Effective Transport Coefficients Research Articles

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.

Effect of Carbon Nanotubes on Chloride Diffusion, Strength, and Microstructure of Ultra-High Performance Concrete.

This study delved into the integration of carbon nanotubes (CNTs) in Ultra-High Performance Concrete (UHPC), exploring aspects such as mechanical properties, microstructure analysis, accelerated chloride penetration, and life service prediction. A dispersed CNT solution (0.025 to 0.075 wt%) was employed, along with a superplasticizer, to ensure high flowability in the UHPC slurry. In addition, the combination of high-strength functional artificial lightweight aggregate (ALA) and micro hollow spheres (MHS) was utilized as a replacement for fine aggregate to not only reduce the weight of the concrete but also to increase its mechanical performance. Experimental findings unveiled that an increased concentration of CNT in CNT1 (0.025%) and CNT2 (0.05%) blends led to a marginal improvement in compressive strength compared to the control mix. Conversely, the CNT3 (0.075%) mixture exhibited a reduction in compressive strength with a rising CNT content as an admixture. SEM analysis depicted that the heightened concentration of CNTs as an admixture induced the formation of nanoscale bridges within the concrete matrix. Ponding test results indicated that, for all samples, the effective chloride transport coefficient remained below the standard limitation of 1.00 × 10-12 m2/s, signifying acceptable performance in the ponding test for all samples. The life service prediction outcomes affirmed that, across various environmental scenarios, CNT1 and CNT2 mixtures consistently demonstrated superior performance compared to all other mixtures.

Improvement of core heat transport in NBI plasmas of heliotron J using high-intensity gas puffing

Controlling the heat transport profile is important for high performance in magnetically confined fusion plasmas. In this study, improved electron heat transport was achieved in neutral beam injection plasmas by applying high-intensity gas puffing (HIGP) on a stellarator/heliotron device called Heliotron J. Compared with conventional gas puffing (GP) fueling discharge, a higher and more peaked electron temperature profile was obtained, and the core ion temperature was slightly higher but similarly shaped. Using similar parameters, the electron density profile for HIGP remained similar and differed from the hollow density profile observed in electron cyclotron heating-eIBT plasma. Transport analysis using the FIT3D and TR-snap codes showed a clear reduction in the effective electron heat transport coefficient in the plasma core region. However, more detailed experiments are required to understand the mechanisms underlying this improvement fully.

A Lumped Model of Water and Heat Transport in a PEMFC Fuel Cell and the Associated Methods for Estimating the Effective Transport Parameters

The fine and quantitative modelling of the coupled phenomena of water and oxygen transport and heat and charge transfer in PEMFCs is difficult from a practical point of view because the interfaces between the different layers are heterogeneous and difficult to characterize. They depend in particular on the mechanical stress field. Moreover, the two-phase flows in the porous layers and feeding channels are by nature stochastic and very difficult to predict. This fine modelling requires a perfect knowledge of the geometry, mechanical and thermal properties, wettability, etc... of the materials, their interfaces and their heterogeneity in space and time. Most of these parameters are unknown and so numerous that it is impossible to estimate them independently of each other by simple experiments. Based on this observation, our philosophy is to develop simple models whose effective transport parameters can be estimated by experiments carried out in situ, for real operating conditions [1]. These models are lumped models that depend on few parameters which integrate the properties of the interfaces. In this presentation, we propose a one-dimensional coupled water and heat transport model (adapted to a differential cell), associated with methods for estimating the unknown water transport and heat transfer parameters. The estimation of the parameters is performed in situ, for an imposed flow field geometry and clamping force. Original experiments are developed to decorrelate the effective diffusion coefficients in the gas phase, adsorbed phase and heat transport properties. The estimation of the parameters is based on simple water balances, i.e. a measurement of the quantities of water leaving the anode and cathode. The model and the experimental set-up are presented. The inverse technique of parameter estimation is detailed. Different materials are implemented in order to observe the resulting impact on the estimated effective transport coefficients. Acknowledgements The authors gratefully acknowledge the financial support of the Lorraine Université d’Excellence program.

Deciphering the physical basis of the intermediate-scale instability

We study the underlying physics of cosmic ray (CR)-driven instabilities that play a crucial role for CR transport across a wide range of scales, from interstellar to galaxy cluster environments. By examining the linear dispersion relation of CR-driven instabilities in a magnetised electron–ion background plasma, we establish that both the intermediate and gyroscale instabilities have a resonant origin, and show that these resonances can be understood via a simple graphical interpretation. These instabilities destabilise wave modes parallel to the large-scale background magnetic field at significantly distinct scales and with very different phase speeds. Furthermore, we show that approximating the electron–ion background plasma with either magnetohydrodynamics (MHD) or Hall-MHD fails to capture the fastest-growing instability in the linear regime, namely the intermediate-scale instability. This finding highlights the importance of accurately characterising the background plasma for resolving the most unstable wave modes. Finally, we discuss the implications of the different phase speeds of unstable modes on particle–wave scattering. Further work is needed to investigate the relative importance of these two instabilities in the nonlinear, saturated regime and to develop a physical understanding of the effective CR transport coefficients in large-scale CR hydrodynamics theories.

Tungsten transport due to the neoclassical toroidal viscosity induced by resonant magnetic perturbation in the EAST tokamak

The impact of neoclassical toroidal viscosity (NTV) induced by resonant magnetic perturbations (RMPs) on tungsten has been studied in EAST. Modeling results from NTVTOK show that the NTV effect on low charge state tungsten ions is greater than that on high charge state tungsten ions, and the effective transport coefficient of W20+ is only on the order of 10−4–10−3 m2/s, while the effective transport coefficient of W1+ can reach 0.1–1 m2/s, which is close to the 2D neoclassical diffusion coefficient of W1+. The flux of W1+ exhibits a clear phase dependence on the RMP spectrum, and the W1+ flux obtained from NTVTOK is higher at low toroidal mode numbers compared to high toroidal mode numbers of RMPs, which is qualitatively consistent with EAST experiments.

Low-frequency heat waves transport in graded Si–Ge alloys

In this work, we consider a rigid heat conductor graded material subjected to an oscillating thermal signal applied on its boundary. We use a recently proposed novel concept, the so-called spectral diffusivity, to characterize the response of the material to an externally applied variable temperature difference. The spectral diffusivity has the physical meaning of an effective transport coefficient. We found a frequency window between 10−2 and 102 Hz wherein the spectral diffusivity increases, showing a maximum. The transport equation was numerically solved to calculate the average heat flowing through the material. We found that it also increased having a maximum in the mentioned range of frequencies. We then investigated the thermal rectification of the material finding a maximum in the same frequency range. The thermal rectification, as well as the spectral diffusivity, improved as the inhomogeneity of the heat conductivity of the material was higher. The spectral diffusivity enables a more in-depth analysis of heat wave transfer, and it contributes to a better understanding of the material response in front of periodic thermal disturbances.

Machine learning-assisted MD simulation of melting in superheated AlCu validates the Classical Nucleation Theory

The validity of the Classical Nucleation Theory (CNT), the standard tool for describing and predicting nucleation kinetics in metastable systems, has been under scrutiny for almost a century. While the CNT is commonly employed to describe liquid → crystal and liquid ↔ vapor phase transitions, its application to the crystal → liquid case has been limited because of the experimental challenges in achieving superheating states and detecting homogeneous liquid nucleation. In this study, we performed comprehensive molecular dynamics (MD) simulations of spontaneous melting of a superheated AlCu crystal under atmospheric pressure at five temperatures, covering a superheating range of T/TL = 1.1–1.3, where TL is the liquidus temperature. Two realistic AlCu models were investigated: one described by the modified embedded atom method (MEAM) and the other by an interatomic potential generated by an artificial neural network machine learning (ML) approach, extensively trained on an ab initio dataset of liquid and crystal configurations. Fifty independent melting events were simulated at each temperature. By analyzing the distribution of melting times using the Poisson law, the homogeneous nucleation rate was determined through the mean lifetime method. Additionally, the Zeldovich factor, critical nucleus size, and work of formation were obtained using the mean first-passage time method, utilizing the disorder parameter based on atomic displacements (liquid-like atoms in the superheated crystal) as the reaction coordinate. Also, the effective atomic transport coefficient across the metastable crystal/critical liquid nucleus interface was determined by MD simulations as the interfacial attachment coefficient for nuclei growth rates. Using these simulation-generated data, the theoretical nucleation rates were calculated by the CNT with no fitting parameters. We found excellent agreement between the theoretically and MD-computed liquid nucleation rates for both MEAM and ML crystals. Notably, the effective solid-liquid interfacial free energy value obtained from the MD data aligns with its recent experimental measure. Moreover, the CNT qualitatively and quantitatively described the underlying details of liquid drop nucleation in our ML solid, unprecedentedly and accurately reproducing the kinetic prefactor and the size, formation energy, and growth rate of the critical nuclei. Thus, the melting of the AlCu model created through machine learning-processed quantum calculations, that is, not relying on hand-crafted interatomic potential functions, was successfully described by the CNT phenomenological formalism, without any adjustable parameters. This finding confirms the CNT as a very reliable descriptor of homogeneous nucleation in the superheated AlCu alloy and generalizes this theory as a powerful tool for analyzing and predicting the kinetics of crystal-liquid transitions.

Pore-Scale Simulation of Effective Transport Coefficients in the Catalyst Layer of Proton Exchange Membrane Fuel Cells

The catalyst layer (CL) of the proton exchange membrane (PEM) fuel cells is reconstructed using the sphere-based simulated annealing (SA) method. By changing carbon phase volume fraction and ionomer loading, the transports of oxygen, water vapor and proton inside the reconstructed CLs are studied using the D3Q7 multiple-relaxation-time (MRT) lattice Boltzmann (LB) method. The results show that Knudsen diffusion has an important role in gas diffusion in CL. The carbon phase distribution influences the gas diffusion process but has little effect on proton conduction. The simulated effective gas diffusivities in CL can fit the experimental data very well if using directly measured porosities, and a fitting formula is proposed to predict the effective diffusivity with porosity. Besides, the simulated effective proton conductivities in CL are in reasonable agreement with the experimental data if considering the ionomer swelling and proton conduction in the condensed water. The influence of the structural randomness of CL during the reconstruction process on the pore-scale simulations is also analyzed. The results show that the relative errors caused by structure randomness for the same structural parameters are not obvious. Therefore, a small number of reconstruction samples are enough to simulate the reasonable transport parameters of CL.

A multi-scale model for impingement drying of porous slab

Air impingement drying of a planar sheets of porous materials offers advantages of high and controllable heat and mass transfer rates. The governing heat and mass transfer phenomena involve multi-scale physical mechanisms ranging from mesoscopic pore scale to macroscopic jet scale. This work presents a pore-scale heat and mass transfer model of an unsaturated porous material based on statistically self-similar fractal scaling laws of pore structures. Furthermore, the effective transport coefficients are derived and applied to develop a cross-scale mathematical model for hot air impingement drying of a slab made of an unsaturated porous material. The flow and thermal fields of jet impingement and drying characteristics of unsaturated porous material are modeled numerically. The quantitative correlations between the mesoscopic pore structure and macroscopic heat and mass transfer properties are explored. The proposed fractal pore-scale model of porous material and cross-scale mathematical model of jet impingement show good agreement with experimental data. The effects of jet velocity, porosity as well as pore and tortuosity fractal dimensions on drying rate are discussed in detail. The computational results show that the mesoscopic pore structures indicate significant effect on the drying rate during later stage of drying. Results of this study provide useful guidance for efficient design of impingement of porous materials. • Meso-scale heat and mass transfer model of unsaturated porous material is proposed. • Multi-scale model for laminar impingement drying of porous slab is developed. • Impingement drying performance of porous slab is predicted. • Effect of mesoscopic structure on drying kinetics of porous material is explored.

Effects of liquid water on the pore structure and transport coefficients in the cathode catalyst layer of PEM fuel cells

We present a pore-scale simulation of the capillary condensation of water in the cathode catalyst layer (CCL) of proton exchange membrane fuel cells by the lattice Boltzmann method. Based on the reconstructed CCL, the capillary condensation process in CCL is simulated under different humidity conditions, and the effects of porosity and especially wettability on the liquid water distribution in CCL are studied. The influence of liquid water on the void pore size distribution and pore connectivity in CCL is evaluated, and the results show that the hydrophilic CCL is more prone to be flooded. Subsequently, the effective transport coefficients of oxygen and proton in partially saturated CCL are investigated. The results reveal that the hydrophobic CCL is beneficial for reducing the gas transport tortuosity but simultaneously causes a higher Knudsen diffusion resistance. By comprehensively considering the changes in tortuosity and Knudsen resistance caused by liquid water, a more practical correlation of effective diffusivity for the partially saturated CCL is proposed. Moreover, this work proves the vital role of liquid water in the proton conduction in CCL. The simulated effective proton conductivity in CCL is more agree with the measurements if the contribution of liquid water to proton transport is considered.

Fluctuating hydrodynamics of dilute electrolyte solutions: systematic perturbation calculation of effective transport coefficients governing large-scale dynamics

We study the transport properties of dilute electrolyte solutions on the basis of the fluctuating hydrodynamic equation, which is a set of nonlinear Langevin equations for the ion densities and flow velocity. The nonlinearity of the Langevin equations generally leads to effective kinetic coefficients for the deterministic dynamics of the average ion densities and flow velocity; the effective coefficients generally differ from the counterparts in the Langevin equations and are frequency-dependent. Using the path-integral formalism involving auxiliary fields, we perform systematic perturbation calculations of the effective kinetic coefficients for ion diffusion, shear viscosity, and electrical conductivity, which govern the dynamics on the large length scales. As novel contributions, we study the frequency dependence of the viscosity and conductivity in the one-loop approximation. Regarding the conductivity at finite frequencies, we derive the so-called electrophoretic part in addition to the relaxation part, where the latter has originally been obtained by Debye and Falkenhagen; it is predicted that the combination of these two parts gives rise to the frequency ω max proportional to the salt density, at which the real part of the conductivity exhibits a maximum. The zero-frequency limits of the conductivity and shear viscosity coincide with the classical limiting laws for dilute solutions, derived in different means by Debye, Falkenhagen, and Onsager. As for the effective kinetic coefficients for slow ion diffusions in large length scales, our straightforward calculation yields the cross kinetic coefficient between cations and anions. Further, we discuss the possibility of extending the present study to more concentrated solutions.

Estimation of porcine pancreas optical properties in the 600–1100 nm wavelength range for light-based therapies

This work reports the optical properties of porcine pancreatic tissue in the broad wavelength range of 600–1100 nm. Absorption and reduced scattering coefficients (µa and µs′) of the ex vivo pancreas were obtained by means of Time-domain Diffuse Optical Spectroscopy. We have investigated different experimental conditions—including compression, repositioning, spatial sampling, temporal stability—the effect of the freezing procedure (fresh vs frozen-thawed pancreas), and finally inter-sample variability. Good repeatability under different experimental conditions was obtained (median coefficient of variation less than 8% and ~ 16% for µa and µs′, respectively). Freezing–thawing the samples caused an irreversible threefold reduction of µs′ and no effect on µa. The absorption and reduced scattering spectra averaged over different samples were in the range of 0.12–0.74 cm−1 and 12–21 cm−1 with an inter-sample variation of ~ 10% and ~ 40% for µa and µs′, respectively. The calculated effective transport coefficient (µeff) for fresh pancreatic tissue shows that regions between 800–900 nm and 1050–1100 nm are similar and offer the lowest tissue attenuation in the considered range (i.e., µeff ranging from 2.4 to 2.7 cm−1). These data, describing specific light-pancreas interactions in the therapeutic optical window for the first time, provide pivotal information for planning of light-based thermotherapies (e.g., laser ablation) and instruction of light transport models for biophotonic applications involving this organ.

Sophisticated 3D microstructural reconstruction for numerical analysis of electrolyte imbibition in Li-ion battery separator and anode

A simplified approach to visualize and create high-fidelity three-dimensional (3D) microstructure reconstruction of Li-ion battery (LIB) separator (Polyethylene - PE) is proposed here, for comprehending the relationship between transport properties (Electrolyte saturation, Residual gas phase, effective transport coefficient - δ, and Macmullin number - Nm) and microstructure characteristics. In the construction of Li-ion battery, since electrolyte filling in separator and electrode is a decisive step that primarily governs the storage capacity, battery life cycle and safety, herein the study was extended to identify the quantity of residual gas in the separator/electrode microstructure for facilitating better wetting and infilling of electrolyte into the electrode and separator. Moreover, the effect of structural and transport properties with different graphite content (50%, 60%, and 70%) in the electrode were investigated followed by contact angle (CA) effect with electrolyte in the separator and graphite is presented. From the results of the study, it is claimed that the graphite contents of anode and contact angle of electrolytes explicitly impact the transport properties, in addition the conductivity of the electrolyte diminishes with respect to the microstructure of separator and anode.

(Digital Presentation) Numerical Characterization of Physical Properties of Microstructures in Lithium-Ion Batteries

In this paper, we present calculations of some of the key physical properties of microstructures of electrodes and separators present in lithium-ion batteries with porous electrode architectures. We analyze three-dimensional models of public domain real commercial porous anodes, cathodes and polyethylene (PE) separator, in order to characterize some of their microstructural properties. First, a pore space analysis of the binarized microstructure reveals the location and distribution of pores of various sizes, the overall porosity distribution and connectivity. Next, diffusion simulations using a random-walk method are performed to compute and accurately validate in-plane and through-plane effective transport coefficients and tortuosities, for different electrodes and calendaring levels. Single phase fluid flow simulations are performed using a commercial Lattice Boltzmann Method (LBM) solver to accurately validate the permeability of the microstructures. Next, multi-phase fluid flow simulations are done using this LBM solver to simulate the electrolyte in-filling process for various solvents. We predict that in-filling process may result in residual gas bubbles, which effect is shown in subsequent diffusion simulations to reduce the effective transport. The calculated McMillan numbers after in-filling show good agreement with experimental results. Next, we simulate the mechanical deformation of these microstructures under compressive strain using a finite element analysis (FEA) solver. This work illustrates how the use of multi-physics simulation tools can help to design these microstructures to satisfy the mechanical and electrochemical properties required of them. Figure 1

Effective transport coefficients of anisotropic disordered materials

A novel effective medium theory for homogenized transport coefficients of anisotropic mixtures of possibly anisotropic materials is developed. Existing theories for isotropic systems cannot be easily extended, because that would require geometric characterizations of anisotropic connectivity. In this work anisotropic connectivity is characterized by introducing a tensor that is constructed from a histogram of local percolating directions. The construction is inspired by local porosity theory. A large number of known and unknown generalized effective medium approximations for anisotropic media are obtained as limiting special cases from the new theory. Among these limiting cases the limit of strong cylindrical anisotropy is of particular interest. The parameter space of the generalized theory is explored, and the advanced results are applied to experiment.Graphic abstract

Elements of future snowpack modeling – Part 1: A physical instability arising from the nonlinear coupling of transport and phase changes

Abstract. The incorporation of vapor transport has become a key demand for snowpack modeling in which accompanied phase changes give rise to a new, nonlinear coupling in the heat and mass equations. This coupling has an impact on choosing efficient numerical schemes for 1D snowpack models which are naturally not designed to cope with mathematical particularities of arbitrary, nonlinear partial differential equations (PDEs). To explore this coupling we have implemented a stand-alone finite element solution of the coupled heat and mass equations in snow using the computing platform FEniCS. We focus on the nonlinear feedback of the ice phase exchanging mass with a diffusing vapor phase with concurrent heat transport in the absence of settling. We demonstrate that existing continuum-mechanical models derived through homogenization or mixture theory yield similar results for homogeneous snowpacks of constant density. When snow density varies significantly with depth, we show that phase changes in the presence of temperature gradients give rise to nonlinear advection of the ice phase amplifying existing density variations. Eventually, this advection triggers a wave instability in the continuity equations. This is traced back to the density dependence of the effective transport coefficients as revealed by a linear stability analysis of the nonlinear PDE system. The instability is an inherent feature of existing continuum models and predicts, as a side product, the formation of a low-density (mechanical) weak layer on the sublimating side of an ice crust. The wave instability constitutes a key challenge for a faithful treatment of solid–vapor mass conservation between layers, which is discussed in view of the underlying homogenization schemes and their numerical solutions.

A Probabilistic Formulation of the Diffusion Coefficient in Porous Media as Function of Porosity

We investigate the upscaling of diffusive transport parameters using a stochastic framework. At sub-REV (representative elementary volume) scale, the complexity of the pore space geometry leads to a significant scatter of the observed diffusive transport. We study a large set of volumes reconstructed from focused ion beam-scanning electron microscopy data. Each individual volume provides us sub-REV measurements on porosity and the so-called transport-ability, being a dimensionless parameter representing the ratio of diffusive flux through the porous volume to that through an empty volume. The detected scatter of the transport-ability is mathematically characterized through a probability distribution function (PDF) with a mean and variance as function of porosity, which includes implicitly the effect of pore structure differences among sub-REV volumes. We then investigate domain size effects and predict when REV scale is reached. While the scatter in porosity observations decreases linearly with increasing sample size as expected, the observed scatter in transport-ability does not converge to zero. Our results confirm that differences in pore structure impact transport parameters at all scales. Consequently, the use of PDFs to describe the relationship of effective transport coefficients to porosity is advantageous to deterministic semiempirical functions. We discuss the consequences and advocate the use of PDFs for effective parameters in both continuum equations and data interpretation of experimental or computational work. The presented statistics-based upscaling technique of sub-REV microscopy data provides a new tool in understanding, describing and predicting macroscopic transport behavior of microporous media.

Electrode fabrication process and its influence in lithium-ion battery performance: State of the art and future trends

Lithium-ion batteries (LIBs) are the main energy storage system used in portable devices. Their outstanding characteristics allied to the growing market of portable devices and electric vehicles provides batteries an increasing trend over the next years. During the past decade, improved materials for LIBs have been developed, with less attention being focused on the manufacturing process, despite its critical influence in battery performance. In the present work, the main electrode manufacturing steps are discussed together with their influence on electrode morphology and interface properties, influencing in turn parameters such as porosity, tortuosity or effective transport coefficient and, therefore, battery performance. A state of art on the main steps of the electrode manufacturing process is presented, together with future directions with respect to LIBs fabrication.

Brownian sieving enhancement of microcapillary hydrodynamic chromatography. Analysis of the separation performance based on Brenner’s macro-transport theory

In a recent article [Analytical Chemistry, 93(17), 6808–6816 (2021)], an unconventional device configuration enforcing a Brownian sieving mechanism was proposed as proof of concept for the efficient implementation of microcapillary hydrodynamic chromatography (MHDC). In this article, we perform a thorough analysis of the device geometry and of operating conditions, in order to single out the optimal configuration maximizing separation resolution. Brenner’s macro-transport theory provides the technical picklock to perform the search for the optimum over a wide choice of device geometries and for a range of values of the particle Péclet number covering most conditions encountered in practical implementations of MHDC. Specifically, effective transport coefficients defining the dynamics of the suspended phase are obtained by the solution of a two-dimensional steady-state advection-diffusion equation defined onto the channel cross-section. The eigenvalue/eigenfunction structure of the associated transient problem is exploited in order to quantify the timescale for reaching the macro-transport regime conditions. Based on this timescale and on the effective transport parameters, an estimate of the column length necessary to achieve a prescribed level of separation resolution is obtained. We identify device geometry and operating conditions where the capillary length is shrunk down by a factor above ten compared to the standard MHDC configuration. Lagrangian stochastic statistics of particle ensembles are used to validate the results obtained through Brenner’s macro-transport approach. The method proposed can be readily generalized to other classes of device geometries enforcing the same Brownian sieving mechanism.