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Intrinsic Viscosity and the Polarizability of Particles Having a Wide Range of Shapes.


pdf icon Intrinsic Viscosity and the Polarizability of Particles Having a Wide Range of Shapes. (3738 K)
Douglas, J. F.; Garboczi, E. J.

Advances in Chemical Physics, Vol. XCI, 85-153, 1995.

Keywords:

viscosity; particles; shapes; composite materials; solid mixtures; equations

Abstract:

The intrinsic viscosity and the electric and magnetic polarizabilities of objects having general shape are required in the calculation of some of the most basic properties of solid-solid composites and fluid-solid mixtures. Specifically, the leading order virial coefficients of diverse properties (viscosity, refractive index, dielectric constant, magnetic permeability, thermal and electrical conductivity, and others) can often be expressed in terms of these functionals of object shape. These virial coefficients also provide basic input into effective medium theories describing higher concentration mixtures. The electric and magnetic polarizability tensors have independent interest in applications involving the scattering of electromagnetic and pressure waves from objects of general shape. We present an argument that the ratio of intrinsic viscosity and electric polarizabilities (the average electric polarizability tensor trace) is an invariant to a good approximation. Many analytical and numerical finite element results for a variety of shapes are presented to support the conjectured relation. Our approximate relation between intrinsic viscosity and electric polarizabilities complements the exact relation between the hydrodynamic virtual mass W and the magnetic polarizability tensors.