Effective Permittivity Of Dielectric Mixture Research Articles

Electromagnetic Modeling of Dielectric Mixtures

Electromagnetic modeling of dielectric materials allows us to study the effects of electromagnetic wave propagation and how such electromagnetic fields influence and interact with them. Dielectric materials are composites or mixtures, which often are made up of at least two constituents or phases. Modelling the electromagnetic behaviour of dielectric mixtures is crucial to understand how geometrical factors (shape and concentration), electromagnetic properties of inclusions and background medium, influence the permittivity of the overall material. The aim of this work is to develop new analytical models for dielectric mixtures, in order to describe their electromagnetic behaviour and design them with desired electromagnetic properties, for specific required applications. In particular, in this paper a new general expression for the effective permittivity of dielectric mixture is presented. The mixtures consist of inclusions, with arbitrary shapes, embedded in a surrounding dielectric environment. We consider the hosting environment and the hosted material as real dielectrics, both of them as dispersive dielectrics. The proposed analytical models simplify practical design tasks for dielectric mixtures and allow us to understand their physical phenomena and electromagnetic behaviours.

Transmission line analogy for calculating the effective permittivity of mixtures with spherical multilayer scatterers

A novel method is presented in this paper to determine the fields of a multilayer sphere in a static field. The solution of the Laplace equation, being of second order, allows two types of radial dependencies. These are interpreted as the forward and backward propagating waves, like in a transmission line. Propagation and scattering matrices relate the amplitudes of these waves in adjacent regions, which permits solving the fields without having to resort to inverting a 2N x 2N matrix for a N-layer sphere. Also the scattered field of a sphere with a continuous permittivity profile is analyzed by deriving a differential equation for the scattered potential and solving this potential for the special case of a linearly decreasing permittivity profile. The results are used in determining the effective permittivity of dielectric mixtures with the multilayer and continuous-permittivity inhomogeneous scatterers. In enumerating this macroscopic effective permittivity, the propagating component of the internal fie...

Estimation of red blood cell volume fraction from overall permittivity measurements

The rapid testing of red blood cell (RBC) volume fraction (“hematocrit”) is becoming increasingly important to identify blood disorders (“hemoglobinopathies”). Electromagnetic techniques provide an advantageous way to measure blood properties, primarily because they are inexpensive, quick and noninvasive. The goal of this paper is to develop estimates of the RBC volume fraction levels of whole blood from macroscopic electromagnetic (permittivity) measurements. The approach taken is to generate volume fraction estimates by inverting classical bounds on the effective permittivity of dielectric mixtures. The usefulness of the approach is that, given the permittivities of the plasma (known), cells (known) and whole mixture (measured), one can determine the cell volume fraction and compare it to the levels found in healthy blood. The deviation of the properties can be used to help characterize certain blood disorders. The expressions developed are not limited to RBC measurement, and are applicable to any cell-in-solution system. Through correlation of our laboratory measurements, the analytical expressions and direct large-scale numerical simulations, the results suggest that RBCs form high-permittivity cell-networks by making cell-to-cell contact, even at relatively low volume fraction.

Determination of the effective permittivity of dielectric mixtures with the transmission line matrix method

In this article, the effective permittivity of two-phase dielectric mixtures is calculated by applying the transmission line matrix (TLM) method. Two slightly different TLM algorithms are considered: a hybrid approach, which combines the TLM method with a subgriding technique based on dual capacitor circuits, to allow a refined description of the material, and a standard or pure TLM approach, which uses a mesh size smaller than the typical dimension of insertions in order to appropriately describe details of the geometry. A study of the statistical distribution of permittivity for insertions in random positions is also presented, showing that the effective permittivity of the mixture tends to concentrate around the mean value as insertions reduce in size. Both TLM techniques are applied to dielectric mixtures in two-dimensional situations. When the concentration of insertions is small, the results are in close agreement with prediction formulae while for higher concentration values, deviations are observed, although basically the results fall within the range predicted by theoretical bounds. Numerical results obtained using the two TLM approaches present a similar qualitative behavior; nevertheless, a clear difference is observed between them. The study of special periodic situations with coated insertions allows us to identify the pure TLM results as more accurate than those of the hybrid approach and also explains why homogeneous distributions provide numerical values close to the theoretical limits. The effects of shape on permittivity are also modeled and deviations to the Wiener bounds are discussed in detail, using two- and three-dimensional examples in practical situations.

Method for Estimating Complex Permittivity Based on Measuring Effective Permittivity of Dielectric Mixtures in Radio Frequency Band

This paper proposes a method for estimating the complex permittivity of a small quantity of a sample such as a biological membrane. The feature of this method is that a material with art unknown complex permittivity is mixed with a material with a known complex permittivity in a number of volume ratios. The unknown complex permittivity is estimated by measuring the effective permittivity of the mixtures and by using the mixing formula, which is applied to the composite material. The validity of this estimation method is evaluated using a phospholipid, which is the primary constituent of a biological membrane, in the frequency range from 0.8 GHz to 6 GHz. We confirm that the measured effective permittivity of the phospholipid mixtures, which comprise the phospholipid and Ringer's solution in a number of volume ratios, corresponds to that of the Lichtenecker formula. Additionally, by preparing a number of samples with varying volume ratios the estimation error can be decreased. This estimation method is considered to be effective in the measurement of the complex permittivity for a biological membrane.

Effective Permittivity of Dielectric Mixture Based on the Electric-Circuit Model

This paper presents three kinds of electric-circuit models for calculating the effective permittivity of a dielectric mixture and a general formula. The average value of three correction factors based on three kinds of electric-circuit models happens to be the value of the correction factor of Maxwell Garnett's formula. These new models can be spontaneously extended to a dielectric mixture with multiple-sized spherical inclusions. Model permittivities are compared with Doyle-Jacobs's model permittivity and iterative model permittivity. The results show that the two other models are the limits of the electric-circuit model for the dielectric mixture with multiple-sized spherical inclusions.

Inclusion of scattering losses in the models of the effective permittivity of dielectric mixtures and applications to wet snow

Several dielectric models have been previously proposed to explain the permittivity of mixtures from the known dielectric constant and volume fractions of the constituents. The materials may be lossy and this leads to a complex effective permittivity for the mixture where the imaginary part stands for the absorption losses of the mixture. However, the scattering losses are not incorporated in the effective permittivity. The result is therefore confined to a low-frequency limit. In this paper an attempt is made to incorporate the scattering losses in the effective permittivity of the medium consisting of the discrete scatterers immersed in a host material. The inclusions are assumed to be spherical. The results are applicable to general multiphase mixtures, and the scattering spheres of the different phases may have size distribution. The results are applied to calculating the complex effective permittivity of wet snow. The prediction of the model seems to agree with the experimental data if the scattering...

Effective permittivity of dielectric mixtures

General mixing formulas are derived for discrete scatterers immersed in a host medium. The inclusion particles are assumed to be ellipsoidal. The electric field inside the scatterers is determined by quasi-static analysis, assuming the diameter of the inclusion particles to be much smaller than one wavelength. The results are applicable to general multiphase mixtures, and the scattering ellipsoids of the different phases can have different sizes and arbitrary ellipticity distribution and axis orientation, i.e. the mixture may be isotropic or anisotropic. The resulting mixing formula is nonlinear and is suitable for iterative solutions. The formula contains a quantity called the apparent permittivity, and with different choices of this quantity, the result leads to the generalized Lorentz-Lorenz formula, the generalized Polder-van Santen formula, and the generalized coherent potential-quasicrystalline approximation formula. The results are applied to calculating the complex effective permittivity of dry and wet snow, and sea ice.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>