Effective Medium Approach Research Articles

Influence of graphene nanoplatelets on the thermal conductivity of heat transfer oils based on the developed hotwire method

The thermal conductivity measurements of graphene nanoplatelets (GNP) loaded mineral oil suspensions are obtained using an unconventional custom-made Transient Hot-Wire setup using tungsten. The presence of a few layers of graphene in the prepared GNP using a single-step ultrasonication of graphite microparticles without the use of a surfactant is verified by AFM, TEM, Raman Spectroscopy, XRD, and XPS techniques. We measured the thermal conductivity and the specific heat capacity ( Cp ) of GNP-loaded mineral oil suspensions. The experimental result shows a maximum of 45.5% increment in the thermal conductivity of the mineral oil with 1 mg ml−1 (11.481 ×10−4 weight fraction) loading of GNP at 30 °C. Despite thermal conductivity enhancements, the results indicate that the Cp is not compromised, since a low concentration of nanoplatelets was used. The experimental results agree with the Maxwell-Garnett effective medium approach (MGEMA) model for the thermal conductivity of nanofluids which we found to be suitable for lower loading of nanoparticles. We propose GNP incorporated mineral oil suspensions are effective when it comes to heat transfer fluids even with the lower volume and mass fractions.

Experimental assessment of the effective-medium approach for disordered monolayers of particles with high scattering losses.

The validity of using an effective-medium approach (EMA) to model the reflectivity of a disordered monolayer of particles that scatter light significantly is tested experimentally. To achieve this, we measured the optical reflectivity versus the angle of incidence in an internal reflection configuration of a disordered monolayer of polymeric particles with negligible optical absorption and a diameter of about half a wavelength (size parameter of 1.2) deposited on a glass-air interface. We found a clear effective-medium film equivalence, even for low particle densities and for angles of incidence well beyond the critical angle, where light penetrates the monolayer less than a particle diameter.

Heat Generation and Diffusion in an Assembly of Magnetic Nanoparticles: Application to Magnetic Hyperthermia

We investigate the thermal generation and transport properties of an assembly of magnetic nanoparticles embedded in a solid or fluid matrix, subjected to an AC magnetic field. For this purpose, we first build the heat equation for the assembly using the effective thermal transport coefficients obtained within the effective medium approach. In the present calculation, the SAR is obtained from the (linear) dynamic response of the assembly to the AC magnetic field. We numerically solve the extended heat equation and, as a preliminary study, we obtain the space-time profile of the temperature and total power absorbed by the system.

Microstructure and performance of carbon fiber reinforced aluminum matrix composites with molybdenum carbide coating on carbon fibers

In this work, a molybdenum carbide coating on the surface of short carbon fibers prepared using molten salt method was proposed to ameliorate the interfacial bonding and improve the performance of carbon fiber/Al composites. The carbon fiber/Al composites were produced using vacuum hot pressing. The characteristics of molybdenum carbide coating were analyzed. Besides, the microstructures, bending strength and thermal properties of the carbon fiber/Al composites were explored. Furthermore, the interfacial thermal resistance of the composites was investigated in relation to theoretical evaluations derived from the combined Maxwell-Garnett effective medium approach and acoustic mismatch model schemes. The results indicated that a homogeneous Mo2C coating with a thickness of 0.5 μm was obtained by proper molar ratio of carbon fibers, MoO3 and chloride salts mixture and heated at 1000 °C for 60 min. The Mo2C coating greatly enhanced the bond between the aluminum matrix and carbon fiber, leading to improvements in the densification behavior and bending strength of the coated composites. The enhanced thermal properties including improved thermal conductivity and reduced coefficient of thermal expansion (CTE) were also achieved by the Mo2C coating. The in-plane thermal conductivity of 60 vol.% Mo2C-coated carbon fiber/Al composite was 221 W·m−1·K−1 enhanced by 92% compared to that of uncoated composite and the CTE was 6.0 × 10–6 K−1 which was suitable for electronic packaging materials.

Mixing Rules for Left-Handed Disordered Metamaterials: Effective-Medium and Dispersion Properties.

Left-handed materials are known to exhibit exotic properties in controlling electromagnetic fields, with direct applications in negative reflection and refraction, conformal optical mapping, and electromagnetic cloaking. While typical left-handed materials are constructed periodic metal-dielectric structures, the same effect can be obtained in composite guest-host systems with no periodicity or structural order. Such systems are typically described by the effective-medium approach, in which the components of the electric permittivity tensor are determined as a function of individual material properties and doping concentration. In this paper, we extend the discussion on the mixing rules to include left-handed composite systems and highlight the exotic properties arising from the effective-medium approach in this framework in terms of effective values and dispersion properties.

Effective-medium approach to the resonance distribution of wave scattering in a random point field

Effective-medium approach to the resonance distribution of wave scattering in a random point field

Modeling of periodical shearing flow in a fibrous space with applications in shear-induced brain injury

This paper presents a theoretical model examining the interaction between a fibrous network and viscous fluid flow driven by an oscillating boundary. The aim is to understand how oscillating impacts are transmitted from the skull, through the arachnoid trabeculae network filled with cerebrospinal fluid, as observed in shaken baby syndrome. The model uses an effective medium approach to determine the fluid velocity field while each fiber is treated as a soft string undergoing deformation. Results indicate that the frequency of oscillation, fiber stiffness, and porous structure resistance significantly influence the oscillating shearing flow, as indicated by the Womersley (Wo), Brinkman (α), and Bingham (Bm) numbers. Application of the model to shaken baby syndrome suggests that oscillations in the cerebrospinal fluid and arachnoid trabeculae can significantly surpass those on the skull, leading to intense shear stress penetration to the brain. This model is the first study to integrate the dynamic response of string-like fibrous networks in fluid flows with oscillating boundaries and offers a quantitative framework for predicting the transmission of shearing forces from the skull to the brain matter.

Converging rainbow trapping silencers for broadband sound dissipation in a low-speed ducted flow

Rainbow trapping filters (RTFs) have been so far investigated to achieve broadband unit sound absorption in closed-end duct terminations. However, opened RTFs have been scarcely explored to realize broadband low-frequency dissipation of sound waves while being traversed by a low speed flow. To bridge the gap, we propose a RTF composed of coiled cavities whose inner radius follows a flow-compliant converging profile, referred to as a converging coiled CCRTF silencer. An effective medium approach and the transfer matrix method (TMM) showed the ability of such devices to produce slow sound, impedance matching and minute sound reflection and transmission over a wide bandwidth, confirmed by finite element simulations and scattering matrix measurements without flow. A causal analysis revealed that a large density of wall resonators enhances the silencer performance while its bandwidth is driven by the coiling factor, convergent contraction ratio and cavities axial growth. Particle swarm optimization of these parameters led to a sub-wavelength CCRTF silencer with near-unit dissipation over 3.5 octaves from 200 Hz upwards. Extended TMM and aeroacoustic measurements showed resilience of the CCRTF performance under upstream or downstream propagation conditions for outlet Mach numbers below 0.16, thereby opening up applications like the design of silent convergent nozzles.

Investigation on Low-Frequency and Broadband Sound Absorption of the Compact Anechoic Coating Considering Hydrostatic Pressure

The anechoic coating capable of absorbing sound energy in low frequencies within broadband is essential to conceal underwater vehicles. However, the geometric deformation and modification of mechanical parameters under hydrostatic pressure affect the prediction of absorption performance in deep water environments. An anechoic coating embedded with tandem resonant voids is proposed in this work to achieve quasi-perfect low-frequency and broadband absorption. The analytical method based on the effective medium approach and numerical simulation are performed to estimate the effects of hydrostatic pressure on sound absorption. When additionally considering the dynamic mechanical parameters of the compressed viscoelastic medium, the original absorption humps in low frequencies are inclined to higher band, accompanied by the expanded absorption bandwidth. Then, the tandem coating specimen is measured in a water-filled impedance tube. The experimental spectra are consistent with the analytical and numerical results under various hydrostatic pressures, demonstrating the efficient absorption (α > 0.7) in broadband low frequencies via ordinary pressure. At the same time, the absorption spectrum under higher hydrostatic pressures is also verified in the tube. Consequently, this work paves the way for a broadband low-frequency underwater absorber design and provides an efficient method to characterize the low-frequency and broadband absorption from the coupled resonant coatings in deep water environments.

Thermal Conductivity of a Fluid-Filled Nanoporous Material: Underlying Molecular Mechanisms and the Rattle Effect.

Nanoporous materials are central to the energy and environmental crisis, with key applications in adsorption, separation, and catalysis. While confinement and surface effects on fluids severely confined in their porosity are well documented, the thermal behavior of nanoporous solids subjected to fluid adsorption remains puzzling in many aspects. With striking phenomena such as the so-called rattle effect, through which fluid/solid collisions decrease the overall thermal conductivity, the solid thermal conductivity and, more generally, heat transfer and dispersion in these complex systems challenge classical approaches (e.g., mixing rules including effective medium approaches fail to capture such effects as shown here). In particular, a robust molecular framework to describe the crossover between the decrease in thermal conductivity through the rattle effect in very narrow pores and the increase in thermal conductivity when replacing vacuum with a fluid phase in larger pores is still missing. Here, using a prototypical model of fluid-filled nanoporous materials (a Lennard-Jones phase confined in an all-silica zeolite), we perform a molecular simulation study to shed light on the parameters that govern the rattle effect in nanoporous solids. First, by varying the fluid/fluid, fluid/solid, and solid/solid interaction strengths as well as the fluid number density and mass density, we unravel the ingredients that lead to the essential coupling between fluid adsorption and phonon transport. Second, despite this complex interplay, inspired by pioneering molecular approaches on the rattle effect, we show that all data obey a simple statistical physics model that relies on the change in the speed of sound due to the fluid adsorbed density and the decrease in phonon lifetime due to scattering by fluid molecules. This framework, which provides a simple formalism to rationalize the thermal behavior of this class of solid/fluid composites, points to a decrease in thermal conductivity upon fluid confinement (up to 30% in some cases). Such an effect paves the way for the design of novel applications involving fluids in interaction with nanoporous materials.

Exascale Computational Fluid Dynamics in Heterogeneous Systems

Abstract Exascale computing has extended the reach of resolved flow simulations in complex, heterogeneous systems far beyond conventional computational fluid dynamics capabilities. As a result, unprecedented pore and microscale resolution have been achieved in domains that have been traditionally modeled by, and limited to, continuum, effective medium approaches. By making use of computational resources on the new exascale supercomputer, Frontier, at the Oak Ridge Leadership Computing Facility, we performed flow simulations that have pushed the limits of domain-to-resolution ratios by several orders of magnitude for heterogeneous media. Our approach is an incompressible, Navier–Stokes CFD solver based on adaptive, embedded boundary (EB) methods supported by the Chombo software framework for applied partial differential equations (PDEs). The computational workhorse in the CFD application code is an elliptic solver framework in Chombo for pressure-Poisson and viscous, Helmholtz terms that leverages a PETSc-hypre software interface tuned for accelerator-based platforms. We demonstrate scalability of the approach by replicating a unit cylinder packed with microspheres to achieve over 400 × 109 degrees-of-freedom simulated. These simulations model domain lengths of over 20 meters with channel volumes of over 400 cm3 and containing millions of packed spheres with 20 micron grid resolution, challenging current understanding of what it means to be a representative elementary volume (REV) of the continuum scale in heterogeneous media. We also simulate a range of Reynolds numbers to demonstrate wide applicability and robustness of the approach.

The interpretation of diverging hydrogen and carbon dioxide permeations with temperature across silica-based membranes

Hydrogen (H2) permeance across silica-based membranes increases with temperature, but carbon dioxide (CO2) permeance decreases. Because of the opposite signs of activation energies for H2 and CO2 permeation, silica-based membranes are widely used in separating H2 and CO2 at high temperatures due to the elevated difference between H2 and CO2 permeabilities. However, there has not been an explanation of the diverging permeance between H2 and CO2 with temperature. This study developed a gas permeation model encompassing gas penetration through silica matrix, Knudsen diffusion, and viscous flow. An Oscillator model with an effective medium approach was used to screen all possible pore size distributions and calculate the gas penetration through the silica matrix. However, no pore size distribution could allow positive activation energy for hydrogen and negative activation energy for carbon dioxide at the same time. After including Knudsen diffusion and viscous flow, the diverging permeance between H2 and CO2 with temperature was successfully interpreted. The pore size distribution and the fractional contribution from Knudsen diffusion and viscous flow, which could best fit experimental activation energies for H2 and CO2 permeation, were identified. In the silica matrix that formed the membranes, 5-membered rings were the dominant structures in pores, which was responsible for the positive apparent activation energy for H2. The negative CO2 apparent activation energy indicated that it was inevitable to have some Knudsen diffusion and viscous flow through some imperfections of the membrane. Our model demonstrated the importance of high-temperature gas separation, as high temperature could minimize the undesirable gas flow through imperfections. This study also implied that further improvement of H2/CO2 separation by silica-based membranes could be achieved by reducing imperfections.

Plasmon resonances of GZO core-Ag shell nanospheres, nanorods, and nanodisks for biosensing and biomedical applications in near-infrared biological windows I and II.

There is currently a great deal of interest in realizing localized surface plasmon resonances (LSPRs) in two distinct windows in the near-infrared (NIR) spectrum for in vivo biosensing and medical applications, the biological window (BW) I and II (BW I, 700-900 nm; BW II, 1000-1700 nm). This study aims to demonstrate that LSPRs of Ga-doped ZnO (GZO) core-silver (Ag) shell structures exhibit promising features for biological applications in the NIR BW I and II. Here, we study three different shapes for nanoshells: the core-shell nanosphere, nanorod, and nanodisk. In the calculation of the optical response of these nanoshells, an effective medium approach is first used to reduce the dielectric function of a nanoshell to that of an equivalent homogenous NP with an effective dielectric function. Then, the LSPR spectra of nanoshells are calculated using the modified long-wavelength approximation (MLWA), which corrects the polarizability of the equivalent NP as obtained by Gans theory. Through numerical investigations, we examine the impacts of the core and shell sizes of the proposed nanoshells as well as the medium refractive index on the position and line width of the plasmon resonance peaks. It is shown that the plasmon resonances of the three proposed nanoshells exhibit astonishing resonance tunability in the NIR region by varying their geometrical parameters. Specifically, the improved spectrum characteristics and tunability of its plasmon resonances make the GZO-Ag nanosphere a more viable platform for NIR applications than the spherical metal colloid. Furthermore, we demonstrate that the sensitivity and figure of merit (FOM) of the plasmon resonances may be significantly increased by using GZO-Ag nanorods and nanodisks in place of GZO-Ag nanospheres. It is found that the optical properties of the transverse plasmon resonance of the GZO-Ag nanodisk are superior to all plasmon resonances produced by the GZO-Ag nanorods and GZO-Ag nanospheres in terms of sensitivity and FOM. The FOM of the transverse plasmon mode of the GZO-Ag nanodisk is almost two orders of magnitude higher than that of the longitudinal and transverse plasmon modes of the GZO-Ag nanorod in BW I and BW II. And it is 1.5 and 2 times higher than the plasmon resonance FOM of GZO-Ag nanospheres in BW I and BW II, respectively.

Minimizing sampling induced errors in Ks-measurements of stone bearing soils

Macropores have a great effect upon the overall saturated hydraulic conductivity (Ks) of soil samples. However, when using steel-cylinders for soil sampling, especially in stone-rich sites, soil core samples often bear sampling induced macropores due to improper sampling operation. The minimization of this macropore related bias of stone bearing soils‘ matrix Ks values is of high concern. To quantify the sampling induced error of Ks values of stony soils, Ks values were measured on a series of soil cores (n = 46) collected at 5 Bavarian sites under arable and grassland management. Based on texture-related tabulated Ks values, so-called Ks factors were extrapolated, which are related to the macropore fraction of the soil (RoGeR model). The overall Ks values of the soil cores were reduced by these Ks factors. The resulting matrix-related Ks values of the stone bearing soils were contrasted against the General Effective Medium (GEM) approach. Here, the shape of stones was parameterized as well as the critical stone fraction (fc). When applying sample specific fc values, the correlation between the RoGeR- and the GEM approach resulted in a good agreement (R² = 0.9) with an acceptable root mean square error (RMSE) of 4.6 cm/d. Ks reduction using the RoGeR approach seems to be a viable way to fit measured Ks values of stone bearing soil cores with sampling induced macropores to matrix conditions. Alternatively, GEM provides a way to calculate matrix Ks values of stone bearing soils based on tabulated Ks values and soil particle information.

Determination of thermal conductivity in nano-oxides under the effect of size, dimension and thermal Kapitza resistance

The author has proposed a simple model to determine the effective thermal conductivity variance in nanomaterials with respect to size under Kapitza thermal resistance effect. The formulation is based on the relation of thermal conductivity with specific heat, sound velocity and mean free path in nanosolids. Using the Jiang’s qualitative approach for melting temperature variation in nanomaterials with dimension and size;the thermal conductivity expression for nanosolids is formulated. Effective thermal conductivity of nanosolid is determined on the basis of effective medium approach. The results obtained from formulation depicts the increase in Effective thermal conductivity of nanomaterial with increase in its size. The present model results are seen in good consistency with the available data of previous workers and matches the variation trend as predicted previously. The exponential drop in thermal conductivity of nanomaterials with their size reduction to nanoscale make them efficient material to be use in thermoelectric devices because of their high figure of merit.

Anisotropy and effective medium approach in the optical response of two-dimensional material heterostructures

Anisotropy and effective medium approach in the optical response of two-dimensional material heterostructures

On the Hybrid Modelling of Rigid Sonic Crystal Embedded in Plenum Chamber at Low Frequencies Using the Effective Medium Approach and Finite Element Method

This study explores the application of homogenization schemes in modelling acoustic wave propagation in a finite array of circular scatterers embedded into a 2D cavity. The cavity is integrated into the 2D waveguide attached to the cavity inlet and outlet. Square-lattice sonic crystal (SC), composed of rigid and radially symmetric circular cylinders, is used to represent the finite array in this study. The model is aimed at informing the novel designs of plenum windows with superior soundproofing performance. The sound transmission performance is analysed with hybrid numerical simulation using the Finite Element Method (FEM) and homogenization scheme. A theoretical homogenization method based on the Effective Medium Approach (EMA) is reviewed and implemented on the modelling of the SC array inside the cavity at low frequencies and then implemented in FEM. Comparison of the transmission loss (TL) reveals a high degree of matching between settings with and without homogenization at low-frequency range. It is observed that performance of the hybrid model maintains a high degree of matching provided the cavity modes are dominated by a single characteristic scale in the low frequency. This includes the case of a narrow plenum chamber with only a single cylinder placed inside the cavity with a width of one lattice constant. This homogenization method is proven to be more computationally efficient in FEM compared to the modelling of exact geometry of the problem.

Magnetization processes in two-dimensional arrays of iron nanowires

Arrays of iron nanowires (NWs) obtained by template-assisted electrodeposition constitute a promising composite material characterized by a combination of high magnetization in the filler and perpendicular magnetic anisotropy. The properties of these composites arise from the interplay between the behavior of individual NWs and their magnetostatic interactions. In this study, we investigated NW arrays with identical wire diameters but varying spatial arrangements. Major hysteresis loops were studied under various field directions relative to the NW axis. Key parameters such as the slope of the magnetization curve, saturation magnetization, and coercive force were quantified. Additionally, FORC (First Order Reversal Curve) measurements were conducted with the field oriented longitudinally with respect to the NW, offering insights into the inhomogeneity of the demagnetizing field influenced by the NW array's configuration. In the sample with the highest NW density, we observed isotropic behavior of the effective demagnetizing field, and we proposed an explanation for this phenomenon using the effective media approach. Micromagnetic simulations revealed that the magnetic behavior of individual NWs with a 100 nm diameter can be described as an interchange between volumes characterized by vortex and uniform magnetization patterns. Calculations of the demagnetizing field using the effective medium model demonstrated excellent agreement with experimental data across arrays featuring different NW densities. Remarkably, the quantitative consistency of coercive field values obtained from micromagnetic simulations and experimental measurements in the range of angles from 0° to 45° for the studied samples underscores the structural homogeneity of the obtained NWs.

Effect of granule sizes on magneto-optical spectra of nanocomposites

The magneto-optical transverse Kerr effect (TKE) spectroscopy allows non-contact investigation of nanostructures, giving valuable information about the microstructure of samples. In this paper, within the framework of effective medium approach we analyze the effect of granule size on the magneto-optical spectra of magnetic nanocomposites. We consider the influence of various microscopic parameters such as plasma frequency, relaxation time, the coefficient of the anomalous Hall effect inside the granule and on its surface on the amplitude and profile of the TKE spectrum. Three main mechanisms are considered: the quasi-classical size effect, spin–orbit interaction enhancement at the granule surface and change of the percolation threshold.

Formation and properties of spatially inhomogeneous plasma density gratings.

Volume plasma density gratings receive increasing interest since, compared to solid-state optical media, they posses significantly higher damage thresholds. The gratings are produced by counterpropagating laser pulses in underdense plasma. When analyzing their optical properties, usually they are assumed to be homogeneous in space. The latter assumption, however, breaks down, especially when the gratings are produced by short high-power laser pump pulses. Then, generically the plasma grating posses an inhomogeneous envelope which results from the superposition of the pump pulses envelopes. The present paper discusses the effect of grating inhomogeneity on reflection and transmission of probe pulses. A Gaussian plasma density grating becomes an apodized grating which offers significant improvement over homogeneous gratings due to side-lobe suppression while maintaining reflectivity and a narrow bandwidth. On the other hand, the reflected probe pulses receive a chirp which depends on the spatial scale. For a Gaussian grating a cubic spectral phase appears. Numerical particle-in-cell simulations are supported by theoretical analysis based on coupled mode equationsas well as an effective medium approach.