Bonnecaze, R. T. and Brady, J. F.
(1991)
*The Effective Conductivity of Random Suspensions of Spherical Particles.*
Proceedings of the Royal Society A: Mathematical, physical, and engineering sciences, 432
(1886).
pp. 445-465.
ISSN 1364-5021.
doi:10.1098/rspa.1991.0025.
https://resolver.caltech.edu/CaltechAUTHORS:20141210-110725362

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## Abstract

The effective conductivity of an infinite, random, mono-disperse, hard-sphere suspension is reported for particle to matrix conductivity ratios of ∞, 10 and 0.01 for sphere volume fractions, c, up to 0.6. The conductivities are computed with a method previously described by the authors, which includes both far- and near-field interactions, and the particle configurations are generated via a Monte Carlo method. The results are consistent with the previous theoretical work of D. J. Jeffrey to O(c^2) and the bounds computed by S. Torquato and F. Lado. It is also found that the Clausius-Mosotti equation is reasonably accurate for conductivity ratios of 10 or less all the way up to 60 % (by volume). The calculated conductivities compare very well with those of experiments. In addition, percolation-like numerical experiments are performed on periodically replicated cubic lattices of N nearly touching spheres with an infinite particle to matrix conductivity ratio where the conductivity is computed as spheres are removed one by one from the lattice. Under suitable normalization of the conductivity and volume fraction, it is found that the initial volume fraction must be extremely close to maximum packing in order to observe a percolation transition, indicating that the near-field effects must be very large relative to far-field effects. These percolation transitions occur at the accepted values for simple (sc), bodycentred (BCC) and face-centred (FCC) cubic lattices. Also, the vulnerability of the lattices computed here are exactly those of previous investigators. Due to limited data above the percolation threshold, we could not correlate the conductivity with a power law near the threshold; however, it can be correlated with a power law for large normalized volume fractions. In this case the exponents are found to be 1.70, 1.75 and 1.79 for sc, BCC and FCC lattices respectively.

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Additional Information: | © 1990 The Royal Society. Received 11 May 1990; accepted 14 September 1990. | ||||||||||||

Issue or Number: | 1886 | ||||||||||||

DOI: | 10.1098/rspa.1991.0025 | ||||||||||||

Record Number: | CaltechAUTHORS:20141210-110725362 | ||||||||||||

Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20141210-110725362 | ||||||||||||

Official Citation: | The Effective Conductivity of Random Suspensions of Spherical Particles R. T. Bonnecaze, J. F. Brady Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 1991 432 445-465; DOI: 10.1098/rspa.1991.0025. Published 8 March 1991 | ||||||||||||

Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||

ID Code: | 52550 | ||||||||||||

Collection: | CaltechAUTHORS | ||||||||||||

Deposited By: | Tony Diaz | ||||||||||||

Deposited On: | 10 Dec 2014 21:00 | ||||||||||||

Last Modified: | 10 Nov 2021 19:42 |

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