TY - JOUR
T1 - Bulk properties of two-phase disordered media. II. Effective conductivity of a dilute dispersion of penetrable spheres
AU - Torquato, S.
N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 1985
Y1 - 1985
N2 - The calculation of the effective electrical conductivity σ* of a dilute dispersion of equisized spheres of radius R distributed with arbitrary degree of penetrability is considered. It is demonstrated that σ*, through second order in the inclusion volume fraction φ2, can be written in terms of the zero-density limits of the pair-connectedness and pair-locking functions, and certain polarizability tensors which involve one and two inclusions. Rigorous upper and lower bounds on σ*, through order φ22, are shown to depend upon, among other quantities, the aforementioned pair distribution functions and are evaluated for two models: an interpenetrable-sphere model and a certain sphere distribution in which the minimum distance between sphere centers is greater than or equal to 2R. An approximate expression obtained for the low-density expansion of σ* for dispersions of penetrable spheres always lies between the derived bounds on σ*. The study demonstrates that the effect of connectivity of the inclusion phase on σ*, through second order in φ2, can be substantial relative to the conductivity of dispersions of spheres characterized by a pair-connectedness function that is zero for all sphere separations.
AB - The calculation of the effective electrical conductivity σ* of a dilute dispersion of equisized spheres of radius R distributed with arbitrary degree of penetrability is considered. It is demonstrated that σ*, through second order in the inclusion volume fraction φ2, can be written in terms of the zero-density limits of the pair-connectedness and pair-locking functions, and certain polarizability tensors which involve one and two inclusions. Rigorous upper and lower bounds on σ*, through order φ22, are shown to depend upon, among other quantities, the aforementioned pair distribution functions and are evaluated for two models: an interpenetrable-sphere model and a certain sphere distribution in which the minimum distance between sphere centers is greater than or equal to 2R. An approximate expression obtained for the low-density expansion of σ* for dispersions of penetrable spheres always lies between the derived bounds on σ*. The study demonstrates that the effect of connectivity of the inclusion phase on σ*, through second order in φ2, can be substantial relative to the conductivity of dispersions of spheres characterized by a pair-connectedness function that is zero for all sphere separations.
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U2 - 10.1063/1.449002
DO - 10.1063/1.449002
M3 - Article
AN - SCOPUS:0345528794
VL - 83
SP - 4776
EP - 4785
JO - Journal of Chemical Physics
JF - Journal of Chemical Physics
SN - 0021-9606
IS - 9
ER -