Intrinsic Viscosity and the Polarizability of Particles Having a Wide Range of Shapes.
Intrinsic Viscosity and the Polarizability of Particles
Having a Wide Range of Shapes.
Douglas, J. F.; Garboczi, E. J.
Advances in Chemical Physics, Vol. XCI, 85-153, 1995.
viscosity; particles; shapes; composite materials; solid
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