Effective Medium Theory

− The shielding properties of carbon fibres in composite materials are compared for two particular lamination examples used in avionics. Plane wave shielding theory and effective medium theory are compared in this work and found to provide the same theoretical ...

Using the transient hot wire and pulsed field gradient nuclear magnetic resonance methods we determined the thermal conductivity and the solvent self-diffusion coefficient (SDC) in aqueous suspensions of quasi-monodisperse spherical silica nanoparticles. The thermal conductivity was found to increase at higher volume fraction of nanoparticles in accordance with the effective medium theory albeit with a smaller slope. On the other hand, the SDC was found to decrease with nanoparticle volume fraction faster than predicted by the effective medium theory. These deviations can be explained by the presence of an interfacial heat-transfer resistance and water retention by the nanoparticles, respectively. We found no evidence for anomalous enhancement in the transport properties of nanofluids reported earlier by other groups.

Firstly the basic theoretical methods of calculating the dielectric properties of heterogeneous mixtures are discussed. These are the mean field and effective medium theories and integral methods. Formulae are presented for systems containing parallel oriented ellipsoids and for randomly oriented ellipsoidal systems. Theoretical formulae are divided into two sub-groups: symmetric equations for statistical mixtures and asymmetric equations for matrix-inclusion type composites. In the former case only the relative amount of the components is important, in the second case phase inversion results in a change of the dielectric properties. Formulae are compared numerically using spherical and spheroidal systems with sharply different components (permittivity ratio is 1 ∶ 100). In the case of asymmetric formulae the effect of phase inversion is studied as well. Percolation behaviour predicted by the equations is demonstrated and discussed. Functional shapes are compared in relation to the theoretical differences. Finally, experimental data are compared with the theoretical results, advantages and drawbacks of the various formulae are discussed. For spherical systems the simplest mean field formula yields somewhat worse values than effective medium or integral equations. The Looyenga equation does not work very well if the permittivity difference is high. For nonspherical systems the fit is better in general, even the simplest formula works satisfactorily. The shape independence predicted by the Looyenga theory for randomly oriented ellipsoids is in conflict with experimental data.

An analytical model for a composite material containing magnetic platelets is presented based on the modified asymmetric Bruggeman's effective medium theory for permeability. The model takes into account crushing of bulk magnetic material and form factors of inclusions.

In this paper, analytical modeling and numerical simulation of the complex effective dielectric, magnetic constants and refractive index of a metallic rod metamaterial in microwave frequency range are presented. Analytical modeling has been done using modified ...

Real-time spectroscopic ellipsometry (SE) data collected during the nucleation and growth of hydrogenated amorphous silicon (a-Si:H) thin films have been analyzed by applying one and two layer optical models incorporating different effective medium theories (EMT's). The ...

An analytical model for a composite material containing magnetic platelets is presented based on the modified asymmetric Bruggeman's effective medium theory for permeability. The model takes into account crushing of bulk magnetic material and form factors of inclusions.