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

J.F. Douglas^a and E.J. Garboczi^b
aPolymers and ^bBuilding Materials Divisions
National Institute of Standards and Technology
Gaithersburg, Maryland 20899

Abstract

The intrinsic viscosity [η] and the electric α_e and magnetic α_m 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 numerous applications involving the scattering of electromagnetic and pressure waves from objects of general shape. We present an argument that the ratio of [η] and < α_e > / V_p (the average polarizability tensor trace per unit object volume) 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 [η] and < α_e > / V_p complements the exact relation between the hydrodynamic virtual mass W and the magnetic polarizability α_e tensors.

• Introduction
• Polarizability, Intrinsic Conductivity, and Virtual Mass
• Intrinsic Viscosity and Its Relation to Intrinsic Conductivity
• Numerical Investigation of the Ratio in d=3
• Intrinsic Viscosity and Intrinsic Conductivity in d=2
• Intrinsic Viscosity and the Polarizability of Plates
• Conclusions and Summary
• Appendix A: Virtual Mass and the Acoustic Index of Refraction
• Appendix B: Polarization Formalism For Ellipsoids
• Appendix C: Intrinsic Viscosity Formalism for Ellipsoids and Other Shapes
• Appendix D: Exact Solution of the Polarization of a Dumbbell
• Appendix E: Finite Element Method Computation of and
• Appendix F: Ellipse Virial Coefficients in d=2
• Acknowledgments
• References

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