Multicomponent Diffusion Research Articles

Cerebral aggregate g-ratio mapping using magnetic resonance relaxometry and diffusion tensor imaging to investigate sex and age-related differences in white matter microstructure

Axonal demyelination is a cardinal feature of aging and age-related diseases. The g-ratio, mathematically defined as the inner-to-outer diameter of a myelinated axon, is used as a structural index of optimal axonal myelination and has been shown to represent a sensitive imaging biomarker of microstructural integrity. Several magnetic resonance imaging (MRI) methods for whole-brain mapping of aggregate g-ratio have been introduced. Computation of the aggerate g-ratio requires estimates of the myelin volume fraction (MVF) and the axonal volume fraction (AVF). While accurate determinations of MVF and AVF can be obtained through multicomponent relaxometry or diffusion analyses, respectively, these methods require lengthy acquisition times making their implementation challenging in a clinical context. Therefore, any attempt to overcome this drawback is needed. Expanding on our previous work, we introduced a new MRI method for whole-brain mapping of aggregate g-ratio. This new approach is based on the use of a single-shell diffusion for AVF determination, reducing the acquisition time by approximately ~10 min from our recently introduced approach, while offering the possibility to investigate g-ratio differences in previous studies with existing data for MVF mapping and single-shell diffusion data for AVF mapping. Our comparison analysis indicates that our newly derived aggregate g-ratio values were similar to those derived from our previous method, which requires a longer acquisition time. Further, in agreement with our previous observations, we found quadratic U-shaped relationships between aggregate g-ratio and age in this much larger study cohort. However, our results show that sexual dimorphism in g-ratio was not significant in any brain region investigated.

Potential Uranium Migration within the Geochemical Gradient of the Opalinus Clay System at the Mont Terri

Transport properties of potential host rocks for nuclear waste disposal are typically determined in laboratory or in-situ experiments under geochemically controlled and constant conditions. Such a homogeneous assumption is no longer applicable on the host rock scale as can be seen from the pore water profiles of the potential host rock Opalinus Clay at Mont Terri (Switzerland). The embedding aquifers are the hydro-geological boundaries, that established gradients in the 210 m thick low permeable section through diffusive exchange over millions of years. Present-day pore water profiles were confirmed by a data-driven as well as by a conceptual scenario. Based on the modelled profiles, the influence of the geochemical gradient on uranium migration was quantified by comparing the distances after one million years with results of common homogeneous models. Considering the heterogeneous system, uranium migrated up to 24 m farther through the formation depending on the source term position within the gradient and on the partial pressure of carbon dioxide pCO2 of the system. Migration lengths were almost equal for single- and multicomponent diffusion. Differences can predominantly be attributed to changes in the sorption capacity, whereby pCO2 governs how strong uranium migration is affected by the geochemical gradient. Thus, the governing parameters for uranium migration in the Opalinus Clay can be ordered in descending priority: pCO2, geochemical gradients, mineralogical heterogeneity.

An explicit iterative scheme for 3D multicomponent heat conducting flow simulation

This paper presents the development and testing of time integration scheme for the system of hydrodynamic equations of gas mixture. These equations take into account the phenomena of multicomponent diffusion and heat transfer. The governing equation system is discretized by the finite volume approach on three-dimensional unstructured grids. According to the algorithm, computation of any single time step is split into the sequence of hyperbolic and parabolic stages. The hyperbolic subtask is solved using the Godunov-type scheme. The parabolic subtask is solved by the explicit iterative Chebyshev scheme, which is algorithmically simple and does not involve tuning parameters. This stage addresses dissipative fluxes (viscosity, multicomponent diffusion and thermal conductivity). The number of the explicit iterations is determined by the convective time step and by the upper bound for the discrete diffusion operator. The resulting scheme ensures the fulfillment of the conservation laws at the discrete level. The computer code can be used in highly parallel computing for large-scale simulation. The proposed approach is recommended for applied problems in which convective and dissipative processes are in close interaction, particularly for problems of plasma physics and astrophysics.

Multicomponent Fickian solution-diffusion model for osmotic transport through membranes

Osmotically-assisted membrane processes (OAMP) are separation technologies that leverage osmotic gradients to recover water from brine. Accurate modeling of the solute-coupling effects for transmembrane transport is integral to the development and subsequent optimization of OAMP unit operations. In the literature, multicomponent transport in OAMP is commonly linearized, and species fluxes are computed using binary solution-diffusion theory and then superposed. However, recent publications highlight the large predictive errors associated with such an approach as the transport coupling between species is ignored. In this paper, we demonstrate that significant improvements in multicomponent species fluxes can be obtained when solute-coupling interactions are incorporated. Here, we present a multicomponent solution-diffusion model, by extending the binary solution-diffusion model with multicomponent diffusion theory. When multicomponent diffusion coefficients are available, we find that the average absolute deviation (AAD) of the model decreased from 21.0% to 3.0% for 7 unique combinations of forward osmosis processes involving ternary mixtures. In the absence of data for multicomponent diffusion coefficients, we demonstrate that the multicomponent model can regress the impact of transport coupling on water and solute fluxes, using excess solute permeabilities. For the case of H2O-NaCl-EtOH forward osmosis process, the AAD of the solution-diffusion model is shown to decrease from 66.1% to 7.2% for NaCl concentrations from 0.0 to 1.5 M and EtOH mass fractions from 0.0 to 0.5. These values are extended to analyze the implications on the thermodynamic and membrane area requirements of the desalination systems employing OAMP.

An analytical model for the evaporation of multi-component spheroidal drops based on Stefan–Maxwell equations

An analytical evaporation model for multi-component spherical and spheroidal drops, based on the analytical solution of the Stefan–Maxwell equations is proposed to study the multi-component steady diffusion in the gas phase. A comparison with the ‘classical’ approach based on the Fick’s law is reported for three families of liquid mixtures, namely alkanes, alcohols and water solutions of alcohols under a wide range of operating conditions. The local vapour fluxes of each vaporising species on the drop surface are correlated with the local Gaussian curvature. The effects of drop shape and of the modelling of constitutive equations on the evaporation rates are discussed. Comparison of the present model with experimental measurements of different compositions of tetradecane–hexadecane drops vaporising in stagnant air shows a rather satisfactory agreement.

An approach combining the lattice Boltzmann method and Maxwell–Stefan equation for modeling multi-component diffusion

The lattice Boltzmann method is an appropriate mesoscopic-scale tool for investigating the diffusion processes. However, since the state-of-the-art multi-component diffusion lattice Boltzmann (LB) models are based on the kinetic theory and start from the lattice Bhatnagar–Gross–Krook model, some defects cannot be avoided: they are only suitable for steady flow and there are limitations for setting the velocity and viscosity in lattice units. We devise a new incompressible LB model for ideal gases in solid oxide fuel cells (SOFCs), which is based on the advection–diffusion equation and coupled with the Maxwell–Stefan (M–S) equation by relaxation time. The coupled M–S equation is used for correction, considering the driving force in a multi-component diffusion system. Our LB model is implemented to predict the concentration overpotentials of a porous anode in a SOFC. The overpotentials are calculated from an H2–H2O–Ar ternary mass transport simulation and compared to the corresponding experimental results and several published continuum-scale and LB computations, demonstrating that our model offers a better consistency with the experimental measurement. Moreover, a Stefan tube is simulated for benchmarking against the local parameters; this is compared with the related experimental data and demonstrates the accuracy of our LB model.

Analytical solution of diffusion equations in multicomponent systems when applying diffusion coatings

For multicomponent coatings, analytical equations are obtained that take into account the diffusion coefficients in the concentration equations. It is shown, that to solve the problem of multicomponent diffusion in a solid solution containing substitutional elements and interstitial elements, it is advisable to use the equations for the concentrations of chemical elements. Keywords: multicomponent coating, solid solution, concentration, diffusion coefficient, analytical solution ariff-1947@mail.ru

Modeling of Reversible Solid Oxide Cell Stacks with an Open-Source Library

This study describes a homogenized model of reversible solid oxide cell (rSOC) stacks. The model enables steady-state simulations of rSOC stacks in both fuel cell and electrolyzer modes to be conducted. It accounts for multi-component species diffusion, and heat and mass transfer, including thermal radiation and electrochemical reactions. An open-source library, OpenFOAM, provides a platform for the model’s implementation. Numerical simulations were performed using an in-house-designed rSOC stack. A previously-developed, one-dimensional Simulink model was also applied to the stack. Both models predict similar output voltages, within 2% difference, under the same operating conditions. Temperature variations were also compared; the stack model’s results were closer to experimental measurements than the Simulink model. The new model was able to perform faster simulations (less than 2 hours) for the prescribed stacks.

A simple yet general model of binary diffusion coefficients emerged from a comprehensive assessment of 18 binary systems

This study is the most comprehensive test to date aiming at defining the optimal number of fitting parameters for a reliable mathematical description of the diffusion behavior of a binary solid solution. Our systematic test of 18 diverse binary systems has yielded a surprisingly simple model with only one fitting parameter/constant which can be evaluated from experimental diffusion data. The rest of the quantities in the model are the self-diffusion and impurity (dilute) diffusion coefficients of the pure elements and the thermodynamic factor which can be computed from a CALPHAD thermodynamic assessment of the pertinent binary system. The 1-parameter Z-Z-Z model has been demonstrated to be very reliable and robust since the 18 binary systems tested in this study include very asymmetrical systems such as Co-Pd and Fe-Pd as well as Nb-Ti whose experimental diffusion coefficient data cover ~9 orders of magnitude and over a temperature range spanning ~1200°C (from ~800°C to ~2000°C). The Z-Z-Z model allows both tracer and intrinsic diffusion coefficients to be reliably computed for any composition at any temperature after the sole constant is evaluated from the interdiffusion or all experimental diffusion data. Extension of such a simple and robust model from binary to ternary and higher order systems will lead to a substantial reduction of fitting parameters and an enhancement of the reliability of future multicomponent diffusion (atomic mobility) databases for simulation of kinetic processes in materials.

Lattice Boltzmann study of miscible viscous fingering for binary and ternary mixtures

The viscous fingering or Saffman-Taylor instability occurs when a less viscous fluid penetrates a more viscous fluid in a porous medium. Fingering patterns refer to the deformation of the interface between the invading and displaced fluids. For mixtures composed of three miscible species, the dynamic of each component varies greatly. In that case, multicomponent diffusion effects are of primary importance, and reverse diffusion could trigger the instability from a configuration that is known to be stable for binary mixtures.

Numerical Calculation of the Diffusion Process in Multicomponent Hydrocarbon Gas Mixtures

Knowledge of the laws of diffusion is necessary in the description, design and calculation of the mass transfer process in the production, operation and transportation of gaseous fuels. In this article, the calculation of diffusion processes for five natural hydrocarbon gas mixtures into the air was carried out. The effective diffusion coefficients and matrix coefficients of multicomponent diffusion were determined. Also the advantages of using effective coefficients in the description of mass transfer were shown.

An Improved Multicomponent Diffusion Model for Compositional Simulation of Fractured Unconventional Reservoirs

Summary Most simulators currently use the advection/diffusion model (ADM), where the total flux comprises Darcian advection and Fickian diffusion. However, significant errors can arise, especially for modeling diffusion processes in fractured unconventional reservoirs, if diffusion is modeled by the conventional Fick’s law using molar concentration. Hence, we propose an improved multicomponent diffusion model for fractured reservoirs to better quantify the multiphase multicomponent transport across the fracture/matrix interface. We first give a modified formulation of the Maxwell-Stefan (MS) equation to model the multicomponent diffusion driven by the chemical potential gradients. A physics-based modification is proposed for the ADM in fractured reservoirs, where fracture, matrix, and their interface are represented by three different yet interconnected flow domains to honor the flux continuity at the fracture/matrix interface. The added interface using a more representative fluid saturation and composition of the interface can hence better capture the transient mass fluxes between fracture and matrix. The proposed approach is also implemented in an in-house compositional simulator. The multicomponent diffusion model is validated with both intraphase and interphase diffusion experiments. Then, the improved model for fracture/matrix interaction is compared with a fine-grid model. The proposed multiple interacting continua (MINC) model with three continua (MINC3) can better match the fine-grid model’s result than the double-porosity (DP) model, which only obtains a fair match at an early time. Then, we simulate a gas huff ‘n’ puff (HnP) well in the Permian Basin to investigate the effect of diffusion within the fractured tight oil reservoir. The simulation reveals that diffusion has a minor effect on the performance of depletion when oil is the dominant phase. For gas HnP, the simulation neglecting diffusion will underestimate the oil recovery factor (RF) but overestimate the gas rate. The DP approach tends to overestimate the RF of heavy components but leads to a similar cumulative oil RF compared with MINC3. With the diffusion included in the simulation, gas HnP performance becomes more sensitive to the soaking time than the model without diffusion. Although increasing the soaking time will lead to a higher RF after considering diffusion, the incremental oil is not sufficiently large to justify a prolonged soaking time.

Ion kinetic effects on the evolution of Richtmyer–Meshkov instability and interfacial mix

Plasma effects, such as the multi-component kinetic diffusion and self-generated electromagnetic fields, are recognized as a pivotal key to understanding the physics of interface evolution in inertial confinement fusion and supernova remnants. In this work, a two-dimensional hybrid fluid-PIC code is used to investigate the ion kinetic effects of the single-mode Richtmyer–Meshkov instability (RMI) at the interface between hydrogen plasma and carbon plasma. After an electrostatic shockwave passing through the perturbed interface, the RMI, which reshapes the interface, grows via the vorticity depositing as well as the self-generated magnetic field. After scaling the growth of the interfacial mix region with time, the density transition layer has been found to exceed the disturbance wavelength and lead to a suppression of the instability evolution finally.

RECENT TRENDS IN OSMOTIC DEHYDRATION OF FRUITS: A REVIEW

The marvel of expulsion of water from lower solvent concentration to higher concentration by a semi-perimeable membrane is osmotic dehydration, resulting in equilibrium state on both sides of the membrane. As it decreases the water activity of fruits. It is found to be most widely used application for preserving food materials. Due to colour, scent, nutritional constituents and flavour compound retention value, osmotic dehydration is favoured over other methods. Drying, shower drying, freezedrying, solidifying, vacuum packing, canning, syrup conservation (osmotic dehydration), sugar crystallization, nourishment illumination and the addition of preservatives or inert gases such as carbon dioxide are typical methods of applying these processes. The solutes used in osmotic parchedness are ordinarily sugar syrup with fruit slices or 3d shapes, and salt (sodium chloride) or vegetable brine. This can be the method of multicomponent diffusion. Water moves from fruits or vegetables to the solution in this process and certain fruit and vegetable components such as minerals, vitamins, fruit acids, etc also pass into the solution along with water to the fruits and vegetables, sugar and salt migrate. Examples that are considered are Gooseberry Murabbas (Aonla), apples, sweets, candies of Different fruits and vegetables, including pethas, parwal, Osmosis-made sweets in sugar syrup are the most popular items of commercial value available in the market made from fruits. It is processed in a brine solution before drying in pickles made from raw mango. In brine, various vegetables are handled to lower their moisture content

Pair-exchange diffusion model for multicomponent alloys revisited

The recently proposed pair-exchange diffusion model for multicomponent diffusion in a random alloy is analyzed in detail. The model defines the differences of chemical potential gradients of two elements as general driving forces for interdiffusion and the corresponding proportionality coefficients as pair-mobilities for atomic exchange fluxes of a pair of elements at the mesoscopic scale. The total fluxes of alloying elements are given as the sum over corresponding pair-contributions, which rely on a set of independent forces and maintain a meaningful symmetric form to satisfy Onsagers reciprocal relations. It is demonstrated that a consistent definition of interdiffusion coefficients requires the fulfillment of the Gibbs-Duhem relation by the applied thermodynamic Gibbs energy description. The expression for the marker velocity for multicomponent random alloy is derived in the pair-wise form as a sum of the differences of chemical potential gradients of two elements with the linear coefficients which are differences between corresponding mobilities. The application of the model to High Entropy Alloys is demonstrated.

Correlation between estimated diffusion coefficients from different types of diffusion couples in multicomponent system

The interdiffusion coefficients can be estimated now purely experimentally from multicomponent diffusion profiles utilizing the recently proposed pseudo-binary and pseudo-ternary diffusion couple methods. One can estimate the composition dependent main interdiffusion coefficients over the composition range and main intrinsic diffusion coefficients at the Kirkendall marker plane from pseudo-binary diffusion couple. On the other hand, main and cross interdiffusion coefficients can be calculated from the pseudo-ternary diffusion couples. In this article, we have first proposed the method of estimation of the tracer diffusion coefficients at the cross of diffusion paths in pseudo-ternary diffusion couples by extending the approach propose by Lane and Kirkaldy in a ternary system but without neglecting the cross phenomenological terms of Onsager formalism. Following, one can even estimate the main and cross intrinsic diffusion coefficients, which is otherwise not possible following the Kirkendall marker experiments in this type of couple. Following we have derived the relation for estimation of the tracer diffusion coefficients at the Kirkendall marker plane in a pseudo-binary diffusion couple. We have chosen NiCoFeCr system to demonstrate the utilization of these methods by comparing the tracer diffusion coefficients estimated directly following radiotracer method. The relations derived in this article help to understand the correlation between estimated data in different types of diffusion couples by neglecting and considering the vacancy wind effect. This method can be now extended to the Al, Ga, Si containing systems in which the estimation of tracer diffusion coefficients following the radiotracer method is difficult/impossible because of various reasons.

Residence time of igneous garnet in Si-rich magmatic systems: Insights from diffusion modeling of major and trace elements

Although garnet is an important accessory phase in many granitic rocks, the petrogenetic history of such garnets is often debated. Explanations range from crystallization from (mostly) peraluminous melts to entrainment of peritectic or xenocrystic garnets originating from country rocks. Here we present a detailed microchemical study of a mid-crustal granodiorite from the Ivrea-Zone (N-Italy), which contains metapelitic enclaves and composite metamorphic-magmatic xeno-phenocryst garnet. Garnets from this locality exhibit high-phosphorus (∼800 ppm) metamorphic cores and multiple igneous overgrowth rims. The high-phosphorus cores appear to originate from granulite facies country-rock, while low-phosphorus rims indicate magmatic overgrowth in two main episodes. Zircon-bearing nanogranitoid inclusions are trapped along embayments between garnet cores and the first magmatic growth zones. Zirconium saturation thermometry indicates a temperature of 820 ± 5°C during the first magmatic overgrowth, and a temperature of 778 ± 10°C for the second overgrowth. The latter temperature agrees with garnet-biotite thermometry using the garnet rim composition, which yields a temperature of 773 ± 29 °C. In order to quantify the duration of the overgrowth episodes, we have numerically modeled Cr, Y, REEs and Hf trace element diffusion, as well as multicomponent major divalent cation diffusion within garnet using available experimental diffusion data and Cr diffusion data retrieved from natural garnets. All modeled diffusants conform to a single temperature-time path, in which the temperatures associated with the first and second magmatic overgrowths persisted for 5.4 and 6.3 kyr, respectively. Composite garnets in Si-rich magmatic systems have the potential to constrain magma transit rates in the continental crust.

Reduced mechanism for flames of propane, n‐butane, and their mixtures for application to burners: Development and validation

AbstractPropane, n‐butane, and their mixtures are commonly used as fuels for various applications. Reliable numerical simulations of flames involving these fuels are most essential to study their efficient use in domestic and industrial burners. Such simulations require a suitable reaction mechanism containing the necessary kinetics to predict key combustion characteristics in flames accurately. However, the use of detailed kinetic mechanisms for these computations is formidable in multidimensional simulations, owing to their large sizes. To address this, in this work, a compact mechanism (45 species, 392 reactions) for propane, n‐butane, and their mixtures, suitable for multidimensional simulations is derived and comprehensively validated against available experimental data in flames. The main oxidation pathways retained in this compact model are showcased. One‐dimensional (1D) computations of premixed and nonpremixed flames are carried out using FlameMaster and Chemkin‐Pro. Two‐dimensional (2D) calculations are performed within ANSYS‐FLUENT. Here, multicomponent diffusion, thermal diffusion, and radiation submodels are used. Laminar flame speeds, extinction strain rates, and amounts of major species in premixed flat flames are validated using 1D computations. Temperature and major species in propane and n‐butane jet diffusion flames are verified in 2D simulations. Further, 2D computations using the compact mechanism also predict the laminar burning velocity of premixed flames of n‐butane and propane mixtures established over a Bunsen burner. The ability of the compact mechanism to predict desired targets in premixed and nonpremixed flames is analyzed from a kinetic basis. Validation using 2D simulations demonstrates the usability of the compact mechanism in multidimensional computations.

Complex diffusion saturation of carbon steel 1045 with boron, chromium, titanium and silicon

The article presents the results of studies on the formation of a diffusion layer upon saturation of steel 1045 with boron together with chromium, titanium and silicon. The results of tests of diffusion coatings on steel 1045 obtained by simultaneous diffusion saturation with boron, chromium, titanium and silicon under the action of a sulfuric acid solution under conditions of abrasive wear are presented. A comparison is made of the service life of knives for shredding lead-acid batteries made of steel HARDOX 600 and steel 1045 after diffusion saturation with boron, chromium, titanium and silicon. It was found that the simultaneous strengthening with boron, chromium, titanium and silicon made it possible to increase the operational durability of knives for shredding lead-acid batteries by 2.4 times. The possibility of highly efficient use of products made of simple carbon steel with a multicomponent (B + Cr + Ti + Si) diffusion coating instead of products made of hardened alloy steel is shown.

Surrogate Model for Multi-Component Diffusion of Uranium through Opalinus Clay on the Host Rock Scale

Multi-component (MC) diffusion simulations enable a process based and more precise approach to calculate transport and sorption compared to the commonly used single-component (SC) models following Fick’s law. The MC approach takes into account the interaction of chemical species in the porewater with the diffuse double layer (DDL) adhering clay mineral surfaces. We studied the shaly, sandy and carbonate-rich facies of the Opalinus Clay. High clay contents dominate diffusion and sorption of uranium. The MC simulations show shorter diffusion lengths than the SC models due to anion exclusion from the DDL. This hampers diffusion of the predominant species CaUO2(CO3)32−. On the one side, species concentrations and ionic strengths of the porewater and on the other side surface charge of the clay minerals control the composition and behaviour of the DDL. For some instances, it amplifies the diffusion of uranium. We developed a workflow to transfer computationally intensive MC simulations to SC models via calibrated effective diffusion and distribution coefficients. Simulations for one million years depict maximum uranium diffusion lengths between 10 m and 35 m. With respect to the minimum requirement of a thickness of 100 m, the Opalinus Clay seems to be a suitable host rock for nuclear waste repositories.