Macroscopic Transport Phenomena Research Articles

Third-order accurate 13-moment equations for non-continuum transport phenomenon

The derivation of analytical equations of non-continuum macroscopic transport phenomena is underpinned by approximate descriptions of the particle distribution function and is required due to the inability of the Navier–Stokes equations to describe flows at high Knudsen number (Kn ∼ 1). In this paper, we present a compact representation of the second-order correction to the Maxwellian distribution function and 13-moment transport equations that contain fewer terms compared to available moment-based representations. The intrinsic inviscid and isentropic assumptions of the second-order accurate distribution function are then relaxed to present a third-order accurate representation of the distribution function, using which corresponding third-order accurate moment transport equations are derived. Validation studies performed for Grad’s second problem and the force-driven plane Poiseuille flow problem at non-zero Knudsen numbers for Maxwell molecules highlight an improvement over results obtained by using the Navier–Stokes equations and Grad’s 13-moment (G13) equations. To establish the ability of the proposed equations to accurately capture the bulk behavior of the fluid, the results of Grad’s second problem have been validated against the analytical solution of the Boltzmann equation. For the planar Poiseuille flow problem, validations against the direct simulation Monte Carlo method data reveal that, in contrast to G13 equations, the proposed equations are capable of accurately capturing the Knudsen boundary layer.

Nonlocal transport phenomena in Weyl metals beyond the mesoscopic scale

Axion electrodynamics governs electromagnetic properties of Weyl metals. Although transmission and reflection measurements of light have been proposed to confirm the axion electrodynamics, there are still lack of theoretical proposals for macroscopic nonlocal transport phenomena in Weyl metals. In this paper, we present nonlocal transport phenomena in time reversal symmetry-broken (TRSB) Weyl metals. Solving the axion electrodynamics numerically, we show that such nonlocal transport phenomena arise from the negative longitudinal magneto-resistivity (NLMR), combined with the anomalous Hall effect (AHE) in the axion electrodynamics. Since this nonlocal transport occurs beyond the mesoscopic scale, we conclude that these nonlocal properties have nothing to do with Fermi arcs, regarded to be clear evidence of the axion electrodynamics in the bulk.

Macroscopic transports in a rotational system with an electromagnetic field

In this work, we explore macroscopic transport phenomena associated with a rotational system in the presence of an external orthogonal electromagnetic field. Simply based on the lowest Landau level approximation, we derive nontrivial expressions for chiral density and various currents consistently by adopting small angular velocity expansion or Kubo formula. While the generation of anomalous electric current is due to the pseudo gauge field effect of the spin-rotation coupling, the chiral density and current can be simply explained with the help of Lorentz boosts. Finally, Lorentz covariant forms can be obtained by unifying our results and the magnetovorticity effect.

Can the microscopic and macroscopic transport phenomena in deep eutectic solvents be reconciled?

Deep eutectic solvents (DESs) have become ubiquitous in a variety of industrial and pharmaceutical applications since their discovery. However, the fundamental understanding of their physicochemical properties and their emergence from the microscopic features is still being explored fervently. Particularly, the knowledge of transport mechanisms in DESs is essential to tune their properties, which shall aid in expanding the territory of their applications. This perspective presents the current state of understanding of the bulk/macroscopic transport properties and microscopic relaxation processes in DESs. The dependence of these properties on the components and composition of the DES is explored, highlighting the role of hydrogen bonding (H-bonding) interactions. Modulation of these interactions by water and other additives, and their subsequent effect on the transport mechanisms, is also discussed. Various models (e.g. hole theory, free volume theory, etc.) have been proposed to explain the macroscopic transport phenomena from a microscopic origin. But the formation of H-bond networks and clusters in the DES reveals the insufficiency of these models, and establishes an antecedent for dynamic heterogeneity. Even significantly above the glass transition, the microscopic relaxation processes in DESs are rife with temporal and spatial heterogeneity, which causes a substantial decoupling between the viscosity and microscopic diffusion processes. However, we propose that a thorough understanding of the structural relaxation associated to the H-bond dynamics in DESs will provide the necessary framework to interpret the emergence of bulk transport properties from their microscopic counterparts.

Transport abnormity and its modulations via gating effect and light illumination at the SrNbO3/SrTiO3 interface

LaAlO3/SrTiO3-based two-dimensional electron gas (2DEG) has been extensively studied because of its intriguing physical properties and potential application prospect. However, seldom researches have related their extraordinary macroscopic transport phenomena to the microscopic domain structure of SrTiO3. This requires some unique technique like scanning superconducting quantum interference device (SQUID) microscopy. In this work, we developed a different 2DEG system at the interface of SrNbO3 thin film and SrTiO3. Using only the electrical methods, we found a pronounced hysteresis behavior in the resistance versus temperature curves, marked by the appearance/disappearance of two resistance peaks in the heating/cooling process. In sharp contrast to the conventional gate effect, the resistance peak grows under positive electric biases applied to backgate with conducting interface being grounded. In addition, a weak light (0.04 mW, 405 nm) can completely eliminate the two resistance anomalies. After a systematic analysis, we attribute the resistance anomaly to the cubic-tetragonal transition of bulk SrTiO3 and surface SrTiO3. The present work presents a promising demonstration to get mesoscopic information on oxide interface via transport behaviors.

Phase-field modeling of macroscopic freezing dynamics in a cylindrical vessel

Freezing is an essential step in pharmaceutical manufacturing processes for a long-term storage of therapeutic proteins. However, the process itself may affect the stability of proteins. Better understanding and quantification of freezing dynamics and the local environment from liquid solution to the frozen state would help to mitigate negative impacts on the protein products during freezing and subsequent manufacturing processes. We present a phase-field approach to resolve the relevant macroscopic transport phenomena including multi-phase flow, heat transfer, phase transition, and freeze concentration effects coupled with interfacial evolution in a cylindrical vessel. The theoretical formulation and modeling results show good agreement with experimental data.

Investigating the Grain Boundary Transport and Resulting Effective Bulk Properties for Polycrystalline Solid Electrolytes

All-solid-state batteries (ASSB) are candidates for the next-generation of safe and high energy density storage systems. In order to reach the full potential in terms of energy and power density the current limiting processes on the microscopic interface level as well as the macroscopic cell level need to be overcome. In this contribution, we explore the working principle of ASSBs and their interfaces in a multi-scale approach. We combine our 3D microstructure-resolved simulation tool BEST [1,2] with a supplementary thermodynamically consistent modelling framework [3] to capture the electrochemical performance and gain insight on - homogeneous solid-solid interface processes. Through this combined approach we are able to provide additional microscopic interface and bulk properties which are transferred as theory-based input parameters to our 3D microstructure-resolved simulations. Our focus lies on the transport limiting phenomena occurring at the homogeneous solid-solid interface e.g. grain boundary resistance in the polycrystalline electrolyte. On the microscopic level we resolve the formation of space charge layers in the solid electrolyte under the influence of grains and grain boundaries. This local electrostatic perturbation of the system through the additional polarization of the crystal grain boundaries is approximated by a mean-field approach to derive an effective dielectric constant for the polycrystalline bulk solid electrolyte. The new effective material parameter depends on the magnitude of the induced polarization and therefore relies on the material specific parameters e.g. grain size, grain width, grain volume fraction. This approach provides a link between microscopic material parameters and macroscopic electrochemical transport phenomena on cell level. Besides the effective material parameter estimation of the system, the three dimensional resolved transport through the granular solid electrolyte e.g., the grain and grain boundary transport is of special interest. In order to account for the lithium ion hopping probability between two neighbouring particles we introduce a modified interface flux at the grain interfaces. By explicit modelling of the polycrystalline electrolyte, the experimentally observed impedance characteristics are reproduced and identified. In an extended study for oxidic garnet type systems the correlation between grain size and grain impedance as well as the varying transport properties between boundary and core phase are presented. The comparison between simulations and experiments demonstrates the importance of interfacial processes and gives directions for the development of future ASSBs.

Aspects of colloid and interface in the engineering science of soil and water with emphasis on the flocculation behavior of model particles

Dynamic aspects of colloidal dispersion form a critical basis of the engineering science of soil and water quality when the relation between microscopic physicochemical and hydrodynamic conditions and macroscopic hydrological transport phenomena is considered. Examples in the paddy and environment can be found in the transportation and diffusion of pollution in the discharge of irrigation water. In this review, I focus on this validity with emphasis on the fact that the majority of colloidal materials in the soil and water environment are apt to flocculate. That is, the mechanical unit of transportation is a floc rather than individual fine matter: fragments of clay particles, insoluble metal oxides and any other natural organic matter, such as protein, polysaccharide and humic substances. On the surface of colloidal materials present in soil and aquatic environments, it is known that many chemical substances, nutrients, agrochemicals and pollutants are concentrated by adsorption or sorption. In addition, such adsorption and sorption behavior will alter the nature of the colloidal surface to induce different types of colloidal flocculation and complexation, which will result in differences in the transport phenomena in the aquatic and soil environments. Therefore, the analysis of flocculation dynamics in relation to adsorption of chemical substances onto colloidal particles is a key factor in comprehensive management of soil and water environments. For this purpose, we have carried out a study of flocculation by choosing four clay minerals: allophane, imogolite, montmorillonite and kaolinite. The choice was rather arbitrary but has been established to cover mostly different shapes and surface properties. Comparison with results obtained for a colloidal system composed of monodispersed spheres and polymeric flocculants is found to clarify the validity of the framework of analysis. The strategy is very useful to accumulate characteristic data and has opened the way to further analysis of the complex system of soil and aquatic environments.

Macroscopic Modeling of Liquid Water Based on Detailed Two-Phase CFD and Application on Full-Cell Scale Multiphysics Simulation

Overview In this work, full-cell scale simulations of PEFC are performed. The simulations deal with the behavior of liquid water in channels and porous structures in GDL and MPL, where the behavior is largely affected by geometry of channels and surface wettability. In order to execute efficient simulations in full-cell scale, all relevant macroscopic transport phenomena in PEFC (mass, chemical species and heat) are considered, where the phenomena are coupled with electrochemical reactions. Computational models for full-cell scale simulations are constructed based on the macroscopic transport models. In order to take into account liquid water flow depending on configurations of channels and porous structures, physical characteristics of liquid flow in channels are extracted from detailed two-phase CFD with resolved single channel with the fine computational mesh whose resolution is order of 10 micrometers. With these simulation techniques, we can estimate effects of liquid water on performances of PEFC. Numerical Modeling and Results A hybrid simulation method of the full-cell scale engineering model simulation and the detailed two-phase CFD is introduced. In order to estimate performance of PEFC cell taking all relevant transport phenomena (mass, chemical species and heat) is solved on the coarse-grained mesh, coupled with electrochemical reactions. The mass transport equation is solved by Darcy’s law, using the distribution of the equivalent hydraulic parameter in flow channels estimated by detailed gas phase CFD. Here mass transport is coupled with heat and chemical species transport equations. Those all transport phenomena are coupled with electrochemical reactions in the MEA. Transport of chemical species and water through the MEA are also considered. Many engineering models are employed in order to consider various transport phenomena, like water up-take into electrolytes and effective transport of oxygen from gas phase to reaction cites in catalyst layers, etc. Electrochemical reactions are modeled by Butler-Volmer equation, in the manner of lumped parameter models. In order to apply this method for conditions in which liquid water is important, two-phase fluid models should be constructed carefully. In our approach, the behavior of liquid water in channels is simulated in advance by the conventional volume-of-fluid model on the fine mesh whose resolution is order of 10 micrometers. Characteristics of gas and liquid transport under the presence of liquid water is extracted as two-phase permeability depending on volume fraction of liquid water and gas flow velocity. Those permeability are imported to the full-cell scale multiphysics simulation on the coarse-grained mesh. Results of calculations show dependence of cell performance on behavior of liquid water, which is effected by geometry of channels and wettability. This method turns out to be efficient to estimate cell performance and all relevant transport phenomena taking liquid water into account.

Hierarchical modeling of plasma and transport phenomena in a dielectric barrier discharge reactor

A novel dual-time hierarchical approach is developed to link the plasma process to macroscopic transport phenomena in the interior of a dielectric barrier discharge (DBD) reactor that has been used for soil remediation (Aggelopoulos et al 2016 Chem. Eng. J. 301 353–61). The generation of active species by plasma reactions is simulated at the microseconds (µs) timescale, whereas convection and thermal conduction are simulated at the macroscopic (minutes) timescale. This hierarchical model is implemented in order to investigate the influence of the plasma DBD process on the transport and reaction mechanisms during remediation of polluted soil. In the microscopic model, the variables of interest include the plasma-induced reactive concentrations, while in the macroscopic approach, the temperature distribution, and the velocity field both inside the discharge gap and within the polluted soil material as well. For the latter model, the Navier–Stokes and Darcy Brinkman equations for the transport phenomena in the porous domain are solved numerically using a FEM software. The effective medium theory is employed to provide estimates of the effective time-evolving and three-phase transport properties in the soil sample. Model predictions considering the temporal evolution of the plasma remediation process are presented and compared with corresponding experimental data.

Modeling of the Coupling of Microstructure and Macrosegregation in a Direct Chill Cast Al-Cu Billet

The macroscopic multiphase flow and the growth of the solidification microstructures in the mushy zone of a direct chill (DC) casting are closely coupled. These couplings are the key to the understanding of the formation of the macrosegregation and of the non-uniform microstructure of the casting. In the present paper we use a multiphase and multiscale model to provide a fully coupled picture of the links between macrosegregation and microstructure in a DC cast billet. The model describes nucleation from inoculant particles and growth of dendritic and globular equiaxed crystal grains, fully coupled with macroscopic transport phenomena: fluid flow induced by natural convection and solidification shrinkage, heat, mass, and solute mass transport, motion of free-floating equiaxed grains, and of grain refiner particles. We compare our simulations to experiments on grain-refined and non-grain-refined industrial size billets from literature. We show that a transition between dendritic and globular grain morphology triggered by the grain refinement is the key to the explanation of the differences between the macrosegregation patterns in the two billets. We further show that the grain size and morphology are strongly affected by the macroscopic transport of free-floating equiaxed grains and of grain refiner particles.

Multiscale modeling and experimental analysis of chemical vapor deposited aluminum films: Linking reactor operating conditions with roughness evolution

When composition and crystallographic structure remain constant, film properties mainly depend on microstructure and surface morphology. In this case, the proper modeling of a growing film allows linking the final surface features with the operating conditions at the reactor scale which in turn enables the control of the properties of the final film. In this work, an experimentally supported, coarse-grained, multiscale framework is applied for the modeling of the surface roughness of aluminum thin films processed by chemical vapor deposition from dimethylethylamine alane. The multiscale framework is developed by linking macroscopic transport phenomena based on continuum mechanics models with nanoscale surface events which are simulated stochastically. The model reproduces experimental data successfully, thus validating the method with good statistics. Finally, modeling of surface roughness enables the estimation of the electrical resistivity in good agreement with corresponding measurements.

Multiscale modeling and run-to-run control of PECVD of thin film solar cells

In this work, we focus on the development of a multiscale modeling and run-to-run control framework with the purpose of improving thin film product quality in a batch-to-batch plasma-enhanced chemical vapor deposition (PECVD) manufacturing process. Specifically, at the macroscopic scale, gas-phase reaction and transport phenomena yield deposition rate profiles across the wafer surface which are then provided to the microscopic domain simulator in which the complex microscopic surface interactions that lead to film growth are described using a hybrid kinetic Monte Carlo algorithm. Batch-to-batch variability has prompted the development of an additional simulation layer in which an exponentially weighted moving average (EWMA) control algorithm operates between serial batch deposition sequences to adjust the operating temperature of the PECVD reactor to overcome drift in the electron density of the plasma. Application of the run-to-run (R2R) control system developed here is shown to reduce offset in the product thickness from 5% to less than 1% within 10 batches of reactor operation. Finally, we propose an extension of the EWMA algorithm to four independent, radial wafer zones in order to improve thickness uniformity in the presence of spatially non-uniform species concentrations. It is demonstrated that the produced thin films can be driven to the desired thickness set-point of 300 nm in less than 10 batches in the presence of both electron density drift and non-uniform deposition rate profiles.

Process-scale modelling of microstructure in direct chill casting of aluminium alloys

The mechanical properties of an alloy being related to its microstructure, the understanding of the mechanisms responsible for the grain structure formation in direct chill casting is crucial. However, the grain size prediction by modelling is difficult since a variety of multi-scale coupled phenomena have to be considered. Nucleation and growth of the grains are interrelated, and the macroscopic transport phenomena such as the motion of grains and inoculant particles with the flow impact the nucleation-gowth competition. Thus we propose to study the grain size distribution of a 5182 alloy industrial scale slab of 510 mm thickness, both non-inoculated and inoculated with Al-3Ti-1B, for which experimental grain size measurements are available. We use a volume-averaged two-phase multi-scale model that describes nucleation from inoculant particles and grain growth, fully coupled with macroscopic transport phenomena: fluid flow induced by natural convection and solidification shrinkage, heat, mass and solute mass transport, grains and inoculant particles motion. We analyze the effect of liquid and grain motion as the effect of grain morphology on microstructure formation and we show in which extent those phenomena are responsible for the grain size distribution observed experimentally. The effect of the refiner level is also studied.

Modeling diffusion-governed solidification of ternary alloys – Part 2: Macroscopic transport phenomena and macrosegregation

Part 1 of this two-part investigation presented a multiphase solidification model incorporating the finite diffusion kinetics and ternary phase diagram with the macroscopic transport phenomena (Wu et al., 2013). In Part 2, the importance of proper treatment of the finite diffusion kinetics in the calculation of macrosegregation is addressed. Calculations for a two-dimensional (2D) square casting (50×50mm2) of Fe–0.45wt.%C–1.06wt.%Mn considering thermo-solutal convection and crystal sedimentation are performed. The modeling result indicates that the infinite liquid mixing kinetics as assumed by classical models (e.g., the Gulliver–Scheil or lever rule), which cannot properly consider the solute enrichment of the interdendritic or inter-granular melt at the early stage of solidification, might lead to an erroneous estimation of the macrosegregation. To confirm this statement, further theoretical and experimental evaluations are desired. The pattern and intensity of the flow and crystal sedimentation are dependent on the crystal morphologies (columnar or equiaxed); hence, the potential error of the calculated macrosegregation caused by the assumed growth kinetics depends on the crystal morphology. Finally, an illustrative simulation of an engineering 2.45-ton steel ingot is performed, and the results are compared with experimental results. This example demonstrates the model applicability for engineering castings regarding both the calculation efficiency and functionality.

Parameterizing the Morse potential for coarse-grained modeling of blood plasma

Multiscale simulations of fluids such as blood represent a major computational challenge of coupling the disparate spatiotemporal scales between molecular and macroscopic transport phenomena characterizing such complex fluids. In this paper, a coarse-grained (CG) particle model is developed for simulating blood flow by modifying the Morse potential, traditionally used in Molecular Dynamics for modeling vibrating structures. The modified Morse potential is parameterized with effective mass scales for reproducing blood viscous flow properties, including density, pressure, viscosity, compressibility and characteristic flow dynamics of human blood plasma fluid. The parameterization follows a standard inverse-problem approach in which the optimal micro parameters are systematically searched, by gradually decoupling loosely correlated parameter spaces, to match the macro physical quantities of viscous blood flow. The predictions of this particle based multiscale model compare favorably to classic viscous flow solutions such as Counter-Poiseuille and Couette flows. It demonstrates that such coarse grained particle model can be applied to replicate the dynamics of viscous blood flow, with the advantage of bridging the gap between macroscopic flow scales and the cellular scales characterizing blood flow that continuum based models fail to handle adequately.

Simulation of Platelets Suspension Flowing Through a Stenosis Model Using a Dissipative Particle Dynamics Approach

Stresses on blood cellular constituents induced by blood flow can be represented by a continuum approach down to the μm level; however, the molecular mechanisms of thrombosis and platelet activation and aggregation are on the order of nm. The coupling of the disparate length and time scales between molecular and macroscopic transport phenomena represents a major computational challenge. In order to bridge the gap between macroscopic flow scales and the cellular scales with the goal of depicting and predicting flow induced thrombogenicity, multi-scale approaches based on particle methods are better suited. We present a top-scale model to describe bulk flow of platelet suspensions: we employ dissipative particle dynamics to model viscous flow dynamics and present a novel and general no-slip boundary condition that allows the description of three-dimensional viscous flows through complex geometries. Dissipative phenomena associated with boundary layers and recirculation zones are observed and favorably compared to benchmark viscous flow solutions (Poiseuille and Couette flows). Platelets in suspension, modeled as coarse-grained finite-sized ensembles of bound particles constituting an enclosed deformable membrane with flat ellipsoid shape, show self-orbiting motions in shear flows consistent with Jeffery's orbits, and are transported with the flow, flipping and colliding with the walls and interacting with other platelets.

Effects of A-EMS processing parameters on semisolid slurry production

A computational model coupling an electromagnetic model with a macroscopic heat and fluid flow model in semisolid Al alloy slurry preparation by A-EMS was developed. The effects of A-EMS processing parameters such as stirring current, stirring frequency and stirring gap width on macroscopic transport phenomena during solidification were analyzed. Both the computational and experimental results showed that more intensively uniform stirring fields and uniformly fine microstructures were obtained by optimizing processing variables.

Effects of annular electromagnetic stirring processing parameters on semi-solid slurry production

A computational model coupling an electromagnetic model with a macroscopic heat and fluid flow model in semi-solid aluminum alloy slurry preparation by annular electromagnetic stirring (A-EMS) was developed. Effects of A-EMS processing parameters, such as stirring current, stirring frequency and stirring gap width, on macroscopic transport phenomena during the solidification were analyzed by commercial software ANSYS 10.0 with corresponding experimental verification. The results show that the magnetic flux density and the melt velocity increase and the temperature difference decreases as stirring gap width and stirring frequency decrease or the stirring current increases. The slurry with the fine and uniform globular grain structure can be gained by adjusting gap width, electromagnetic frequency and current, such as under the conditions of 10 mm of gap width,10 Hz of electromagnetic frequency and 50 A of current. The calculated results are in reasonably good agreement with the measured ones.

Modeling the impacts of feed spacer geometry on reverse osmosis and nanofiltration processes

Maximizing mass transfer and minimizing hydraulic losses in spiral wound elements is critical for designing effective and efficient reverse osmosis (RO) and nanofiltration (NF) processes. Herein we describe a multi-scale modeling approach, which links microscopic and macroscopic transport phenomena in spiral wound elements. Model simulations elucidate the impacts of feed spacer geometry on full-scale RO/NF system performance considering four representative water treatment scenarios: (1) RO membranes used to desalt ocean water, (2) low-pressure RO membranes used to desalt brackish water, (3) ultra-low pressure RO membranes used to purify wastewater, and (4) NF membranes used to soften a hard, fresh water. According to model simulations, feed spacer geometry had little impact on mass transfer; hence, engineering spacers to improve concentration polarization, trans-membrane osmotic pressure, or product water quality may prove difficult and yield limited benefits. In contrast, thinner filaments spread further apart significantly reduced hydraulic losses with negligible impacts to mass transfer. In addition, a few non-circular filament shapes produced even lower hydraulic losses, which might prove beneficial for RO/NF treatment of low salinity waters where hydraulic losses through spiral wound elements contribute significantly to the total process energy consumption. In high salinity waters, improved spacer designs may not significantly reduce energy consumption because hydraulic losses through spiral wound elements are relatively small.