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A gas model of diffusion in liquid metals is presented. In this model, ions of liquid metals are assumed to behave like the molecules in a dense gas. Diffusion coefficient of solute is discussed with reference to its mass, ionic size, and pair potential. The model is applied to the case of solute diffusion in liquid silver. An attempt was made to predict diffusion coefficients of solutes with reasonable accuracy.
In light water reactor fuel, gaseous fission products segregate to grain boundaries, resulting in the nucleation and growth of large intergranular fission gas bubbles. Based on the mechanisms established from density functional theory (DFT) and empirical potential calculations 1, continuum models for diffusion of xenon (Xe), uranium (U) vacancies and U interstitials in UO 2 have been derived for both intrinsic conditions and under irradiation. Segregation of Xe to grain boundaries is described by combining the bulk diffusion model with a model for the interaction between Xe atoms and three different grain boundaries in UO 2 ( Σ5 tilt, Σ5 twist and a high angle random boundary),as derived from atomistic calculations. All models are implemented in the MARMOT phase field code, which is used to calculate effective Xe and U diffusivities as well as redistribution for a few simple microstructures.
The wide use of diffusers, in various fields of technology, has resulted in several experimental projects to study the action and design of diffusers. Most of the projects dealt with steam (steam turbine nozzles). But diffusers have other applications - that is, ventilators, smoke ducts, air coolers, refrigeration, drying, and so forth. At present there is another application for diffusers in wind-tunnel design. Because of higher requirements and increased power of such installations more attention must be paid to the correctness of work and the decrease in losses due to every section of the tunnel. A diffuser, being one of the component parts of a tunnel , can in the event of faulty construction introduce considerable losses. Therefore, in the design of the new CAHI wind tunnel, it was suggested that an experimental study of diffusers be made, with a view to applying the results to wind tunnels. The experiments conducted by K. K. Baulin in the laboratories of CAHI upon models of diffusers of different cross sections, lengths, and angles of divergence, were a valuable source of experimental data. They were of no help, however, in reaching any conclusion regarding the optimum shape because of the complexity and diversity of the factors which all appeared simultaneously, thereby precluding the.study of the effects of any one factor separately. On the suggestion of the director of the CAHI,Prof. B. N. Ureff, it was decided to experiment on a two-dimensional diffuser model and determine the effect, of the angle of divergence. The author is acquainted with two experimental projects of like nature: the first was conducted with water, the other with air. The first of these works, although containing a wealth of experimental data, does not indicate the nature of flow or its relation to the angle of divergence. The second work is limited to four angles - that is, 12 deg, 24 deg, 45 deg, 90 deg. The study of this diffuser did not supply any information about the effect of smaller angles which, because of their advantages, are more commonly used, The author was able to acquaint himself with the second work only after the experiments were started. For these reasons, as well as because on the basis of those works no conclusion can be reached regarding the nature of flow distribution, of eddies, and so forth, experimental work was continued. The need for determining flow patterns follows from the fact that from them are determined methods of measurement - that is, the determination of velocities by means of the pitot tube, which, as is well known, gives correct indications only when placed with its axis parallel to the axis of flow. The data contained in this report were obtained from experiments conducted by the Aerodynamical Laboratories of the CAHI. The solutions to some. of the mathematical problems connected with the experiments are due to Prof. S. A, Chapligin.
Dendrite formation on the electrode surface of high energy density lithium (Li) batteries causes safety problems and limits their applications. Suppressing dendrite growth could significantly improve Li battery performance. Dendrite growth and morphology is a function of the mixing in the electrolyte near the anode interface. Most research into dendrites in batteries focuses on dendrite formation in isotropic electrolytes (i.e., electrolytes with isotropic diffusion coefficient). In this work, an anisotropic diffusion reaction model is developed to study the anisotropic mixing effect on dendrite growth in Li batteries. The model uses a Lagrangian particle-based method to model dendrite growth in an anisotropic electrolyte solution. The model is verified by comparing the numerical simulation results with analytical solutions, and its accuracy is shown to be better than previous particle-based anisotropic diffusion models. Several parametric studies of dendrite growth in an anisotropic electrolyte are performed and the results demonstrate the effects of anisotropic transport on dendrite growth and morphology, and show the possible advantages of anisotropic electrolytes for dendrite suppression.
A high-fidelity model of kinetic and equilibrium sorption and diffusion is developed and exercised. The gas-diffusion model is coupled with a triple-sorption mechanism: Henry’s law absorption, Langmuir adsorption, and pooling or clustering of molecules at higher partial pressures. Sorption experiments are conducted and span a range of relative humidities (0-95%) and temperatures (30-60°C). Kinetic and equilibrium sorption properties and effective diffusivity are determined by minimizing the absolute difference between measured and modeled uptakes. Uncertainty quantification and sensitivity analysis methods are described and exercised herein to demonstrate the capability of this modeling approach. Water uptake in silica-filled and unfilled poly(dimethylsiloxane) networks is investigated; however, the model is versatile enough to be used with a wide range of materials and vapors.
Albedo and diffuse plane of array (DPOA) measurements are used in addition to standard global horizontal irradiance (GHI), direct normal irradiance (DNI), diffuse horizontal irradiance (DNI), and plane of array irradiance (POA) measurements to determine the impact of albedo on transposition model performance. Albedo measurements averaged 0.214. Daily albedo values ranged from 0.148 to 0.236 and were found to be correlated to daily relative humidity. DPOA measurements were compared to calculated DPOA values (from POA and DNI), and helped identify a suspected deviation from due south in the azimuth of the POA measurement. Since the measured albedo average was close to the typical fixed $^{albedo = 0.2}$ assumption, little difference was seen between using measured and fixed albedo (~0.15% differences in mean bias difference (MBD) and root mean squared difference (RMSD)). However, evaluation of transposition models at other fixed albedos showed an albedo change of 0.1 is found to increase total modeled insolation by approximately 1%. Thus, for locations with different ground surfaces (e.g., persistent snow cover of black surfaces), the impact of using measured albedo instead of the fixed $^{albedo = 0.2}$ assumption may be greater. Measurement deviations resulted in up to 2% changes in MBD and RIVISD when switching between interrelated measurements (e.g., GHI and DHI as inputs to transposition models versus DNI and DHI as inputs). Variation among transposition models was also up to 2% MBD and RMSD. Thus, for this data set, measurement deviation and transposition model selection are found to have more impact than using measured albedo instead fixed albedo.
Far-from-equilibrium evolution of metallic nanocluster shapes is highly sensitive to the atomistic-level details of surface diffusion for diverse local surface configurations. A stochastic model was developed incorporating realistic values for the multiple diffusion barriers (contrasting previous unrealistic generic prescriptions) based upon insights from homoepitaxial film growth. Kinetic Monte Carlo simulation then elucidates the conversion of Ag nanocubes to Wulff polyhedra mediated by nucleation of new {100} facets, the pinch-off of sufficiently elongated Ag nanorods, and key aspects of sintering for orientationally aligned Ag and Au nanoclusters. In conclusion, the time scale for sintering of Au nanoclusters observed in high-resolution transmission electron microscopy studies was also recovered.
Abstract Geophysical models for pressure solution are typically developed for diffusion‐controlled or reaction‐controlled scenarios. We present a unified analytical model that considers fully coupled diffusion and reaction during pressure solution. The model recovers the diffusion‐controlled and reaction‐controlled models in the literature as specific limiting cases. When diffusion and reaction exhibit comparable influences, we validate the proposed model against independent numerical simulations. The proposed model is then employed in interpreting experimental measurements, demonstrating a better agreement compared to previous interpretations.
A common approach to closing turbulent species flux in multicomponent Reynolds-averaged Navier-Stokes models is to use the standard gradient diffusion approximation. While such an approach has been shown to work well when applied to many canonical turbulent mixing configurations, a gradient diffusion approach is fundamentally limited in its ability to capture complex phenomena such as countergradient transport. For this reason, complicated mixing applications may benefit by treating the turbulent diffusivity with a model transport equation in a manner analogous to second-moment momentum closure in Reynolds-stress transport models. Here, the present work explores the development and application of two different scalar flux transport (SFT) models. Self-similarity constraints are derived for these models, and they are evaluated against gradient-diffusion-based models in several one- and two-dimensional problems of turbulent mixing. It is found that the new SFT models out-perform gradient diffusion models in problems involving rapid acceleration reversal and in problems involving anisotropic transport of materials. In addition, it is found that even a hybrid-SFT approach, in which an SFT equation is utilized along with a gradient diffusion closure, provides some measure of improvement over models that transport the mass flux rather than the scalar flux.
TRISO fuel particles are candidates for use in next generation reactors including gas reactors, fluoride salt-cooled high temperature reactors, and micro-reactors. The UCO fuel kernel consists of a uranium dioxide (UO) and uranium carbide mixture. The addition of UC helps suppress the formation of carbon monoxide gas, which led to failures during initial TRISO development. The addition of uranium carbide alters the chemistry of the UO kernel, which is known to influence performance parameters such as fission gas diffusivity, although the impact has not been quantified and no models exist that take the change in chemistry into account. Therefore, better understanding and more accurate models of the impact of chemistry on fuel performance are of high priority. In this paper, a first-principles density functional theory (DFT) and empirical potential based multi-scale study has been carried out to model the diffusivity of fission gas xenon (Xe) in UCO TRISO fuel kernels. The focus is on the UO component in the UCO fuel kernels, as that represents the largest volume fraction of the fuel kernels. The study relies on DFT and empirical potential calculations to determine Xe and point defect properties, which are then used in thermodynamic and kinetic models to predict diffusion for intrinsic conditions. In addition, the information is utilized in cluster dynamics simulations using the Centipede code to estimate the impact of irradiation on defect transport. Additionally, the presence of UC or UC in the UCO fuel kernels is shown to have a substantial impact on the UO non-stoichiometry by inducing oxygen vacancies and driving UO sub-stoichiometric, which causes much slower Xe diffusion in UCO compared to light water reactor UO fuel. The application of this model in fuel performance simulations using the Bison code is also demonstrated.
Supernova remnants (SNRs) have commonly been considered as a source of the observed PeV cosmic rays (CRs) or a Galactic PeV particle accelerator ('Pevatron'). In this work, we study Sagittarius A* (Sgr A*), which is the low-luminosity active galactic nucleus of the Milky Way Galaxy, as another possible canditate of the Pevatron, because it sometimes became very active in the past. We assume that a large number of PeV CRs were injected by Sgr A* at the outburst about 10{sup 7} yr ago when the Fermi bubbles were created. We constrain the diffusion coefficient for the CRs in the Galactic halo on the condition that the CRs have arrived on the Earth by now, while a fairly large fraction of them have escaped from the halo. Based on a diffusion-halo model, we solve a diffusion equation for the CRs and compare the results with the CR spectrum on the Earth. The observed small anisotropy of the arrival directions of CRs may be explained if the diffusion coefficient in the Galactic disk is smaller than that in the halo. Our model predicts that a boron-to-carbon ratio should be energy-independent around the knee, where the CRs from Sgr A* become dominant. It is unlikely that the spectrum of the CRs accelerated at the outburst is represented by a power-law similar to the one for those responsible for the gamma-ray emission from the central molecular zone (CMZ) around the Galactic center.
We present a study of the compatibility of some current models of the diffuse Galactic continuum gamma-rays with EGRET data. A set of regions sampling the whole sky is chosen to provide a comprehensive range of tests. The range of EGRET data used is extended to 100 GeV. The models are computed with our GALPROP cosmic-ray propagation and gamma-ray production code. We confirm that the "conventional model" based on the locally observed electron and nucleon spectra is inadequate, for all sky regions. A conventional model plus hard sources in the inner Galaxy is also inadequate, since this cannot explain the GeV excess away from the Galactic plane. Models with a hard electron injection spectrum are inconsistent with the local spectrum even considering the expected fluctuations; they are also inconsistent with the EGRET data above 10 GeV. We present a new model which fits the spectrum in all sky regions adequately. Secondary antiproton data were used to fix the Galactic average proton spectrum, while the electron spectrum is adjusted using the spectrum of diffuse emission it- self. The derived electron and proton spectra are compatible with those measured locally considering fluctuations due to energy losses, propagation, or possibly de- tails of Galactic structure. This model requires a much less dramatic variation in the electron spectrum than models with a hard electron injection spectrum, and moreover it fits the y-ray spectrum better and to the highest EGRET energies. It gives a good representation of the latitude distribution of the y-ray emission from the plane to the poles, and of the longitude distribution. We show that secondary positrons and electrons make an essential contribution to Galactic diffuse y-ray emission.
Sorption of small molecule gases in materials can play a significant role in their long‐term stability and compatibility within multi‐material assemblies. While many material properties of the insensitive high explosive TATB (1,3,5‐triamino‐2,4,6‐trinitrobenzene) are well understood, very little is known regarding its permeability to gases. TATB crystal exhibits a graphitic‐like layered packing structure that evokes a mental schema in which the layers form nanoscopic channels, but it is unclear whether this structure promotes gas transport. Here, we use molecular dynamics (MD) simulations to predict transport of small molecules through TATB single crystal. An approach to fit classical force fields is developed to model TATB interactions with H 2 O, He, Ne, and Ar, which is then combined with steered MD to probe gas transport along selected directions in the crystal. We find that small molecule transport occurs via a hopping mechanism that exhibits distinct jumps between interstitial sites and is substantially faster normal to the layers as compared to through them. This result stems from the finding that intralayer junctions between adjacent TATB molecules are the most stable interstitial sites and that energetic barriers are lower for hopping between adjacent layers. An empirical model for diffusion rate based on the MD data shows that the rate decays exponentially with increasing molecular radius and is negligibly small for all molecules larger than He, including common atmospheric gases. These findings have implications for the interpretation of experiments that measure surface area, material response to extreme conditions, and are expected to help constrain models for material aging.
The numerical vertical diffusivity K(num), embedded in a numerical ocean general circulation model with nonuniform vertical grid, is estimated. It is shown that in a downwelling region, K(num) is negative for a grid with grid size increasing with depth. When the grid size increment, or the downward vertical velocity, is large, K(num) may exceed the vertical diffusivity specified and may result in a negative effective vertical diffusivity. Therefore care needs to be taken to specify the vertical diffusivity in a numerical model with nonuniform grid, and a lower bound is generally imposed in order to avoid an unphysical negative value. Some possible effects of the negative effective diffusivity are discussed.
A reaction–diffusion shrinking core model describing the decay in diffusivity of supported amine sorbents upon CO 2 sorption under both simulated direct air capture and point source capture conditions is described. The decay in CO 2 diffusivity is associated with crosslinking in the aminopolymer samples and general pore blockage in the amino-silane derived samples, which occurs as CO 2 is adsorbed. The model is used to extract four kinetic parameters that govern the CO 2 uptake kinetics and working capacity: an apparent reaction rate constant, an initial effective diffusivity, and two dimensionless decay parameters. Ideally, an initially reaction limited system would allow for direct determination of the intrinsic reaction rate constant; however, sorption experiments suggest mass transfer resistances related to gas mixing, external boundary layers and intraparticle diffusion are present. Reaction rate constants are determined and agree well with theoretical values predicted with the Eyring equation parameterized using density functional theory energies from literature sources. The kinetic performance is expressed as the average effective diffusivity as a function of average conversion, which can be correlated to the dispersion of sorption sites on the support and the morphology of the active sorbent phase. Four supports are impregnated or grafted with amines, SBA-15, single-walled zeolite nanotubes (ZNT), Syloid SiO 2 , and γ-Al 2 O 3 . Due to its pore structure, γ-Al 2 O 3 supported amines can be modeled at the μm scale or at the nm scale, where the shell balance is on the μm-sized macroporous particle aggregate or on the nm-sized amine film on the surface of the Al 2 O 3 nanoparticles, which comprise the spherical particle aggregates. Faster diffusion rates are maintained under 400 ppm rather than 10% CO 2 due to a slower reaction rate giving a slower decay in diffusivity. In conclusion, this work provides a first principles kinetic analysis of CO 2 sorption where previous models are semi-empirical and use arbitrary kinetic parameters.
The interplay between the contributions of electron thermal flux and interface scattering to the Kapitza conductance across metal-metal interfaces through measurements of thermal conductivity of copper-niobium multilayers was studied. Thermal conductivities of copper-niobium multilayer films of period thicknesses ranging from 5.4 to 96.2 nm and sample thicknesses ranging from 962 to 2677 nm are measured by time-domain thermoreflectance over a range of temperatures from 78 to 500 K. The Kapitza conductances between the Cu and Nb interfaces in multilayer films are determined from the thermal conductivities using a series resistor model and are in good agreement with the electron diffuse mismatch model. The results for the thermal boundary conductance between Cu and Nb are compared to literature values for the thermal boundary conductance across Al-Cu and Pd-Ir interfaces, and demonstrate that the interface conductance in metallic systems is dictated by the temperature derivative of the electron energy flux in the metallic layers, rather than electron mean free path or scattering processes at the interface.
In this study, several variable turbulent Prandtl number formulations are examined for boundary layers, pipe flow, and axisymmetric jets. The model formulations include simple algebraic relations between the thermal diffusivity and turbulent viscosity as well as more complex models that solve transport equations for the thermal variance and its dissipation rate. Results are compared with available data for wall heat transfer and profile measurements of mean temperature, the root-mean-square (RMS) fluctuating temperature, turbulent heat flux and turbulent Prandtl number. For wall-bounded problems, the algebraic models are found to best predict the rise in turbulent Prandtl number near the wall as well as the log-layer temperature profile, while the thermal variance models provide a good representation of the RMS temperature fluctuations. In jet flows, the algebraic models provide no benefit over a constant turbulent Prandtl number approach. Application of the thermal variance models finds that some significantly overpredict the temperature variance in the plume and most underpredict the thermal growth rate of the jet. The models yield very similar fluctuating temperature intensities in jets from straight pipes and smooth contraction nozzles, in contrast to data that indicate the latter should have noticeably higher values. For the particular low subsonic heated jet cases examined, changes in the turbulent Prandtl number had no effect on the centerline velocity decay.