Finite-element calculations for dielectric relaxation of one-sphere systems in a parallel-electrode measuring cell

Using the finite-element method (FEM), the frequency dependence of conductivity and relative permittivity was calculated for a heterogeneous specimen in which a sphere was placed in a medium. The FEM calculations were made for the whole system in which the specimen was located in a measuring cell comprising two parallel electrodes and a spacer with a cylindrical sample cavity, as in practical measurements. Values of the conductivity and the permittivity of the sphere and the medium were chosen so as to simulate specimens of water-in-nitrobenzene (W/N) and oil-in-water (O/W) types. When the volume ratio of the sphere to the sample cavity p was below 0.1, the frequency dependence of conductivity and permittivity was in good agreement with that described by Wagner's theory for both the W/N and O/W specimens. When p was greater than 0.1, deviations from Wagner's theory were found for limiting values of the conductivity and permittivity at low and high frequencies for both the W/N and O/W specimens, and for the relaxation time for the W/N specimens. Received: 15 July 1998 Accepted in revised form: 5 November 1998