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Anomalous transport of multi-species plasma is considered with the generalized Hasegawa–Wakatani model. It is shown that the transport of all plasma species is described by fractional diffusion equations with the same effective diffusion coefficient. Strongly enhanced perturbations of heavy impurity density are found in long-living plasma flow vortices.
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The understanding of the sorption/desorption kinetics is essential for practical applications of moisture-controlled CO 2 sorption. We introduce an analytic model of the kinetics of moisture-controlled CO 2 sorption and its interpretation in two limiting cases. In one case, chemical reaction kinetics on pore surfaces dominates, in the other case, diffusive transport through the sorbent defines the kinetics. Here, we show that reaction kinetics, which is dominant in the first case, can be expressed as a linear combination of 1st and 2nd order kinetics in agreement with the static isotherm equation derived and validated in a previous paper. The interior transport kinetics can be described by non-linear diffusion equations. By combining all carbon species into a single equation, we can eliminate — in certain limits — the source terms associated with chemical reactions. In this case, the governing equation is ∂θ/∂t = –∇ · (–D eff ∇ θ ). For a sorbent in a form of a flat sheet or a membrane, one can maintain the same functional form of a diffusion equation by introducing a generalized effective diffusivity D M that combines contributions from both surface chemical reaction kinetics and interior diffusive transport kinetics. Experimental data of transient CO 2 flux in a preconditioned commercial anion exchange membrane fit well to the 1st order model as long as very dry states are avoided, validating the theory. The observed DM for a preconditioned commercial anion exchange membrane ranges from 6.6× 10 -14 to 7.1× 10 -14 m 2 s -1 at 35°C. These small values compared to typical ionic diffusivities imply a very slow kinetics, which will be the largest issue that needs to be addressed for practical application. The collected transient CO 2 flux data are used to predict the magnitude of a continuous CO 2 pumping flux in an active membrane that transports CO 2 against a CO 2 concentration gradient. The pumped CO 2 flux is supported by water flux due to a water concentration gradient.
Gas sorption and non-Darcy flow are two important issues for shale gas reservoirs. The sorption consists of dissolution and adsorption. Dissolved gas and adsorbed gas are different. The former is dissolved in the shale matrix, while the latter is concentrated near the solid walls of pores. In this paper, the Langmuir equation is used to describe adsorption and Henry’s law is used to describe dissolution. The K coefficient in Henry’s law of 0.052 mmol/(MPa g TOC) is obtained by matching experimental data. The amount of dissolved gas increases linearly when pressure increases. Using only the Langmuir equation without considering dissolution can lead to a significant underestimation of the amount of sorbed gas in shales. For non-Darcy gas flow, the apparent permeability model for free gas is established by combining slip flow and Knudsen flow. For adsorbed gas, the surface diffusion effect is also considered in this model. Here, the surface diffusion coefficient is suggested to be of the same scale as the gas self-diffusion coefficient, and the corresponding effective permeability is derived. When
Molecular diffusion plays an important role in oil and gas migration in tight shale formations. However, there are insufficient reference data in the literature to specify the diffusion coefficients within porous media. This study aims at calculating diffusion coefficients of shale gas, shale condensate, and shale oil at reservoir conditions with CO 2 injection for EOR/EGR. The large nano-confinement effects including large gas-oil capillary pressure and critical property shifts could alter the phase behaviors. This paper estimates the diffusivities of shale fluids in nanometer-scale shale rock from two perspectives: 1) examining the shift of diffusivity caused by nanopore confinement effects from phase change (phase composition and fluid property) perspective, and 2) calculating the effective diffusion coefficient in porous media by incorporating rock intrinsic properties (porosity and tortuosity factor). The tortuosity is obtained by using tortuosity-porosity relations as well as the measured tortuosity of shale from 3D imaging techniques. The results indicated that nano-confinement effects could affect the diffusion coefficient through altering the phase properties, such as phase compositions and densities. Compared to bulk phase diffusivity, the effective diffusion coefficient in porous shale rock is reduced by 10 2 to 10 4 times as porosity decreases from 0.1 to 0.03.
Evaluation of the long-term retention mechanisms and potential release rates for the primary constituents of potential concern (COPCs) (i.e., Tc, I, Se, and nitrate) is necessary to determine if Cast Stone, a radioactive waste form, can meet performance objectives under near-surface disposal scenarios. In this work, a mineral and parameter set accounting for the solubility of I and Se in Cast Stone was developed based on pH-dependent and monolithic diffusion leaching test results, to extend a geochemical speciation model previously developed. The impact of oxidation and carbonation as environmental aging processes on the retention properties of Cast Stone for primary COPCs was systematically estimated. Physically, the effective diffusion coefficients of 4 COPCs in Cast Stone were increased after carbonation and/or oxidation, reflecting an increase in permeability to diffusion. Chemically, i) pH & pe conditions in the original Cast Stone were favorable for the stabilization of Tc, but not for I, Se, and N; ii) oxidation (with/without carbonation) of Cast Stone changed the pe & pH conditions to be detrimental for Tc stabilization; and iii) carbonation (with/without oxidation) of Cast Stone modified the pH & pe conditions to be beneficial for the stabilization of I (in system with Ag added) and Se.
Iron-chromium-aluminum (FeCrAl) alloys such as APMT (advanced powder metallurgy tubing) are candidate materials to replace zirconium alloys for the light water reactor fuel cladding. This alloy meets the requirements to be a material more tolerant of high-temperature accidents than the current zirconium alloys. One concern is that the use of FeCrAl may result in an increase in tritium presence in the coolant compared to the current design. The aim of the current research was to obtain effective diffusion coefficients (D eff ) for hydrogen through APMT using the Devanathan-Stachurski cell. Results showed that at 30°C the D eff value was 2.8 × 10 -8 cm 2 /s. Results also showed a linear relationship between the permeated hydrogen flux and the inverse of the test specimen thickness, which demonstrated the validity of the permeation measurements.
Knowledge of the exchange of carbon isotopes between dissolved inorganic carbon and calcite minerals is of long-standing importance for the interpretation of sedimentary paleoclimate records and 14 C transport in the geosphere. To assess the mechanism and rates of carbon isotope exchange, we equilibrated 12 C-pure synthetic calcite particles in water, first in a glovebox and then in contact with atmospheric P CO 2 and 13 C/ 12 C ratio, at two different temperatures. Cavity ring-down infrared spectroscopy δ 13 C measurements of the solid revealed sustained 13C incorporation for over a period of 500 days (21 °C) and 125 days (50 °C). We developed a quantitative model for recrystallization and isotope exchange, assuming that the interfacial free energy provides a thermodynamic driving force for the growth of larger particles at the expense of smaller ones. Furthermore, this Ostwald ripening model did not reproduce the kinetics of 13C uptake and required greater coarsening than observed. Rather, the data were best explained by a mechanism involving surface exchange and solid-phase diffusion of 13C into the particles with an inferred effective diffusion constant at 21 °C of about 10 –25 m 2 /s. Although this work cannot rule out the possibility that structural or chemical aspects of the synthetic particles enabled faster 13 C uptake than could be observed in natural systems, this study adds to the body of the recent work, suggesting that fast exchange processes are possible, likely through grain boundaries and other defects.
In this paper, we describe our work on spin polarization in high-energy electron storage rings which we base on the Full Bloch equation (FBE) for the polarization density and which aims towards the [Formula: see text] option of the proposed Future Circular Collider (FCC-ee) and the proposed Circular Electron Positron Collider (CEPC). The FBE takes into account non spin-flip and spin-flip effects due to synchrotron radiation including the spin-diffusion effects and the Sokolov–Ternov effect with its Baier–Katkov generalization as well as the kinetic-polarization effect. This mathematical model is an alternative to the standard mathematical model based on the Derbenev–Kondratenko formulas. For our numerical and analytical studies of the FBE, we develop an approximation to the latter to obtain an effective FBE. This is accomplished by finding a third mathematical model based on a system of stochastic differential equations (SDEs) underlying the FBE and by approximating that system via the method of averaging from perturbative ODE theory. We also give an overview of our algorithm for numerically integrating the effective FBE. This discretizes the phase space using spectral methods and discretizes time via the additive Runge–Kutta (ARK) method which is a high-order semi-implicit method. We also discuss the relevance of the third mathematical model for spin tracking.
Generation IV reactors and future fusion reactor designs have led to more demanding materials performance requirements due to their increased operating temperatures, corrosive coolants, and increased radiation doses compared to the current light-water reactor fleet. Among the innovative nuclear technologies under development, molten salt reactors stand out for their potential to offer superior fuel utilization, intrinsic safety characteristics, and economic viability. Of the proposed Generation IV designs, the gas fast reactor operates at 450 to 850°C and the molten salt reactor operates at 565 to 850°C, with the molten salt reactor design needing molten salt corrosion resistant materials [1, 2]. These increased temperatures and more extreme corrosion environments necessitate higher material performance, such as creep strength, radiation-tolerant microstructures, corrosion resistance, and high-temperature tensile properties. Hastelloy-N, a nickel-based alloy with additions of molybdenum and chromium, has been successfully employed to contain molten fluoride salt at temperatures up to 705°C. However, Hastelloy-N becomes embrittled upon neutron irradiation, primarily due to the accumulation of helium produced by (n,a) transmutation reactions. Furthermore, the corrosive nature of molten fluoride and chloride salts presents a formidable challenge, as these salts can react with and dissolve alloying elements such as Cr, Mo, and Fe, leading to selective leaching, loss of protective oxide layers, and accelerated degradation. High entropy alloys (HEAs) and refractory high entropy alloys (RHEAs) have emerged as a prominent area of interest, due to their ability to achieve tailored chemical compositions for specific applications. Unlike conventional alloys, HEAs are characterized by having multiple principal elements in equimolar or near equimolar ratios, leading to an unconventional alloying strategy [3]. This alloying strategy is believed to promote unique properties, such as single-phase stabilization of chemically compatible elements, lattice distortion effects due to atomic radius differences, and proposed sluggish diffusion effects. For extreme-environment applications, RHEAs have garnered much research interest because of the possibility of creating relatively ductile materials that can operate in extremely high-temperature environments, beyond the operating temperatures where other Ni-based superalloys begin to lose strength [4-6]. Idaho National Laboratory (INL) initiated a joint international effort with the Czech Republic to explore the feasibility of manufacturing HEAs for high-temperature nuclear applications using advanced manufacturing. This effort was funded at INL by the United States Department of Energy's Office of Nuclear Energy under the Advanced Reactor Technologies and Advanced Materials and Manufacturing Technologies (AMMT) Program. The HEAs were specifically designed for the corrosive and irradiation environments experienced in gas-cooled fast reactors, molten salt reactors, and fusion power. These alloys have been manufactured by multiple processes to determine the impact of manufacturing processes on the performance of the alloys in corrosive and irradiation environments. Preliminary molten salt corrosion testing showed that equimolar MoNbTiV and MoNbTi alloys exhibit exceptional performance, with arc-melted variants demonstrating only minimal degradation after 1000 hours of exposure to molten chloride salt at 700°C. Conversely, Nb2TiVZr2 showed significant molten salt corrosion susceptibility and microstructural instability during high-temperature molten salt exposures, and was, therefore deemed unfit for molten salt reactor applications. The MoNbTiV, MoNbTi, and Nb2TiVZr2 alloys were further evaluated through ion irradiation experiments conducted at the Michigan Ion Beam Laboratory at the University of Michigan. The microstructural stability and the evolution of irradiation-induced defects were characterized to assess the irradiation resistance of each of these alloys.
We investigate wave propagation in rotationally symmetric tubes with a periodic spatial modulation of cross section. Using an asymptotic perturbation analysis, the governing quasi-two-dimensional reaction-diffusion equation can be reduced into a one-dimensional reaction-diffusion-advection equation. Assuming a weak perturbation by the advection term and using projection method, in a second step, an equation of motion for traveling waves within such tubes can be derived. Both methods predict properly the nonlinear dependence of the propagation velocity on the ratio of the modulation period of the geometry to the intrinsic width of the front, or pulse. As a main feature, we observe finite intervals of propagation failure of waves induced by the tube’s modulation and derive an analytically tractable condition for their occurrence. For the highly diffusive limit, using the Fick-Jacobs approach, we show that wave velocities within modulated tubes are governed by an effective diffusion coefficient. Furthermore, we discuss the effects of a single bottleneck on the period of pulse trains. We observe period changes by integer fractions dependent on the bottleneck width and the period of the entering pulse train.
We propose a mathematical model for uptake and diffusion of air plasma-generated reactive nitrogen species (RNS) in a model keratinized membrane, such as a thin slice of bovine hoof or human nail material. An experimental system consisting of a surface microdischarge (SMD) in air was designed for the purpose of developing and validating a reaction-diffusion model to describe this system. Key variables such as membrane effective diffusivity, surface reaction rate coefficients, and other parameters are determined through comparison between the model predictions and experimental measurements. The model results yield spatial and temporal concentration profiles of RNS inside the keratinized membrane, leading to an improved understanding of transport and reaction of plasma generated RNS through the membrane. This work offers insights into possible mechanisms underlying plasma treatment of toenail fungus.
Frequency-modulated (FM) combs based on active cavities like quantum cascade lasers have recently emerged as promising light sources in many spectral regions. Unlike passive modelocking, which generates amplitude modulation using the field’s amplitude, FM comb formation relies on the generation of phase modulation from the field’s phase. They can therefore be regarded as a phase-domain version of passive modelocking. However, while the ultimate scaling laws of passive modelocking have long been known—Haus showed in 1975 that pulses modelocked by a fast saturable absorber have a bandwidth proportional to effective gain bandwidth—the limits of FM combs have been much less clear. Here, we show that FM combs based on fast gain media are governed by the same fundamental limits, producing combs whose bandwidths are linear in the effective gain bandwidth. Not only do we show theoretically that the diffusive effect of gain curvature limits comb bandwidth, but we also show experimentally how this limit can be increased. By adding carefully designed resonant-loss structures that are evanescently coupled to the cavity of a terahertz laser, we reduce the curvature and increase the effective gain bandwidth of the laser, demonstrating bandwidth enhancement. Our results can better enable the creation of active chip-scale combs and be applied to a wide array of cavity geometries.
The rapid carburization of mild steel is demonstrated via the electrochemical deposition of solid carbon, followed by thermochemical iron-carbon (Fe-C) reaction using a molten lithium-potassium carbonate (LiKCO 3 ) salt electrolyte and carbon dioxide as the carbon source. Depth-dependent microstructural and compositional changes in the steel are shown to be controlled by the applied cell voltage and reaction temperatures. Reaction temperatures above the Fe-C eutectoid temperature promote faster carburization due to carbon dissolution into austenite. The carbon deposition rate is regulated by the applied cell voltage: At - 2.4 V, carbon deposition occurs much faster than its diffusion into the steel, resulting in the accumulation of a carbon-rich layer exceeding 1 mm, which does not diffuse into the steel. In contrast, at - 1.8 V, all deposited carbon effectively diffuses into the steel, leaving a minimal external deposit. In both cases, carbon ingress forms a carbide-rich surface layer and precipitates additional carbides along the grain boundaries within the steel electrode. This method offers a potential approach to increase the carbon content of mild or low-carbon steel feedstocks, such as scrap or direct reduced iron, for industrial applications.
High-efficiency, four-terminal tandem solar cells composed of thin GaAs films mechanically stacked onto interdigitated back contact silicon solar cells with a glass interlayer are demonstrated. The optimal thickness of the absorber layer of a rear heterojunction GaAs subcell for use in four terminal tandem solar cells was studied. GaAs top cells with absorber layer thicknesses of 1.5, 1.9, 2.3, 2.8, and 3.5 µm were fabricated on glass and mechanically stacked onto interdigitated back-contact Si bottom cells. All tandem cells were found to have efficiencies above 30% under the AM1.5 G spectrum demonstrating a relatively weak sensitivity to thickness in the four-terminal configuration. We found the 2.8 µm absorber layer cell to have the highest top cell and tandem cell efficiency at 26.38% and 32.57%, respectively. Optical modeling with transfer matrix method for the planar top cell and Lambertian light trapping in the textured Si subcell, along with drift-diffusion Hovel equations, were used to show photon recycling enhancement to the effective diffusion length and VOC of the top cell as a result of the low-index glass interlayer.
Self-propelled active matter can exhibit vastly different behavior than systems with purely Brownian motion. In Eur. Phys. J. E 40, 23 (2017), Zeitz, Wolf, and Stark compared an active matter particle with a Brownian particle moving in a random obstacle array. They showed that near the obstacle percolation density, both Brownian and active particles exhibit the same subdiffusive behavior, but the active particle reaches a steady state more rapidly. They also found that for high activity, the active particle has a lower effective diffusion than the Brownian particle due to the increased self-trapping effect generated by the activity. This result opens new directions for the study of active matter in disordered media, including bacteria in porous media, active colloids on quenched disorder, and active particles in crowded environments.
To investigate a novel alternative diffusion-weighted imaging (DWI) approach using oscillating gradients preparation (OGSE) to obtain much shorter effective diffusion times (Δ{sub eff}) for tumor response monitoring by apparent diffusion coefficient (ADC) mapping in a glioblastoma mouse model.
The edge turbulence model Hermes (Dudson et al 2017 Plasma Phys. Control. Fusion 59 05401) is set up for plasma boundary simulations with an radiofrequency (RF) antenna, using parameters characteristic of a tokamak edge. Cartesian slab geometry is used with thin plate limiters representing the ion cyclotron range of frequency (ICRF) antenna side-wall limiters. Ad-hoc DC electric biasing of the limiters, motivated by calculations with VSim (Nieter et al 2004 J. Comput. Phys. 196 448), represents an induced RF sheath rectified potential in the plasma turbulence model. Flux-driven turbulence simulations demonstrate a realistic distribution of plasma profiles and fluctuations. There is a clear effect of the antenna sheath voltage leading to formation of convective cells; bias-induced convective transport flattens the scrape-off layer density profile and fluctuations penetrate into the shadow region of the limiters as the bias voltage increases. Turbulent transport for impurity ions is inferred by following ion trajectories in the simulated plasma turbulence fields, showing Bohm-like effective diffusion rates. All in all, the model elucidates the key physical phenomena governing the effects of ICRF-induced antenna biasing on the tokamak boundary plasma.