Intrinsic Conductivity of Objects Having Arbitrary Shape and Conductivity.
Intrinsic Conductivity of Objects Having Arbitrary Shape
and Conductivity.
(852 K)
Garboczi, E. J.; Douglas, J. F.
Physical Review E, Vol. 53, No. 6, 6169-6180, June
1996.
Keywords:
electrical resistivity; arbitrary shape; conductivity;
thermal conductivity
Abstract:
We study the electrical conductivity sigma of a
dispersion of randomly oriented and positioned particle
inclusions having common shape or conductivity,
suspended in an isotropic homogeneous matrix of
conductivity. For this problem, the mixture
conductivity is a scalar and we concentrate on the
leading order concentration virial coefficient, the
"intrinsic conductivity." Results for [sigma] are
summarized for limiting cases where there is a large
mismatch between the condictivities of the inclusions
and the suspending matrix. For a general particle
shape, we then treat the more difficult case of
arbitrary relative conductivity through the introduction
of a Pade approximant that incorporates (exact or
numerical) information for limits. Comparison of this
approximation for [sigma (delta)] to exact and finite
element calculations for a variety of particle shapes in
two and three dimensions shows excellent agreement over
the entire range of delta. This relation should be
useful for inferring particle shape and property
information from conductivity measurements on dilute
particle dispersions. The leading order concentration
virial coefficient for other mixture properties (thermal
conductivity, dielectric constant, refractive index,
shear modulus, bulk modulus, viscosity, etc.) are
equally well described by a similar Pade approximant.
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