## Abstract

An accurate first-passage simulation technique formulated by the authors [J. Appl. Phys. 68, 3892 (1990)] is employed to compute the effective conductivity σ_{e} of distributions of penetrable (or overlapping) spheres of conductivity σ_{2} in a matrix of conductivity σ_{1}. Clustering of particles in this model results in a generally intricate topology for virtually the entire range of sphere volume fractions φ_{2} (i.e., 0≤φ_{2}≤1). Results for the effective conductivity σ_{e} are presented for several values of the conductivity ratio α=σ_{2}/σ_{1}, including superconducting spheres (α=∞) and perfectly insulating spheres (α=0), and for a wide range of volume fractions. The data are shown to lie between rigorous three-point bounds on σ_{e} for the same model. Consistent with the general observations of Torquato [J. Appl. Phys. 58, 3790 (1985)] regarding the utility of rigorous bounds, one of the bounds provides a good estimate of the effective conductivity, even in the extreme contrast cases (α≫1 or α≅0), depending upon whether the system is below or above the percolation threshold.

Original language | English (US) |
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Pages (from-to) | 2727-2735 |

Number of pages | 9 |

Journal | Journal of Applied Physics |

Volume | 71 |

Issue number | 6 |

DOIs | |

State | Published - 1992 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)