceram. Soc. 33(9), 14871495 (2013).CrossRefGoogle Scholar
Pennec, F., Alzina, A., Tessier-Doyen, N., Nait-Ali, B., and Smith, D.S.: Probabilistic thermal conductivity analysis of dense stabilized zirconia ceramics. Comput. Mater. Sci. 67, 207215 (2013).CrossRefGoogle Scholar
Krauss Juillerat, F., Gonzenbach, U.T., Studart, A.R., Gauckler, L.J.: Self-setting particle-stabilized foams with hierarchical pore structures. Mater. Lett. 64, 14681470 (2010).CrossRefGoogle Scholar
Gonzenbach, U.T., Studart, A.R., Tervoort, E., and Gauckler, L.J.: Ultrastable particle-stabilized foams. Angew. Chem. Int. Ed. 45, 35263530 (2006).CrossRefGoogle ScholarPubMed
Gonzenbach, U.T., Studart, A.R., Tervoort, E., and Gauckler, L.J.: Stabilization of foams with inorganic colloidal particles. Langmuir 22, 1098310988 (2006).CrossRefGoogle ScholarPubMed
Pennec, F., Alzina, A., Tessier-Doyen, N., Nait-Ali, B., Mati-Baouche, N., De Baynast, H., and Smith, D.S.: A combined finite-discrete element method for calculating the effective thermal conductivity of bio-aggregates based materials. Int. J. Heat Mass Transfer 60, 274283 (2013).CrossRefGoogle Scholar