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Effective conductivities of composite materials composed of cubic arrangements of spherical particles embedded in an isotropic matrix

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Abstract

Results are presented for the effective conductivities of simple, face-centered, and body-centered cubic arrays of isotropic spherical particles embedded in an isotropic medium possessing a different conductivity. With the use of a multipole expansion technique, numerical and conceptual errors in the prior work of others are corrected. Agreement with existing experimental data is found to be excellent.

Zusammenfassung

Für die Leitfähigkeit einer einfachen körper-zentrierten kubischen Anordnung von isotropen kugelfömigen Teilchen, die in einem isotropen Medium mit einer verschiedenen Lefähigkeit eingebettet sind, werden Resultate angegeben. Mit Hilfe einer Multipole-Entwicklung werden gewisse numerische und konzeptuelle Fehler früherer Arbeiten korrigiert. Sehr gute Uebereinstimmung mit den vorhandenen experimentellen Resultaten wurde festgestellt.

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Author notes

  1. M. Zuzovsky

    Present address: Pulp and Paper Research Institute of Canada, McGill University, Montreal, Canada

  2. H. Brenner

    Present address: Dept. of Chemical Engineering, University of Rochester, 14627, Rochester, New York

Authors and Affiliations

  1. Dept. of Chemical Engineering, Carnegie-Mellon University, Pittsburgh, Pennsylvania, USA

    M. Zuzovsky & H. Brenner

Authors
  1. M. Zuzovsky
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  2. H. Brenner
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Zuzovsky, M., Brenner, H. Effective conductivities of composite materials composed of cubic arrangements of spherical particles embedded in an isotropic matrix. Journal of Applied Mathematics and Physics (ZAMP) 28, 979–992 (1977). https://doi.org/10.1007/BF01601666

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  • DOI: https://doi.org/10.1007/BF01601666

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