Analytical and Numerical Studies of Effective Medium Mixing Problems in Electromagnetics

Abstract

Electromagnetically Functionalized Colloidal Dispersions (EFCDs) have been utilized in several applications in electromagnetics such as reconfigurable antennas. The colloidal dispersions vary the electrical properties depending on the volume fraction relative to the background fluid. The classical Maxwell-Garnett mixing formulas are an effective medium theory that provides a capable framework for approximating the effective electromagnetic properties of these EFCD mixtures. However, the theory only accounts for first-order interactions of the mixed inclusions at lower volume fractions, so deviations from the theory occur at high volume fraction. Thus, accurately modeling and predicting the effective permittivity of a mixture is still a problem to be solved.

This thesis presents an analytical and numerical study of the effective properties for EFCDs. An analysis in the quasi-static regime leads to the development of a new model that adds higher-order interactions to the Maxwell Garnett theory. Additionally, finite-element simulations using both COMSOL and Computer Simulation Technology Microwave Studio are performed to compute the effective medium permittivity. Several particle distributions are analyzed using a frequency dependent potential boundary condition to validate the analytical model as well as study the effects of percolation at high volume fractions. These results will show that the Maxwell-Garnett theory clearly breaks down at higher volume fractions.