The Dielectric Constants of Nonconducting Suspensions

Abstract

The electric permittivity of a composite can be expressed in terms of the electric permittivity of the components and the average of the electric potential on the surface of a filler particle. The expression obtained is developed in powers of the volume fraction c of filler particles. Both the term linear in c and the term which is quadratic in c . are derived explicitly for two systems: (a) the particles are spheres; (b) the particles are circular cylinders perpendicular to the external field. Two methods are used. The first is an approximate treatment which is based on successive "reflections" of the perturbation caused by one particle off a second particle. The assumption is made that each reflection can be calculated as though the perturbation of the field is seen by the particle as a homogeneous field. This approach is worked out for cylinders and for spheres. The second method is carried through only for cylinders. It is based on the use of bipolar coordinates and is rigorous. The results obtained are compared with those of two approxi mate theories published previously: that of Polder and Van Santen and that of Kerner. This comparison can be found in the last section.