Classical Effective Medium Theory Research Articles

High-pressure rheology of alumina-silicone oil nanofluids

The effect of high-pressure on the rheological characteristics of alumina-silicone oil nanofluids at room temperature is investigated in this paper. Nanofluids are engineered colloidal suspensions of nano-sized particles dispersed in a basefluid. The rheological characteristics of nanofluids are studied with pressures up to 100MPa and particle concentrations up to 8% by mass using a high-pressure viscometer. The addition of nanoparticles is observed to increase the apparent viscosity of the nanofluids. A non-Newtonian, shear-thinning behavior is observed for both the basefluid and the nanofluids at all pressures at the higher shear rates. The critical shear rate at which shear thinning occurs is observed to be strongly influenced by particle addition. An increase in the pressure is observed to have an equal effect on the basefluid and on the nanofluids, which results in an average pressure-viscosity coefficient for both to be approximately 0.015mm2/N. The relative increase in the viscosity of the nanofluid to that of the basefluid was not affected by the pressure and was several orders higher than that predicted by the classical effective medium theory.

Simulating far infrared spectra of Zn1-xMnxSe/GaAs epifilms, MnSe/ZnSe superlattices and predicting impurity modes of N, P defects in Zn1-xMnxSe

A comprehensive lattice dynamical study is reported to emphasize the vibrational behavior of perfect/imperfect zinc-blende (zb) ZnSe, MnSe and Zn1−xMnxSe alloys. Low temperature far-infrared (FIR) reflectivity measurements performed on a series of molecular beam epitaxy grown Zn1−xMnxSe/GaAs (001) epilayers have a typical ‘intermediate-phonon-mode’ behavior. Besides perceiving ZnSe- and MnSe-like TO-phonon resonances, the study also revealed a weak Mn alloy-disorder mode below MnSe band. A classical effective-medium theory of multilayer optics is used to evaluate dielectric tensors of both epilayers and substrate for simulating reflectivity and transmission spectra of ultrathin epifilms and superlattices at near normal and/or oblique incidence. In the framework of a realistic rigid-ion model and exploiting an average t-matrix Greens function (ATM-GF) theory we appraised the vibrational properties of nitrogen and phosphorous doped Zn-Mn chalcogenides. Lattice relaxations around isolated NSe (PSe) defects in ZnSe and zb MnSe are evaluated by first principles bond-orbital model that helped construct perturbation models for simulating the localized vibrational modes (LVMs). Calculated shift of impurity modes for isotopic 14NSe (15NSe) defects in ZnSe offered a strong revelation of an inflexible defect–host interaction. By retaining force constant change parameter of 14NSe (15NSe) in heavily N-doped ZnSe, the ATM-GF theory predicted (a) three non-degenerate LVMs for the photoluminescence defect center V Se-Zn-14NSe (V Se-Zn-15NSe) of C s symmetry, and (b) six impurity modes for the second nearest-neighbor NSe-Zn-NSe pair defect of C 2v symmetry. From the range of simulated defect modes, we have ruled out the possibility of N-pairs and justified the presence of VSe-Zn-NSe complex centers – likely to be responsible for the observed large absorption bandwidth in highly N-doped ZnSe. High resolution measurements of FIR absorption and/or Raman scattering spectroscopy are needed to validate the accuracy of our theoretical conjectures.

Nanocomposites for thermoelectrics and thermal engineering

Abstract

Effective conductivity of spiral and other radial symmetric assemblages

Assemblies of circular inclusions with spiraling laminate structure inside them are studied, such as spirals with inner inclusions, Spirals with Shells, assemblies of “wheels” – structures from laminates with radially dependent volume fractions, complex axisymmetric three-dimensional micro-geometries called Connected Hubs and Spiky Balls. The described assemblages model structures met in rock mechanics, biology, etc. The classical effective medium theory coupled with hierarchical homogenization is used. It is found that fields in spiral assemblages satisfy a coupled system of two second order differential equations, rather than a single differential equation; a homogeneous external field applied to the assembly is transformed into a rotated homogeneous field inside of the inclusions. The effective conductivity of the two-dimensional Star assembly is equivalent to that of Hashin–Shtrikman coated circles, but the conductivity of analogous three-dimensional Spiky Ball is different from the conductivity of coated sphere geometry.

Field-tuned superconductor-insulator transition in BaPb1−xBixO3

BaPb${}_{1\ensuremath{-}x}$Bi${}_{x}$O${}_{3}$ is found to exhibit a field-tuned superconductor to insulator transition for Bi compositions 0.24 $\ensuremath{\le}x\ensuremath{\le}$ 0.29. The magnetoresistance of optimally doped samples manifests a temperature-independent crossing point and scaling of the form $\ensuremath{\rho}(T,H)={\ensuremath{\rho}}_{c}F(|H\ensuremath{-}{H}_{c}|{T}^{\ensuremath{-}1/z\ensuremath{\nu}})$, where ${H}_{c}$ is the field determined by the temperature-independent crossing point, and $z\ensuremath{\nu}$ $=$ 0.69 $\ifmmode\pm\else\textpm\fi{}$ 0.03. High-resolution transmission electron microscopy measurements reveal a complex intergrown nanostructure comprising tetragonal and orthorhombic polymorphs. Data are analyzed in terms of both a classical effective medium theory and a field-tuned quantum phase transition, neither of which provides a completely satisfactory explanation for this remarkable phenomenology.

Effects of aggregation on the thermal conductivity of alumina/water nanofluids

Nanofluids display enhanced heat transfer properties, and several mechanisms, including Brownian motion and aggregation of the suspended particles, have been proposed to explain this enhancement. Agreement on a unified understanding of the mechanism has yet been reached. The role of particle aggregation is particularly controversial, and requires further study. Thus, this work analyzes the effects of particle aggregation on the thermal conductivity of alumina/water nanofluids. The thermal conductivity of the nanofluids was measured using the 3ω method by varying the aggregation state until gelled nanofluids are formed. Brownian motion and sedimentation effects could thereby be removed from the analysis. The viscosity of the nanofluids was measured to quantify the aggregation state. The alumina/water nanofluids showed non-Newtonian characteristics in the low shear rate regime. The thermal conductivity could be explained by the classical Maxwell effective medium theory. High aggregation in the gel state produced large enhancements in the nanofluid thermal conductivity.

Multicomponent Effective Medium–Correlated Random Walk Theory for the Diffusion of Fluid Mixtures through Porous Media

Molecular transport in nanoconfined spaces plays a key role in many emerging technologies for gas separation and storage, as well as in nanofluidics. The infiltration of fluid mixtures into the voids of porous frameworks having complex topologies is common place to these technologies, and optimizing their performance entails developing a deeper understanding of how the flow of these mixtures is affected by the morphology of the pore space, particularly its pore size distribution and pore connectivity. Although several techniques have been developed for the estimation of the effective diffusivity characterizing the transport of single fluids through porous materials, this is not the case for fluid mixtures, where the only alternatives rely on a time-consuming solution of the pore network equations or adaptations of the single fluid theories which are useful for a limited type of systems. In this paper, a hybrid multicomponent effective medium-correlated random walk theory for the calculation of the effective transport coefficients matrix of fluid mixtures diffusing through porous materials is developed. The theory is suitable for those systems in which component fluxes at the single pore level can be related to the potential gradients of the different species through linear flux laws and corresponds to a generalization of the classical single fluid effective medium theory for the analysis of random resistor networks. Comparison with simulation of the diffusion of binary CO(2)/H(2)S and ternary CO(2)/H(2)S/C(3)H(8) gas mixtures in membranes modeled as large networks of randomly oriented pores with both continuous and discrete pore size distributions demonstrates the power of the theory, which was tested using the well-known generalized Maxwell-Stefan model for surface diffusion at the single pore level.

Nanofluids and Their Properties

Nanofluids belong to a new class of fluids with enhanced thermophysical properties and heat transfer performance. A broad spectrum of applications in science and engineering could potentially benefit from them. The potential market for nanofluids in heat transfer applications is estimated to be over 2 billion dollars per year, and likely to grow even further in the next few years. The available literature on nanofluids will be thoroughly reviewed in this article. Starting from their definition, and their scientific and engineering significance, the discussion will then turn to the literature. A review of the most noteworthy and recent experiments in thermal conductivity, viscosity, heat convection and specific heat will be mentioned, together with various speculations on the meaning of the results. A comprehensive list of empirical models available in the literature based on these speculations will be discussed next. To complete the literature review, numerical studies on nanofluids will also be discussed. The paper will close with a closer look at the various challenges of nanofluids, both in their production and their application. The vast majority of the experiments in the literature shows enhancement in the thermal conductivity, viscosity, and heat convection of nanofluids. However, the enhancements do not seem to follow classical effective medium theories, and an explanation for this anomalous behavior of nanofluids is still largely unknown.

On the dielectric function tuning of random metal-dielectric nanocomposites for metamaterial applications

The potential of random metal-dielectric nanocomposites as constituent elements of metamaterial structures is explored. Classical effective medium theories indicate that these composites can provide a tunable negative dielectric function with small absorption losses. However, the tuning potential of real random composites is significantly lower than the one predicted by classical theories, due to the underestimation of the spectral range where topological resonances take place. This result suggests that a random mixture consisting of a metal matrix with embedded isolated dielectric inclusions is a promising design guideline for the fabrication of tunable composites for metamaterial purposes.

Mechanisms and Models of Effective Thermal Conductivities of Nanofluids

The physical mechanisms and mathematical models of the effective thermal conductivities of nanofluids have long been of interest to the nanofluid research community because the effective thermal conductivities of nanofluids cannot generally be fully explained and predicted by classical effective medium theories. This review article summarizes considerable progress made on this topic. Specifically, the physical mechanisms and mathematical models of the effective thermal conductivities of nanofluids are reviewed, the potential contributions of those physical mechanisms are evaluated, and the comparisons of the theoretical predictions and experimental data are presented along with opportunities for future research.

Alloying effects on the optical properties ofGe1−xSixnanocrystals from time-dependent density functional theory and comparison with effective-medium theory

We present the optical spectra of Ge$_{1-x}$Si$_x$ alloy nanocrystals calculated with time-dependent density-functional theory in the adiabatic local-density ap proximation (TDLDA). The spectra change smoothly as a function of the compositio n $x$. On the Ge side of the composition range, the lowest excitations at the ab sorption edge are almost pure Kohn-Sham independent-particle HOMO-LUMO transitio ns, while for higher Si contents strong mixing of transitions is found. Within T DLDA the first peak is slightly higher in energy than in earlier independent-par ticle calculations. However, the absorption onset and in particular its composit ion dependence is similar to independent-particle results. Moreover, classical depolarization effects are responsible for a very strong suppression of the abs orption intensity. We show that they can be taken into account in a simpler way using Maxwell-Garnett classical effective-medium theory. Emission spectra are in vestigated by calculating the absorption of excited nanocrystals at their relaxe d geometry. The structural contribution to the Stokes shift is about 0.5 eV. Th e decomposition of the emission spectra in terms of independent-particle transit ions is similar to what is found for absorption. For the emission, very weak tra nsitions are found in Ge-rich clusters well below the strong absorption onset.

Generalized effective-medium theory of induced polarization

A rigorous physical-mathematical model of heterogeneous conductive media is based on the effective-medium approach. A generalization of the classical effective-medium theory (EMT) consists of two major parts: (1) introduction of effective-conductivity models of heterogeneous, multiphase rock formations with inclusions of arbitrary shape and conductivity using the principles of the quasi-linear (QL) approximation within the framework of the EMT formalism and (2) development of the generalized effective-medium theory of induced polarization (GEMTIP), which takes into account electromagnetic-induction (EMI) and induced polarization (IP) effects related to the relaxation of polarized charges in rock formations. The new generalized EMT provides a unified mathematical model of heterogeneity, multiphase structure, and the polarizability of rocks. The geoelectric parameters of this model are determined by the intrinsic petrophysical and geometric characteristics of composite media: the mineralization and/or fluid content of rocks and the matrix composition, porosity, anisotropy, and polarizability of formations. The GEMTIP model allows one to find the effective conductivity of a medium with inclusions that have arbitrary shape and electrical properties. One fundamental IP model of an isotropic, multiphase, heterogeneous medium is filled with spherical inclusions. This model, because of its relative simplicity, makes it possible to explain the close relationships between the new GEMTIP conductivity-relaxation model and an empirical Cole-Cole model or classical Wait’s model of the IP effect.

Ab Initio calculations of the anisotropic dielectric tensor of GaAs/AlAs superlattices.

The static dielectric properties of (001)(GaAs)(p)/(AlAs)(p) superlattices have been calculated as a function of their period p for 1< or = p < or =12, starting from density-functional theory. The interplay between quantum confinement and local field effects is shown to be crucial. For light polarized in the growth direction it leads to the otherwise surprising justification of the use of a classical effective medium theory, even for the smallest periods. Only the inclusion of both contributions allows in ab initio and in semiempirical calculations to reproduce the experimentally observed birefringence.

Foam rheology in the wet and dry limits

Understanding the rheological behavior of wet foams is important as a basic problem in fluid physics, and as a practical problem in many industries. This lecture will describe research into the wet and dry limits of foam rheology by a relatively new experimental technique in which foam drops are acoustically levitated and driven into motion. In the dry limit, the drops behave as viscoelastic solids. The effective moduli of the foam are estimated by observing the resonances of the drops and matching them to an analytical model for viscoelastic sphere vibrations. Analytical explorations of the wet limit have proceeded by considering the dynamics of a single bubble in a volume of liquid determined by the foam’s void fraction. The linearized result is a wave equation, from which the natural frequencies and mode shapes of wet foam drops are determined. Relationships between this wave equation and those of classical effective medium theories will be described. [Work supported by NASA.]

Dielectric properties of rat liver in vivo: analysis by modeling hepatocytes in the tissue architecture

The audio/radiofrequency dielectric dispersion of rat liver is analyzed by applying several competent mixture theories combined with a realistic model of hepatocytes. A naive application of the Maxwell–Wagner (interfacial-polarization) theory could not fully explain the observed dielectric behavior especially at frequencies below 1 MHz. The Bruggeman–Hanai-type effective-medium theory (EMT) proved competent to some extent in simulating the observation on liver at low frequencies, although some sizeable discrepancies between theory and observation still remained unexplained. These remaining discrepancies, however, were minimized when we applied a novel theory developed in this study. This theory introduces second-order corrections for possible dipole–dipole interaction (DDI) effects to the classical EMT for a concentrated suspension of particles. Analysis by simulations based on the EMT-DDI revealed that this theory can predict: (i) the effective size and shape of hepatic cell plates within the liver tissue, (ii) values of the specific capacitance for plasma, nuclear and mitochondrial membranes associated with the hepatocyte, and (iii) cytosolic as well as nucleoplasmic conductivities of physiological interest.

Entropic model for the optical properties of heterogeneous media: Validation on granular gold films near percolation

A tool for the morphological analysis of heterogeneous media, namely, the normalized configuration entropy, is applied to the study of the specific morphology of granular metallic thin films. The proposed method allows us to determine the typical length ${l}_{o}$ that is characteristic of the disorder of the image and we have developed an optical model for heterogeneous media, that is based on the partition of the actual image of the medium at the size ${l}_{o}.$ The model accounts well for the optical properties of thin granular gold films near the percolation threshold, where the classical effective-medium theories fail. The sensitivity of our model to local fluctuations in the morphology is tested on simulated images that are generated by using different algorithms.

Photoconductivity and the photo-Hall effect in inhomogeneous semiconductor alloys

The classical effective-medium theory for the calculation of the conductivity and Hall coefficient of inhomogeneous semiconductor alloys with the presence of photogenerated nonequilibrium charge carriers is developed. Using the composite spherical inclusions model it is shown that the Hall mobility is always less than the initial one, while the Hall concentration of free charge carriers is defined mainly by the concentration of charge carriers in the connected region and does not coincide with the sample mean concentration. The Lux - Ampère characteristic of inhomogeneous semiconductor alloys is shown to be a linear function for weak and logarithmic function for high illumination intensities.

Anisotropic effective medium theories

The optical properties of anisotropic inhomogeneous media are studied within the framework of the classical 3D effective medium theories of Maxwell Garnett and Bruggeman, and the 2D theory of Yamaguchi et at. The origin of the anisotropy is either the nonspherical shape of the metallic inclusions in the 3D systems, or the distribution of the inclusions (even if spherical) on a substrate in the 2D configuration. In both cases, it leads to an anisotropic effective medium. In this paper, it is shown that this surrounding anisotropic medium induces a fictitious deformation of the inclusions which reduces the anisotropy and shifts the resonance wavelengths toward the sphere plasmon resonance. In the case of the mean field theory of Bruggeman, it also affects the percolation threshold value. Although some of these theories are now quite old, they are still extensively used, especially for the predictions of the absorption of the composite media. Therefore the effect presented here for the first time should be taken into account

A material multipole theory of elastic dielectric composites

This article is concerned with the study of the overall mechanical and electrical properties of elastic dielectric composites by using the concept of material multipoles. In particular, by developing a statistical continuum material multipole theory, the effects of the microstructure of the inhomogeneities on the overall properties of the composites can be derived. In this theory, inhomogeneities are modelled as point material-induced multipoles. The macroscopic fields obtained from the ensemble average of the microscopic fields in the composite with statistically-distributed inhomogeneities in a uniform matrix are described by statistical continuum material multipoles in the matrix. This theory, in comparison with classical effective medium theory, has the possibility of attacking rather complicated problems such as, for instance, electromagnetoelaslic composites. It is shown that the statistical anisotropy and shape effects of microscopic ellipsoidal particles and their orientations on the overall effective properties of dielectric composites may be obtained in an explicit form. Also, the macroscopic constitutive relations of elastic dielectric composites and their macroscopic material parameters accounting for electroelastic interaction may be derived with the use of this statistical continuum multipole theory.

Effective Medium Theory for the Hall Effect in Disordered Materials

We present a classical effective-medium theory for the magnetoconductivity tensor in disordered materials which undergo a metal-nonmetal transition via a microscopically inhomogeneous transport regime.