Fourth-order bounds on the effective conductivity for a system of fully penetrable spheres
- 8 April 1994
- journal article
- Published by The Royal Society in Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences
- Vol. 445 (1923) , 247-256
- https://doi.org/10.1098/rspa.1994.0059
Abstract
An expression for the intersection volume of four equi-sized spheres is derived. This expression is used to construct the four-point correlation function for a system of fully penetrable spheres dispersed in a matrix. The knowledge of this four-point correlation function enables us to numerically calculate the microstructural parameter B ‡ , that appears in the fourth-order bounds on the effective conductivity due to Phan-Thien & Milton ( Proc. R. Soc. Lond . A380, 333 (1982)).Keywords
This publication has 8 references indexed in Scilit:
- Bounds on the effective thermal conductivity of a dispersion of fully penetrable spheresInternational Journal of Engineering Science, 1985
- Correlation of the electromagnetic and elastic properties of composites and microgeometries corresponding with effective medium approximationsAIP Conference Proceedings, 1984
- New bounds on the effective thermal conductivity of N -phase materialsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1982
- Bounds and exact theories for the transport properties of inhomogeneous mediaApplied Physics A, 1981
- Use of the vibrational approach to determine bounds for the effective permittivity in random mediaIl Nuovo Cimento (1869-1876), 1965
- The volume internal to three intersecting hard spheresMolecular Physics, 1964
- The triplet distribution function in a fluid of hard spheresMolecular Physics, 1963
- Viscous Flow through Porous Media. II. Approximate Three-Point Correlation FunctionPhysics of Fluids, 1962