Effective permittivity of mixtures: numerical validation by the FDTD method

Kärkkäinen, Kimmo; Sihvola, Ari; Nikoskinen, K.

doi:10.1109/36.843023

Cited by 293 publications

(173 citation statements)

References 17 publications

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“…The quasistatic limit has also been used to argue that EM scattering will not be significant in heterogeneous media at long wavelengths, and thus the EM field will be insensitive to microstructural variations at the size scale of the inclusions. 36,37 However, the aggregation results in this study showed that small changes in microstructure affected macroscopic properties in the quasistatic limit, although the macroscopic composition (average particle volume fraction) remained constant. Additionally, the simulation results were by and large insensitive to the scale of the heterogeneities with respect to the incident field wavelength.…”

Section: Applicability Of the Quasistatic Limitmentioning

confidence: 52%

“…16 FE calculations have also been combined with the method of boundaryintegral equations (BIE) to simulate single inclusions of various shapes, including ellipsoids and cylinders, in 2D and 3D unit cells. 14 Similarly, the FDTD method has been used to model 2D mixtures containing up to 265 inclusions (1.0 inclusion volume fraction), 36,37 and to model the EM properties of biological tissues using periodic stacks of 30-100 spherical cells; 21 Other 6 approaches used to model the permittivity of random media include the transmission line matrix (TLM) method, which was applied to 2D simulations of 64-127 inclusions in a square periodic unit cell (0.5-1.0 inclusion volume fraction), 38 and the lattice Boltzmann method, which used 2D simulations to model fluid aggregation (wetting) in multiphase microporous materials. 39 Multipole expansion methods are efficient tools for modeling field interactions in arbitrary 3D configurations of spherical particles since the fields for a particle can be defined by a relatively small number of expansion coefficients rather than a large number of grid values as required for approaches such as the FE method.…”

Section: Introductionmentioning

confidence: 99%

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Effects of aggregation on the permittivity of random media containing monodisperse spheres

Doyle

Tew

Jain

et al. 2009

Journal of Applied Physics

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The NERC and CEH trade marks and logos ('the Trademarks') are registered trademarks of NERC in the UK and other countries, and may not be used without the prior written consent of the Trademark owner. AbstractNumerical simulations were used to calculate the effective permittivities of three-dimensional random particle suspensions containing up to 2440 particles and exhibiting two types of particle aggregation. The particles were modeled as 200-µm spheres that were aggregated into either large spherical clusters or into foam-type microstructures with large spherical voids. Multiple scattering of 0.01-10.0 GHz electromagnetic fields was simulated using a first-principles iterative multipole approach with matrix and particle permittivities of 1.0 and 8.5, respectively.The computational results showed both significant and highly significant trends. Aggregation 2 into spherical clusters decreased the effective permittivity by up to 3.2 ± 0.2%, whereas aggregation into foam-type microstructures increased the effective permittivity by up to 3.0 ± 1.6%. The effective permittivity trends exhibited little change with frequency. These results were compared to effective medium approximations that predicted higher permittivities than those from the simulations and showed opposite trends for cluster aggregation. Three theories are proposed to explain the simulation results. The first theory invokes a waveguide-like mechanism. The simulations indicate that the wave fields propagate more through the continuous paths of greater or lesser particle density created by aggregation, rather than through the isolated particle clusters or large voids. This quasi-continuous phase, or quasi-matrix, therefore behaves like a random waveguide structure in the material. A second theory is proposed where the quasicontinuous phase governs the behavior of the system by a percolation-like process. In this theory, the multipole interactions are modeled as the percolation of virtual charges tunneling from one particle to another. A third mechanism for the permittivity changes is also proposed involving collective polarization effects associated with the particle clusters or large voids. The simulation results challenge the general applicability of the quasistatic limit for heterogeneous media by showing how microstructural changes much smaller than the electromagnetic wavelength can alter the effective permittivity by a statistically significant degree. The results also provide a quantitative indication of the effects of aggregation and hierarchical microstructures on the electromagnetic properties of random media, and have application to the remote and in situ sensing of soils, the rational design and nondestructive evaluation of composites, and the study of biological tissues and other random materials.3

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Section: Applicability Of the Quasistatic Limitmentioning

confidence: 52%

Section: Introductionmentioning

confidence: 99%

Effects of aggregation on the permittivity of random media containing monodisperse spheres

Doyle

Tew

Jain

et al. 2009

Journal of Applied Physics

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show abstract

“…(17) is the lower bound for the predication of effective permittivity, 14 numerical results is slightly higher than analytical solutions.…”

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confidence: 86%

Modeling of the effective permittivity of insulating presspaper

et al. 2016

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Effective permittivity model of insulating presspaper is built on the basis of the microstructure of the material. Due to the essentially layered structure in z-direction of presspaper, air voids inside the mixture can be treated as right prismatic inclusions. Analytical formula for the prediction of the effective permittivity of insulating presspaper is derived. Interestingly, the derived formula equals to the mixing equation applied for dielectrics in series. Numerical simulation was used to validate the analytical results by considering the air voids as cubical inclusions. Results show a good agreement between the analytically and numerically calculated effective permittivity values. Furthermore, dielectric permittivity results of commercial kraft paper and laboratory-made presspaper at 50 Hz were measured and compared with modeled data. It turns out that the deduced results give a good accuracy for the effective permittivity determination.

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“…The idea is to start from the Maxwell-Garnett equation (I) and to treat arbitrary volume fractions f by selfconsistently embedding the matrix and inclusion phases in an effective medium. It is also known as the Polder-van Santen formula, self-consistent field theory (SCF) or simply effective medium theory [16,17]. In solid state physics, the Bruggeman theory is closely related to the coherent-potential approximation (CPA) for binary alloys [IS, 19,20].…”

Section: Scientific Background: Bruggeman Modelmentioning

confidence: 99%

Length scales of interactions in magnetic, dielectric, and mechanical nanocomposites

et al. 2011

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It is investigated how figures of merits of nanocomposites are affected by structural and interaction length scales, Aside from macroscopic effects without characteristic lengths scales and atomic-scale quantum-mechanical interactions there are nanoscale interactions that reflect a competition between different energy contributions. We consider three systems, namely dielectric media, carbon-black reinforced rubbers and magnetic composites. In all cases, it is relatively easy to determine effective materials constants, which do not involve specific length scales. Nucleation and breakdown phenomena tend to occur on a nanoscale and yield a logarithmic dependence of figures of merit on the macroscopic system size. Essential system-specific differences arise because figures of merits are generally nonlinear energy integrals. Furthermore, different physical interactions yield different length scales. For example, the interaction in magnetic hardsoft composites reflects the competition between relativistic anisotropy and nonrelativistic exchange interactions, but such hierarchies of interactions are more difficult to establish in mechanical polymer composites and dielectrics.

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Effective permittivity of mixtures: numerical validation by the FDTD method

Cited by 293 publications

References 17 publications

Effects of aggregation on the permittivity of random media containing monodisperse spheres

Effects of aggregation on the permittivity of random media containing monodisperse spheres

Modeling of the effective permittivity of insulating presspaper

Length scales of interactions in magnetic, dielectric, and mechanical nanocomposites

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