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Highly porous cellular materials: A statistical model of geometric structure

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Inorganic Materials: Applied Research Aims and scope

Abstract

A comparative study of various idealized models for geometric structure of highly porous cellular materials is carried out. The study is based on statistical parameters describing the geometric structure of these materials. A tetrakis dodecahedron model is chosen as the closest to the geometry of cells of highly porous cellular material and relatively simple for creation of physical and functional models of the material.

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References

  1. Tikhomirov, V.K., Peny. Teoriya i praktika ikh polucheniya i razrusheniya (Foams. Theory and Practice of Their Formation and Decomposition), Moscow: Mir, 1985.

    Google Scholar 

  2. Hudson, D., Statistics for Physicists Geneva,: CERN, 1964; Moscow: Mir, 1970.

    Google Scholar 

  3. Thomson, W., On the division of space with minimum partitional area, Acta Mathem., 1887, vol. 11, pp. 121–134.

    Article  Google Scholar 

  4. Rivier, N., Seifenblasenrhetorik, or the sound of the last trumpet, Forma, 1996, vol. 11, pp. 195–198.

    Google Scholar 

  5. Weaire, D. and Phelan, R., A counter-example to Kelvin’s conjecture on minimal surfaces, Philos. Mag. Lett., 1994, vol. 69, pp. 107–110.

    Article  CAS  Google Scholar 

  6. Kusner, R. and Sullivan, J.M., Comparing the Weaire- Phelan equal-volume foam to Kelvin’s foam, Forma, 1996, vol. 11, pp. 233–242.

    Google Scholar 

  7. Aboav, D.A., Kelvin’s “division of space”, and its aftermath, Forma, 1996, vol. 11, pp. 243–254.

    Google Scholar 

  8. Phelan, R., Generalisations of the Kelvin problem and other minimal problems, Forma, 1996, vol. 11, pp. 287–302.

    Google Scholar 

  9. Honda, H., Morita, T., and Tanabe, A., Establishment of epidermal cell columns in mammalian skin: Computer simulation, J. Theor. Biology, 1979, vol. 81, pp. 745–759.

    Article  CAS  Google Scholar 

  10. Gabbrielli, R., A new counter-example to Kelvin’s conjecture on minimal surfaces, Philos. Mag. Lett., 2009, vol. 89, pp. 483–491.

    Article  CAS  Google Scholar 

  11. Krishnan, S., Murthy, J.Y., and Garimella, S.V., Direct simulation of transport in open-cell metal foam, J. Heat Transfer, 2006, vol. 28, pp. 793–800.

    Article  Google Scholar 

  12. Matzke, E.B., The three-dimensional shape of bubbles in foam–an analysis of the role of surface forces in three-dimensional cell shape determination, Am. J. Botany, 1946, vol. 33, pp. 58–80.

    Article  CAS  Google Scholar 

  13. Dai, Z., Nawaz, K., Park, Y.G., Bock, J., and Jacobi, A.M., Correcting and extending the Boomsma-Poulikakos effective thermal conductivity model for three-dimensional, fluid-saturated metal foams, Int. Commun. Heat Mass Transfer, 2010, vol. 37, pp. 575–580.

    Article  CAS  Google Scholar 

  14. Mahjoob, S. and Vafai, K., A synthesis of fluid and thermal transport models for metal foam heat exchangers, Int. J. Heat Mass Transfer, 2008, vol. 51, pp. 3701–3711.

    Article  Google Scholar 

  15. Mechanics of Cellular Plastics, Ed. by Hilyard, N.C., London: Appl. Sci., 1982; Moscow: Mir, 1985.

  16. Dement’ev, A.G. and Tarakanov, O.G., Struktura i svoistva penoplastov (Structure and Properties of Foam Plastics), Moscow: Khimiya, 1983.

    Google Scholar 

  17. Danchenko, Yu.V., High-porous penetrable cellular materials for cooled telescopic laser mirrors, Candidate’s (Eng.) Dissertation, Perm’, 1986.

    Google Scholar 

  18. Apollonov, V.V., Granovskii, M.S., Danchenko, Yu.V., et al., Hogh-porous materials on laser optic. Problems and Prospects, in Kvantovaya radiofizika (Quantum Radiophysics), Preprint of Inst. General Physics of Acad. Sci. USSR, Moscow, 1988.

    Google Scholar 

  19. Hagen, G., Information and Self-organization. Macroscopic Approach to Complex Systems Berlin: Springer- Verlag, 1988; Moscow: Mir, 1991.

    Google Scholar 

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Correspondence to A. A. Makarov.

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Original Russian Text © A.A. Makarov, 2016, published in Materialovedenie, 2016, No. 2, pp. 23–28.

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Makarov, A.A. Highly porous cellular materials: A statistical model of geometric structure. Inorg. Mater. Appl. Res. 7, 576–581 (2016). https://doi.org/10.1134/S2075113316040213

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  • DOI: https://doi.org/10.1134/S2075113316040213

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