Classical Effective Medium Theory Research Articles

Microscopic thermal characteristics of parallelly arranged nanowires in a liquid: the role of interface thermal resistance, solid-like liquid layer, and the restricted phonon transport

Nanofluids based on extended nanostructures, such as nanowires, have been demonstrated improved thermal conductivities (κ). However, the lack of a complete understanding at the microscopic level hinders the development of such nanofluids towards practical applications. We aim to provide it by investigating how the interface thermal resistance (R b ), ballistic phonon transport, and the solid-like liquid layer affect the heat conduction in nanowire-based nanofluids. By employing Non-Equilibrium Molecular Dynamics (NEMD), it is found that the heat conduction in the parallelly arranged liquid and the nanowires exhibit a coupled thermal behavior owing to the R b . This contradicts the predictions of the classical parallel heat conduction model, therefore, a novel model is proposed taking this coupled behavior into account. Using this model, it is shown that the high κ of the solid phase has a limited contribution to the effective κ of nanofluids having short nanowires due to the dominant R b effect. For the case of long nanowires, however, the individual nanowire κ becomes a vital parameter defining the effective κ. Further, NEMD calculations reveal that the κ of suspended nanowires in a liquid is markedly reduced, questioning the validity of classical effective medium theories which use the bulk parameters. This reduction is attributed to surface atoms’ restricted vibrational freedom and the nanowire’s phonon-boundary scattering. By substituting this reduced κ of the solid phase into the new mathematical model, the theoretical predictions align closely with the NEMD calculations, exhibiting deviations below 10%. The sole contribution from the solid-like liquid layer to the κ enhancement lies between 20%–30% in the nanofluids presently considered. Therefore, the findings of this study highlight the important roles play by the identified microscopic thermal characteristics in defining the effective κ of nanofluids based on nanowires.

A molecular dynamics study of thermal conductivity and viscosity in colloidal suspensions: From well-dispersed nanoparticles to nanoparticle aggregates

This study investigates the microscopic transport behavior of nanofluids addressing some debatable points including the anomalous thermal conductivity (κ), against the predictions of classical effective medium theories. International Nanofluid Property Benchmark Exercise (INPBE) [J. Buongiorno et al., J. Appl. Phys. 106 (2009) 094312] has shown that no such anomaly found in well-dispersed nanofluids after conducting experiments for range of different types of nanofluids. However, a number of molecular dynamics based studies reported otherwise making inconsistent conclusion with INPBE. In this work, it is argued that the over predicted κ values reported in previous computational studies can be attributed to the ill-defined partial enthalpy formulation of the Green-Kubo method for multicomponent systems. Present study begins by addressing this issue via non-equilibrium molecular dynamics and shows that the results are in agreement with the conclusions of INPBE. Further, it is shown that the contribution of potential micro-mechanisms such as micro-convection due to Brownian motion, and the solid-like liquid layering are either absent or suppressed by the interface thermal resistance. The observed decreasing trend of viscosity enhancement to thermal conductivity enhancement ratio (Cη/Cκ) with increasing particle size indicates the improved heat transfer performance in nanofluids with larger nanoparticles. The effect of nanoparticle aggregation, the proposed originative mechanism of anomalous κ, is evaluated arranging nanoparticles as chain-like structures. A 67% improvement in κ is achieved with negligible viscosity variation. This rapidly reduces Cη/Cκ indicating better heat transfer performance with the presence of conductive paths due to the aggregation or in general extended nanostructures.

Quantum Optical Effective-Medium Theory for Layered Metamaterials at Any Angle of Incidence

The quantum optics of metamaterials starts with the question of whether the same effective-medium theories apply as in classical optics. In general, the answer is negative. For active plasmonics but also for some passive metamaterials, we show that an additional effective-medium parameter is indispensable besides the effective index, namely, the effective noise-photon distribution. Only with the extra parameter can one predict how well the quantumness of states of light is preserved in the metamaterial. The fact that the effective index alone is not always sufficient and that one additional effective parameter suffices in the quantum optics of metamaterials is both of fundamental and practical interest. Here, from a Lagrangian description of the quantum electrodynamics of media with both linear gain and loss, we compute the effective noise-photon distribution for quantum light propagation in arbitrary directions in layered metamaterials, thereby detailing and generalizing our previous work. The effective index with its direction and polarization dependence is the same as in classical effective-medium theories. As our main result, we derive both for passive and for active media how the value of the effective noise-photon distribution too depends on the polarization and propagation directions of the light. Interestingly, for s-polarized light incident on passive metamaterials, the noise-photon distribution reduces to a thermal distribution, but for p-polarized light it does not. We illustrate the robustness of our quantum optical effective-medium theory by accurate predictions both for power spectra and for balanced homodyne detection of output quantum states of the metamaterial.

Prediction on the relative permittivity of energy storage composite dielectrics using convolutional neural networks: A fast and accurate alternative to finite-element method

The relative permittivity is one of the essential parameters determines the physical polarization behaviors of the nanocomposite dielectrics in many applications, particularly for capacitive energy storage. Predicting the relative permittivity of particle/polymer nanocomposites from the microstructure is of great significance. However, the classical effective medium theory and physics-based numerical calculation represented by finite element method are time-consuming and cumbersome for complex structures and nonlinear problem. The work explores a novel architecture combining the convolutional neural network (ConvNet) and finite element method (FEM) to predict the relative permittivity of nanocomposite dielectrics with incorporated barium titanite (BT) particles in polyvinylidene fluoride (PVDF) matrix. The ConvNet was trained and evaluated on big datasets with 14266 training data and 3514 testing data generated form a programmatic algorithm. Through numerical experiments, we demonstrate that the trained network can efficiently provide an accurate agreement between the ConvNet model and FEM by virtue of the significant evaluation metrics <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$R^{2}$</tex> , which reaches as high as 0.9783 and 0.9375 on training and testing data, respectively. The strong universality of the presented method allows for an extension to fast and accurately predict other properties of the nanocomposite dielectrics.

Multi‐scale characterization of granular media by in situ laboratory X‐ray computed tomography

AbstractInvestigations of biphasic monodisperse soft (rubber) and stiff (glass) particle mixtures under hydrostatic conditions show an interesting behavior with regard to the effective stiffness. P‐wave modulus measured by acoustic wave propagation at ultrasonic frequencies showed a significant decline while more soft particles are added, that is, higher rubber volume fractions, due to a change in the microstructure of the granular medium. However, for small volume fractions of soft particles, it could be observed that the P‐wave modulus is increasing. This result cannot be explained by classical mixture rules or effective medium theories. For the understanding of those effects, a detailed insight into the microstructure of the granular medium is necessary. To gain this information and link it later back to the measured effective mechanical properties, high‐resolution micro X‐ray computed tomography (XRCT) imaging is a well‐established tool. With XRCT imaging, the granular microstructure can be visualized in 3D and characterized subsequently. Combining classical effective characterization methods with XRCT imaging can help to solve a variety of multi‐scale problems. Performing the characterization step in situ, meaning inside the laboratory‐based XRCT scanner, has the advantage that exactly the same samples are mechanically characterized and visualized. To address the mentioned observation above, we designed a low X‐ray absorbing oedometer cell with integrated broadband piezoelectric P‐wave transducers which enables this kind of investigation inside a laboratory‐based XRCT scanner. The focus of this contribution is on the general experimental methodology which can be transferred to other multi‐scale problems. It starts with a description of the image acquisition and ends with the post‐processing of the in situ acquired image data. To demonstrate this, cylindrical samples consisting of the same monodisperse rubber and glass particle mixtures that were studied before under hydrostatic stress conditions are considered. Selected results are presented to explain the single steps.

Thermally conductive silicone rubber composites with vertically oriented carbon fibers: A new perspective on the heat conduction mechanism

The continual increase in power density and consumption of modern electronic devices calls for high-performance thermal interface materials (TIMs). In this work, silicone rubber composites with vertically oriented magnetic carbon fibers (o-MCF/SR) were successfully prepared via the cast molding and filler orientation upon uniform magnetic field in a vacuum environment. The through-plane thermal conductivity of o-MCF/SR composites showed an unusual power-law growth with increasing MCF loading. At a 9 vol% MCF loading, the o-MCF/SR composite exhibited a maximum through-plane thermal conductivity of 4.72 W/(m·K) with 2045.5 % TCE, about 3.55 W/(m·K) higher than that of SR composites with randomly dispersed MCF (λ = 1.17 W/(m·K), TCE = 431.8 %). To reveal the underlying through-plane heat conduction mechanism of o-MCF/SR composites, finite element simulation combined with classical effective medium theory model and machine learning method was used. A homogeneous unit fiber-filled composite (HUFC) was modelled, and a new parameter influencing the through-plane thermal conductivity, i.e., shape factor (b/a), was introduced here for the first time. Theoretically, this shape factor was dependent on the filler content and indirectly reflected the assembly of matrix and 1D filler in HUFC fit to a parallel-series hybrid model. Furthermore, a decrease of b/a was practically found with increasing MCF loading, and the dominant series-type assembly gradually transformed to parallel-type assembly of the o-MCF/SR composites. This work not only developed a method to fabricate desirable TIMs that hold great promise for advanced thermal management, but also introduced a new parameter to reveal the underlying mechanism for heat conduction capacity of polymer composites.

3D finite-element modeling of effective elastic properties for fracture density and multiscale natural fractures

AbstractNatural fractures are usually multiscale in size, orientations and distribution, resulting in complex anisotropic characteristics. Analytical methods for quantifying the associated effective elastic properties are based on some assumptions, such as dilute fracture concentration and regular-shaped fractures, which do not occur in actual reservoirs. Here, we conduct anisotropic finite-element modeling of effective elastic properties of complex fractured rocks using the least-square fitting method. The algorithm is developed for a 3D case and validated by classical effective medium theories for models with different fracture densities. The results of the 3D numerical method agree well with the theoretical predictions at low fracture density. The model also considers the interactions among fractures to calculate equivalent stiffness tensors at high fracture density. Three 2D fracture models are simulated to demonstrate the basic behavior of stress interactions and their effect on the overall elasticity under different fracture densities. We applied the developed model to 3D natural fractures built from a real outcrop, and we found that the fracturing pattern significantly affects the effective anisotropy properties. The resultant P-wave phase velocities as functions of the incidence angle and frequency are anisotropic. This study provides a great potential to calculate equivalent stiffness tensors and anisotropic properties of 3D multiscale natural fractures.

Thermal metadevices with geometrically anisotropic heterogeneous composites

The classical effective medium theory (EMT) provides a powerful tool in designing heterogeneous-composite functional thermal metadevices. But it is usually appropriate for spatially symmetric or geometrically isotropic systems, which limits the flexibility or adjustability in control. Here, we develop a generalized EMT to predict effective thermal conductivities of heterogeneous systems with elliptical (or ellipsoidal) inclusions. With the generalized EMT, omnidirectional thermal invisibility and directional Janus thermal illusion are designed and experimentally demonstrated just by tuning orientations of shape-anisotropy particles. In particular, we try to clarify the respective scopes of the generalized Maxwell-Garnett and Bruggeman theory based on both theoretical interpretations and numerical simulations. Our work may offer a promising fundamental framework and application prototype in elaborating thermal metadevices with asymmetry, irregularity, or anisotropy in configuration.

Homogenization of layered media: Intrinsic and extrinsic symmetry breaking

A general homogenization procedure for periodic electromagnetic structures, when applied to layered media with asymmetric lattice cells, yields an effective tensor with magnetoelectric coupling. Accurate results for transmission and reflection are obtained even in cases where classical effective medium theory breaks down. Magnetoelectric coupling accounts for symmetry breaking in reflection and transmission when a non-symmetric structure is illuminated from two opposite sides.

Hall‐effect Measurements and Transport Properties of Heterostructures in the Model System NiTe2‐Sn12Sb2Te15

In composite materials of NaCl‐type Sn12Sb2Te15 with x equivalents of CdI2‐type NiTe2 (x = 0.2; 1; 2), both phases are stable from room temperature up to 500 °C without a significant extent of mutual doping. The thermoelectric properties of this model system, complemented by Hall measurements, show clear trends with increasing x. Both electrical and thermal conductivities increase significantly whilst Seebeck coefficients decrease due to an increase in charge carrier concentrations. The overall Figure of merit zT is slightly impaired upon heterostructuring with NiTe2. However, the good reproducibility and cyclability of the measurements renders these composites an intriguing model system to qualitatively examine the applicability of a simple single parabolic band (SPB) model based on Hall‐effect data to rather metallic heterostructures. This model is best applicable to composites with lower fractions of NiTe2 and gives the direction for tuning the charge carrier concentrations toward the optimum upon heterostructuring. These findings are in accordance with B‐factor analysis and classical effective medium theory for spheroidal precipitates.

Rheological analysis of nitrate molten salts with suspended particles for solar thermal plants

Binary alkali nitrate molten salts are currently the heat transfer fluid (HTF) and thermal energy storage (TES) media of choice in commercial solar thermal energy (STE) power plants. This paper studies the rheological properties of binary alkali nitrate molten salts containing two distinct classes of suspended particles with unique practical applications and dynamics. Phase change salt slurries (liquid/solid suspensions) can appear during plant start-up after local freezing in pipes. Molten salt-nanoparticle suspensions are being proposed in the literature as an advanced HTF with enhanced properties. The phase change slurries were analyzed by rheological measurement of off-eutectic salt mixtures at sub-liquidus temperatures combined with determination of solid fraction through differential scanning calorimeter (DSC) testing in a novel approach. Molten salts with a range of silica nanoparticle loadings were also studied in the rheometer. Both suspension types exhibit non-Newtonian, shear thinning behavior, with a dramatic increase in viscosity compared to the base fluid. Additionally, both suspension types show that measured viscosity depends on the shear history, but the trends in viscosity with shear history differs between the two systems. The increase in viscosity with solid volume fraction of the nanofluid is significantly higher than that of a partially-crystallized salt slurry at a given volume fraction. Particle aggregation, particle/cluster aspect ratio, cluster breakage and restructuring are considered as determining factors in the observed rheological behavior. Deviations from classical effective medium theories of well-dispersed systems are discussed. Differing trends suggest that unique physical phenomena govern the rheological behaviors of the molten salt mixtures with different suspended solid particles. Thus, engineers and scientists must exercise caution when extrapolating rheological results to unique applications. • Molten salt slurries and nanoparticle suspensions are investigated experimentally. • Rheology and calorimetry are combined to determine the viscosity dependence on solid volume fraction. • Viscosity of molten salt nanofluids follows a modified Batchelor expansion. • Viscosity depends on suspension type and shear history, and exhibits shear thinning/thickening.

Effective Medium Theory for the Elastic Properties of Composite Materials with Various Percolation Thresholds.

It is discussed that the classical effective medium theory for the elastic properties of random heterogeneous materials is not congruous with the effective medium theory for the electrical conductivity. In particular, when describing the elastic and electro-conductive properties of a strongly inhomogeneous two-phase composite material, the steep rise of effective parameters occurs at different concentrations. To achieve the logical concordance between the cross-property relations, a modification of the effective medium theory of the elastic properties is introduced. It is shown that the qualitative conclusions of the theory do not change, while a possibility of describing a broader class of composite materials with various percolation thresholds arises. It is determined under what conditions there is an elasticity theory analogue of the Dykhne formula for the effective conductivity. The theoretical results are supported by known experiments and show improvement over the existing approach. The introduction of the theory with the variable percolation threshold paves the way for describing the magnetorheological properties of magnetoactive elastomers. A similar approach has been recently used for the description of magneto-dielectric and magnetic properties.

Multiscale simulation of gas transport in mixed-matrix membranes with interfacial polymer rigidification

Abstract We investigate permeation in non-ideal mixed-matrix membranes (MMMs) having interfacial defects based on a multiscale simulation approach, involving sequential nanoscale and macroscale simulations. Our approach combines insight from equilibrium molecular dynamics (EMD) simulation of the transport in the individual phases, and in the interfacial region, with macroscopic simulation of the transport through solution of coupled 3-D partial differential equations (PDEs) via a finite-element method (FEM). Thus, unlike existing adaptations of classical effective medium theory (EMT), our approach avoids the empirical fitting of filler-polymer interfacial properties, such as interfacial thickness and permeability, against experimental permeation data. While the proposed multiscale simulation approach is general and applicable to any MMM system, it is illustrated in the context of single CO 2 and CH 4 permeation in two different polyimide-based MMMs; with one using MFI-type zeolite as filler phase and the other using carbon molecular sieves (CMS). For both systems, our nanoscale simulations reveal an interfacial region with rigidification of the polymer and reduced permeability at the polymer-adsorbent interface. Comparison of permeability predictions of classical EMT-based models considering interfacial rigidification, with our macroscale simulations, demonstrates the former to be best at low particle loadings. Further, our macroscale simulations reveal the existence of an optimum filler particle size, never discussed before, which maximizes the permeability in non-ideal MMMs; this arises from the competing effects of decrease in permeability and decrease of the relative interfacial resistance with increase of filler particle size. Moreover, the CO 2 / CH 4 perm-selectivity is found strongly sensitive to the interfacial resistance for both finite uniform and non-uniform particle size distributions, an effect not captured by existing EMT models and overlooked in prior fundamental approaches.

Magnetic Field Effect on Thermal, Dielectric, and Viscous Properties of a Transformer Oil-Based Magnetic Nanofluid

Progress in electrical engineering puts a greater demand on the cooling and insulating properties of liquid media, such as transformer oils. To enhance their performance, researchers develop various nanofluids based on transformer oils. In this study, we focus on novel commercial transformer oil and a magnetic nanofluid containing iron oxide nanoparticles. Three key properties are experimentally investigated in this paper. Thermal conductivity was studied by a transient plane source method dependent on the magnetic volume fraction and external magnetic field. It is shown that the classical effective medium theory, such as the Maxwell model, fails to explain the obtained results. We highlight the importance of the magnetic field distribution and the location of the thermal conductivity sensor in the analysis of the anisotropic thermal conductivity. Dielectric permittivity of the magnetic nanofluid, dependent on electric field frequency and magnetic volume fraction, was measured by an LCR meter. The measurements were carried out in thin sample cells yielding unusual magneto-dielectric anisotropy, which was dependent on the magnetic volume fraction. Finally, the viscosity of the studied magnetic fluid was experimentally studied by means of a rheometer with a magneto-rheological device. The measurements proved the magneto-viscous effect, which intensifies with increasing magnetic volume fraction.

Single-parameter scaling in the magnetoresistance of optimally doped La2−xSrxCuO4

We show that the recent magnetoresistance data on thin-film La$_{2-x}$Sr$_{x}$CuO$_4$ (LSCO) in strong magnetic fields ($B$) obeys a single-parameter scaling of the form MR$(B,T)=f(\mu_H(T)B)$, where $\mu_H^{-1}(T)\sim T^{\alpha}$ ($1\le\alpha\le2$), from $T=180$K until $T\sim20$K, at which point the single-parameter scaling breaks down. The functional form of the MR is distinct from the simple quadratic-to-linear quadrature combination of temperature and magnetic field found in the optimally doped iron superconductor BaFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$. Further, low-temperature departure of the MR in LSCO from its high-temperature scaling law leads us to conclude that the MR curve collapse is not the result of quantum critical scaling. We examine the classical effective medium theory (EMT) previously used to obtain the quadrature resistivity dependence on field and temperature for metals with a $T$-linear zero-field resistivity. It appears that this scaling form results only for a binary, random distribution of metallic components. More generally, we find a low-temperature, high-field region where the resistivity is simultaneously $T$ and $B$ linear when multiple metallic components are present. Our findings indicate that if mesoscopic disorder is relevant to the magnetoresistance in strange metal materials, the binary-distribution model which seems to be relevant to the iron pnictides is distinct from the more broad-continuous distributions relevant to the cuprates. Using the latter, we examine the applicability of classical effective medium theory to the MR in LSCO and compare calculated MR curves with the experimental data.

Experimental study of crack density influence on the accuracy of effective medium theory

SUMMARYEffective medium theory plays an important role in the characterization of fractured reservoirs. The main goal of this paper is to assess the accuracy of three classical effective medium theories (compliance-based non-interaction approximation, Hudson theory and anisotropic self-consistent approximation) and investigate their applicable frequency range. To evaluate the crack density limitation of these models, we construct a series of physical models with crack density varying from 0 to 12 per cent. To satisfy the long-wavelength approximation of effective medium theory, we consider a crack diameter and aperture of 3 and 0.12 mm, respectively. To study their appropriate high-frequency laboratory condition, we use the ultrasonic transmission method to measure the elastic wave velocities at frequencies of 500, 250 and 100 kHz. The experimental results are then compared with the effective medium theories to discuss their accuracy. We also highlight and compare the accuracy of these theories for the inversion procedure to quantify the crack density.

E-Wave software: EBSD-based dynamic wave propagation model for studying seismic anisotropy

The study of seismic anisotropy has benefited from the wide application of the electron backscatter diffraction (EBSD) technique that provides complete information on the crystallographic and shape preferred orientations in 2D sections. Classical effective medium theory statistically approximates the seismic anisotropy based on the crystallographic preferred orientation, but the shape preferred orientation is often idealized as e.g. parallel layering or oriented inclusions. Due to higher demands in precisely quantifying seismic anisotropy in natural rocks and taking full advantage of the EBSD technique, dynamic wave propagation methods have received broad attention. This paper presents the MATLAB program E-Wave based on a novel approach to directly use EBSD data for 2D numerical wave propagation simulation. The complete mechanical formulation and numerical benchmarks with simple model setups are presented. The E-Wave program allows straightforward EBSD data import, finite-difference simulations with one-button click, and automatic result analysis. The E-Wave program can be a helpful and independent tool in future works to shed light on the relationship between microstructures and seismic anisotropy, and contribute from the modelling perspective to studies in seismology, geodynamics and rock physics.

Classical and non-classical effective medium theories: New perspectives

Future research in electrodynamics of periodic electromagnetic composites (metamaterials) can be expected to produce sophisticated homogenization theories valid for any composition and size of the lattice cell. The paper outlines a promising path in that direction, leading to non-asymptotic and nonlocal homogenization models, and highlights aspects of homogenization that are often overlooked: the finite size of the sample and the role of interface boundaries. Classical theories (e.g. Clausius–Mossotti, Maxwell Garnett), while originally derived from a very different set of ideas, fit well into the proposed framework. Nonlocal effects can be included in the model, making an order-of-magnitude accuracy improvements possible. One future challenge is to determine what effective parameters can or cannot be obtained for a given set of constituents of a metamaterial lattice cell, thereby delineating the possible from the impossible in metamaterial design.

A theoretical and numerical study on the gas-contributed thermal conductivity in aerogel

In this paper, a modified model for predicting the gaseous thermal conductivity in aerogel pores is proposed based on the kinetic theory of gases and the data from Direct Simulation Monte Carlo (DSMC) method. With the proposed modified model and the classical Effective Medium Theory (EMT) model, a gas-contributed thermal conductivity model which includes the equivalent gaseous thermal conductivity and the solid-gas coupling thermal conductivity is derived. The present gas-contributed model is validated by available experiment results for different types of aerogels. Comparisons between the present model and existing models show that the present gas-contributed model has a higher accuracy without complex calculations and assumptions.

Effective dielectric constants and spectral density analysis of plasmonic nanocomposites

Cermet or ceramic-metal composite coatings promise great potentials in light harvesting, but the complicated composite structure at the nanoscale induces a design challenge to predict their optical properties. We find that the effective dielectric constants of nanocomposites predicted by finite-difference-time-domain (FDTD) simulation results match those of different classical effective medium theories in their respective validity range. However, a precise prediction of the fabricated nanocomposite properties for different filling factors is very challenging. In this work, we extract the spectral density functions in the Bergman representation from the analytical models, numerical simulations, and experimental data of plasmonic nanocomposites. The spectral density functions, which only depend on geometry of the nanocomposite material, provide a unique measure on the contribution of individual and percolated particles inside the nanocomposite. According to the spectral density analysis of measured dielectr...