Multicomponent Diffusion Model Research Articles

Phase-Field Modeling of Kinetics of Diffusive Phase Transformation in Compositionally-Graded Ni-Based Superalloys

AbstractKinetics of the $$\gamma$$ γ /$$\gamma ^{\prime}$$ γ ′ phase transformation and the interdiffusion phenomena in single-crystal Ni-based superalloys, under isothermal annealing and composition gradient, is investigated through the phase-field and continuum diffusion models. The employed models in the present work exploit CALPHAD-based thermodynamics and kinetics databases, in order to perform realistic simulations. We specifically predict the interdiffusion of elements for a hypothetical alloy AlCoCrTaNi/Ni diffusion couple, equivalent to the CMSX-10/Ni diffusion couple, at 1323 K. Accordingly, the phase fraction and morphology of $$\gamma ^{\prime}$$ γ ′ precipitations in the $$\gamma$$ γ matrix is simulated as well. The implemented multi-component diffusion model takes into account vacancies and pore formation, reflecting Kirkendall effect. Furthermore, the time evolution of morphology parameters of the precipitate-depleted zone in the diffusive region (i.e., the position and the size) are estimated.

The effect of micromechanical stresses on vacancy formation and stress-driven mass-transport in polycrystalline Fe–Au alloy

In recent years, a new class of super saturated binary and ternary alloys have demonstrated the ability for the self-healing of creep-induced voids formed at the grain boundaries. However, a clear understanding of the parameters affecting the self-healing mechanism is still not yet complete. One of the main challenges is understanding the effect of microstructure and micromechanical stresses on the redistribution of the healing-solute and vacancies. To this end, we address this issue using a CALPHAD-informed diffusion model coupled with crystal plasticity. In principle, the approach is general and can be used for any binary Fe–X alloy, but in this work Fe–Au binary system is used since it experimentally showed the best healing efficiency. First, we present a multicomponent diffusion model considering cross and stress-driven diffusion. The effect of stress was also considered on the equilibrium vacancy concentration. To investigate the effect of the micromechanical stresses, a representative volume element (RVE) was obtained using the phase-field method. The results showed that the maximum vacancy concentration is at the grain boundaries (GBs) with the highest hydrostatic tensile stresses. These were also the regions of the highest Au enrichment. A crucial factor to achieve this is the high diffusivity of Au compared to the Fe matrix. Increasing the stresses, lead to an increase both in vacancy and Au concentration. The accompanying increased stress triaxiality is suggested to be the reason for the reduced self-healing efficiency observed in previous experimental studies.

On the structure of continuum thermodynamical diffusion fluxes—A novel closure scheme and its relation to the Maxwell–Stefan and the Fick–Onsager approach

This paper revisits the modeling of multicomponent diffusion within the framework of thermodynamics of irreversible processes. We briefly review the two well-known main approaches, leading to the generalized Fick–Onsager multicomponent diffusion fluxes or to the generalized Maxwell–Stefan equations. The latter approach has the advantage that the resulting fluxes are consistent with non-negativity of the partial mass densities for non-singular and non-degenerate Maxwell–Stefan diffusivities. On the other hand, this approach requires computationally expensive matrix inversions since the fluxes are only implicitly given. We propose and discuss a novel and more direct closure which avoids the inversion of the Maxwell–Stefan equations. It is shown that all three closures are actually equivalent under the natural requirement of positivity for the concentrations, thus revealing the general structure of continuum thermodynamical diffusion fluxes. As a special case, the new closure also gives rise to a core-diagonal diffusion model in which only those cross-effects are present that are necessary to guarantee consistency with total mass conservation, plus a compositional dependence of the diffusivity. This core-diagonal closure turns out to provide a rigorous fundament for recent extensions of the Darken equation from binary mixtures to the general multicomponent case. As an outcome of our investigation, we also address different questions related to the sign of multicomponent thermodynamic or Fickian diffusion coefficients. We show rigorously that, in general, the second law requires positivity properties for tensors and operators rather than for scalar diffusivities.

Thermodynamically consistent phase-field modelling of activated solute transport in binary solvent fluids

Active diffusion of substances in binary immiscible and incompressible fluids with different densities occurs universally in nature and industry, but relevant mathematical models and numerical simulation have been studied scarcely so far. In this paper, a thermodynamically consistent phase-field model is established to describe the activated solute transport in binary fluids with different densities. A mixed free-energy function for multiple solutes is proposed, which leads to different solute chemical potentials in binary solvent fluids, thus it has the ability to characterize the solubility difference of the solutes in two solvents. The two-phase flow is governed by a general hydrodynamic phase-field model that can account for general average velocity and different densities. The proposed model is derived rigorously using the second law of thermodynamics. Moreover, a general multi-component solute diffusion model is established using the Maxwell–Stefan approach, which involves the crossing influences between different solutes. To solve the model effectively, an efficient, linearized and decoupled numerical method is proposed for the model as well. The proposed numerical method can preserve the thermodynamical consistency, i.e. obeying an energy dissipation law at the discrete level, as well as guarantee the mass conservation law for the solutes and solvent fluids. Numerical experiments are carried out to show that the proposed model and numerical method can simulate various processes of the solute active diffusion in two-phase solvent fluids.

Theoretical and Experimental Considerations for Investigating Multicomponent Diffusion in Hydrated, Dense Polymer Membranes.

In many applications of hydrated, dense polymer membranes—including fuel cells, desalination, molecular separations, electrolyzers, and solar fuels devices—the membrane is challenged with aqueous streams that contain multiple solutes. The presence of multiple solutes presents a complex process because each solute can have different interactions with the polymer membrane and with other solutes, which collectively determine the transport behavior and separation performance that is observed. It is critical to understand the theoretical framework behind and experimental considerations for understanding how the presence of multiple solutes impacts diffusion, and thereby, the design of membranes. Here, we review models for multicomponent diffusion in the context of the solution-diffusion framework and the associated experiments for characterizing multicomponent transport using diffusion cells. Notably, multicomponent effects are typically not considered when discussing or investigating transport in dense, hydrated polymer membranes, however recent research has shown that these effects can be large and important for understanding the transport behavior.

The Steady State Characteristics of Multicomponent Diffusion in Micro- and Mesoporous Media for Adsorbable and Nonadsorbable Species.

The study addresses one of the fundamental issues in the mathematical modeling and quantitative process analysis of complex multicomponent diffusion in meso- and microporous materials. The model presented here incorporates combined molecular diffusion, Knudsen diffusion, viscous flow, and surface diffusion. A methodology and algorithm for the determination of steady states of such complex diffusive processes are proposed. The adopted form of the surface diffusion model does not require the calculation of the thermodynamic factor matrix. The method was verified by comparing the profiles of the state variables with those obtained from the dynamic model for sufficiently long diffusion times. The application of the method is illustrated for two diffusion processes involving three components. In the first one, all components are subject to adsorption. In the other, one gaseous component is an inert and is therefore not adsorbed and does not participate in surface diffusion. It is shown that the presence of inerts as well as their number does not impede the application of the proposed algorithm for the determination of steady states.

Formation of calcium chloride brines in volcaniclastic-rich sediments

The Amami-Sankaku Basin, located in the Philippine Sea, records approximately 50 million years of sediment accumulation and diagenesis of volcanic ash derived from the Kyushu-Palau and Kyushu-Ryukyu arcs. Analyses of porewater and sediment samples from the 1461-m core recovered at IODP Expedition 351, Site U1438, included major and trace elements, strontium radiogenic isotope ratio (87Sr/86Sr), and taxonomic identification of archaeal classes and bacterial orders. Sediment X-ray diffraction and thin section analyses show that smectite, zeolites and chlorite are the main authigenic minerals. A multicomponent solute diffusion and reaction numerical model was developed to simulate the long-term diagenesis that took place in this sedimentary sequence and to account for the transition to a calcium chloride brine at about 670 mbsf. Numerical results indicate that 45% of the initial amount of volcanic ash has been dissolved at 750 mbsf. At this depth, 13% of the initial water (H2O) in the pore space is estimated to have been transferred to the solid phase by the formation of zeolites, which accounts for an increase in porewater chloride concentration. In contrast, dissolution of anorthite and volcanic ash combined with sodium uptake by zeolites accounts for the predominance of calcium in the brine. In the upper 160 m of the sedimentary column, the electrochemical migration of solutes causes chloride to move in the opposite direction of the concentration gradient, i.e., uphill diffusion, sustaining downward diffusion of seawater chloride into the sediments.

Simulation of diffusion with non-equilibrium vacancies, Kirkendall shift and porosity in single-phase alloys

In an alloy subject to vacancy-mediated diffusion, differences in intrinsic diffusivities tend to produce vacancy excess and deficit. These are accommodated by mechanisms such as dislocation climb and pore formation. This is of concern in high temperature alloy-coating systems used in industrial applications, as pores may develop at the interface between the alloy and the coating, which is undesired. This paper presents a multicomponent diffusion model with two types of vacancy sinks/sources: one is associated with dislocation climb and generates lattice shift, the other one is associated with porosity increase/decrease. The model is designed toward a 1D implementation, and porosity is described with a local average volume fraction. Thermodynamic properties and mobility are modeled according to the Calphad method to allow future application to engineering materials. Finite-difference simulations run on two binary systems, NiCr and NiSi, illustrate the role of the two types of sinks in interdiffusion and pore development. Diffusion is found to be more sensitive to the sink strengths in the NiSi system, where intrinsic diffusivities have a stronger composition dependence. This work provides a basis for the evaluation of the parameters involved in vacancy generation/annihilation (e.g. dislocation density) from experimental data, such as concentration profiles obtained from diffusion couple experiments, and for the prediction of porosity in engineering materials.

Investigation of Multicomponent Diffusion in Numerical Simulation on H2-O2 Detonation Transition Process

A numerical calculation method for detonation transition process using an experimental-scale grid was proposed in this study. This method consists of multicomponent diffusion model. Detonation transition experiments were conducted to investigate the usefulness of the proposed method. A detonation was generated in rectangular tube with a square cross section of 30 mm per side. The tube was filled with an oxyhydrogen mixture with an initial pressure of 100 kPa, and an equivalent ratio of 1.0. The time history of the flame front position was obtained by observation with a high-speed camera. The time history of flame front position by the proposed numerical method were compared with one by the experimental results. As a result, the results obtained by the proposed numerical model are in good agreement with the experimental results. It was also found that the effect of thermal diffusion can be neglected in the simulation of the detonation transition process.

Testing the equilibrium model: An example from the Caledonian Kalak Nappe Complex (Finnmark, Arctic Norway)

AbstractThe equilibrium model has been tested using Barrovian garnet‐zone micaschists of the Kalak Nappe Complex. In our model, equilibrium in the MnNCKFMASHT system was established across the entire rock volume during prograde metamorphism except for garnet, which developed growth zoning preserved at levels controlled by the kinetics of intracrystalline diffusion. The preservation potential of the disequilibrium fluctuations required for nucleation of garnet has been considered in our simulations, using a moving boundary multicomponent diffusion and growth model. Results indicate that the core of garnet that crystallizes during regional metamorphism does not retain the major element composition of the nucleus but reflects the compositional signature of the immediate overgrowth. The differences between the metamorphic conditions of successive garnet growth steps of the samples indicate characteristic trends in their pressure‐temperature evolutions that can be predicted with the equilibrium model. There is some latitude with regard to the absolute metamorphic conditions due to the inherent uncertainty of the thermodynamic data and the approximation of the reactive volume composition. However, the slopes of the pressure‐temperature paths together with systematic trends in the lithological, geochemical, and Lu–Hf garnet whole‐rock isotopic properties of the rocks, as well as their garnet crystal size frequency distributions, enable the identification of the Veidnes, Bekkarfjord, and Kolvik Nappes involved in the Caledonian Orogeny and provide new insight into their metamorphic evolutions. According to our findings, the base of the Kalak Nappe Complex experienced wide‐spread Barrovian‐type metamorphism at c. 420 Ma with a gradient of ∼40 bar/°C and peak conditions of ∼560°C and 6.7 kbar in the Bekkarfjord and Veidnes Nappes, whereas the hinterland‐placed Kolvik Nappe was metamorphosed at peak conditions of ∼590°C and 7.5 kbar. This event was preceded by moderate‐pressure metamorphism at c. 423 Ma resulting in garnet crystallization exclusively in the Bekkarfjord Nappe, along a gradient of ∼20 bar/°C and peak conditions of ∼570°C and 6.0 kbar. We consider both of these metamorphic and deformational episodes to be different stages of the Scandian phase during the Caledonian Orogeny. An additional orogenic event at c. 464 Ma is preserved in the Veidnes Nappe, which was juxtaposed with the Scandian Nappes by repeated out‐of‐sequence thrusting associated with the final continent–continent collision. This nappe provides a unique insight into an earlier stage of the Caledonian Orogeny, indicating a low‐pressure Barrovian‐type metamorphic history with a gradient of ∼15 bar/°C and peak conditions of ∼560°C and 4.5 kbar.

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.

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.

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.

Assessing the impact of multicomponent diffusion in direct numerical simulations of premixed, high-Karlovitz, turbulent flames

Implementing multicomponent diffusion models in numerical combustion studies is computationally expensive; to reduce cost, numerical simulations commonly use mixture-averaged diffusion treatments or simpler models. However, the accuracy and appropriateness of mixture-averaged diffusion has not been verified for three-dimensional, turbulent, premixed flames. In this study we evaluated the role of multicomponent mass diffusion in premixed, three-dimensional high Karlovitz-number hydrogen, n-heptane, and toluene flames, representing a range of fuel Lewis numbers. We also studied a premixed, unstable two-dimensional hydrogen flame due to the importance of diffusion effects in such cases. Our comparison of diffusion flux vectors revealed differences of 10–20% on average between the mixture-averaged and multicomponent diffusion models, and greater than 40% in regions of high flame curvature. Overall, however, the mixture-averaged model produces small differences in diffusion flux compared with global turbulent flame statistics. To evaluate the impact of these differences between the two models, we compared normalized turbulent flame speeds and conditional means of species mass fraction and source term. We found differences of 5–20% in the mean normalized turbulent flame speeds, which seem to correspond to differences of 5–10% in the peak fuel source terms. Our results motivate further study into whether the mixture-averaged diffusion model is always appropriate for DNS of premixed turbulent flames.

Numerical Study of Quenching Distances for Side-Wall Quenching Using Detailed Diffusion and Chemistry

The numerical investigation of quenching distances in laminar flows is mainly concerned with two setups: head-on quenching (HOQ) and side-wall quenching (SWQ). While most of the numerical work has been conducted for HOQ with good agreement between simulation and experiment, far less analysis has been done for SWQ. Most of the SWQ simulations used simplified diffusion models or reduced chemistry and achieved reasonable agreement with experiments. However, it has been found that quenching distances for the SWQ setup differ from experimental results if detailed diffusion models and chemical reaction mechanisms are employed. Side-wall quenching is investigated numerically in this work with steady-state 2D and 3D simulations of an experimental flame setup. The simulations fully resolve the flame and employ detailed reaction mechanisms as well as molecular diffusion models. The goal is to provide data for the sensitivity of numerical quenching distances to different parameters. Quenching distances are determined based on different markers: chemiluminescent species, temperature and OH iso-surface. The quenching distances and heat fluxes at the cold wall from simulations and measurements agree well qualitatively. However, quenching distances from the simulations are lower than those from the experiments by a constant factor, which is the same for both methane and propane flames and also for a wide range of equivalence ratios and different markers. A systematic study of different influencing factors is performed: Changing the reaction mechanism in the simulation has little impact on the quenching distance, which has been tested with over 20 different reaction mechanisms. Detailed diffusion models like the mixture-averaged diffusion model and multi-component diffusion model with and without Soret effect yield the same quenching distances. By assuming a unity Lewis number, however, quenching distances increase significantly and have better agreement with measurements. This was validated by two different numerical codes (OpenFOAM and FASTEST) and also by 1D head-on quenching simulations (HOQ). Superimposing a fluctuation on the inlet velocity in the simulation also increases the quenching distance on average compared to the reference steady-state case. The inlet velocity profile, temperature boundary condition of the rod and radiation have a negligible effect. Finally, three dimensional simulations are necessary in order to obtain the correct velocity field in the SWQ computations. This however has only a negligible effect on quenching distances.

Multicomponent diffusion of F, Cl and OH in apatite with application to magma ascent rates

Chemical zoning in igneous minerals is a potential record of the time, processes, and thermal evolution during the lifetime of a given magma reservoir. Abundances of volatiles (OH, Cl and F) in apatite from terrestrial and extraterrestrial plutonic and volcanic rocks have been used to study volatile behavior in magmas, however, volatile diffusivities in apatite are poorly constrained. Here we report new experimental results on Cl, F and OH diffusivities in apatite and apply them to estimate magma ascent times and rates. The experiments were carried out on oriented natural Durango fluorapatite crystals at 800–1100°C, 1-atm, and oxygen fugacity at the wüstite-magnetite buffer. Experimental charges and chemical profiles were investigated with a variety of methods, including scanning electron microscopy, transmission electron microscopy, electron probe microanalysis, secondary ion mass spectrometry, and nuclear reaction analysis.We find that the concentration profiles of Cl show evidence of uphill diffusion that is likely related to the co-existence of three monovalent anions, i.e., OH−, Cl−, F−, at the same site of the apatite structure. Chemical gradients of OH, Cl and F were reproduced using a multicomponent diffusion model to extract the tracer diffusion coefficient (Di⁎) of each component (i). The calculated values of Di⁎ parallel to the c-axis show a general relation of DF⁎>DCl⁎>DOH⁎, and define the following Arrhenius relations (parallel to the c-axis, at 1 bar) as:DCl⁎=7(+12−4)×10−5×[exp(−294(±12) kJ⋅mol−1RT)] m2⋅s−1DF⁎=5(+49−5)×10−4×[exp(−308(±76) kJ⋅mol−1RT)] m2⋅s−1DOH⁎=4(+11−3)×10−2×[exp(−401(±39) kJ⋅mol−1RT)] m2⋅s−1The activation energy for Cl diffusion that we determined (294 kJ⋅mol−1) is within the range of that reported by Brenan (1994), but the pre-exponential factor is smaller and thus we obtain in general slower diffusivities than Brenan (1994). DCl⁎ and DOH⁎ parallel to the a-axis are 1 to 2 orders of magnitude slower than those parallel to the c-axis, indicating anisotropic diffusion of Cl and OH. Preliminary results on S diffusivity (parallel to the c-axis) at 800–900°C show values between those of Cl and OH. The diffusion coefficients and model proposed in this study can be used to estimate the timescales of volatile re-equilibration in apatite in a variety of contexts from plutonic rocks and layered intrusions, to volcanic rocks and meteorites. We show that, for example, magma ascent rates can be determined by modelling Cl zoning in volcanic apatite. These applications provide new opportunities for understanding the influence of magma ascent rates on the eruption styles of volcanoes, thus having potential contributions to improving volcano forecasting and hazard assessments.

Flame structure and kinetic analysis of diffusion autoignition of pressurized hydrogen

In this work, the spontaneous ignition of high-pressure accidentally released hydrogen in a one-dimensional tube was numerically studied using the high-order WENO reconstruction method, multi-component diffusion model and detailed kinetics mechanism. The result shows that the spontaneous ignition of high-pressure hydrogen jet is essentially a non-premixed ignition process between compressed hot air and expanded low-temperature fuel. It is found that increasing the molecular weight of the fuel can greatly reduce the air temperature and thereby improve the storage safety. Further analysis of the reacting mixing layer reveals that the autoignition occurs in a fuel-lean condition where the fuel mass fraction is less than 0.02. During the reaction front propagation, two types of flames are observed in the H2/air diffusion layer, which are a diffusion flame near the stoichiometric position and a premixed flame in the fuel-rich space. The reaction pathway analysis demonstrates that the two types of flames are controlled by the low temperature radical destruction reaction (R1: H + O2(+M) <=> HO2(+M)) and the high temperature radical formation reaction (R9: H + O2 <=> O + OH), respectively. Moreover, the sensitivity evaluation of different reactions on the ignition delay indicates that the two reactions also play a dominate role on the overall combustion rate. In the end, the flame front displacement speed calculation shows that the contribution of diffusion to the reaction front evolution is always slightly greater than that of chemistry except the ignition timing.

Multicomponent diffusion in ionic crystals: theoretical model and application to combined tracer- and interdiffusion in alkali feldspar

We present a model for multicomponent diffusion in ionic crystals. The model accounts for vacancy-mediated diffusion on a sub-lattice and for diffusion due to binary exchange of different ionic species without involvement of vacancies on the same sub-lattice. The diffusive flux of a specific ionic species depends on the self-diffusion coefficients, on the diffusion coefficients related to the binary exchanges, and on the site fractions of all ionic species. The model delivers explicit expressions for these dependencies, which lead to a set of coupled non-linear diffusion equations. We applied the model to diffusion of ^{23}Na, ^{39}K, and ^{41}K in alkali feldspar. To this end, gem-quality crystals of alkali feldspar were used together with ^{41}K doped KCl salt as diffusion couples, which were annealed at temperatures between 800^circ and 950^circC. Concentration-distance data for ^{23}Na, ^{39}K, and ^{41}K were obtained by Time of Flight Secondary Ion Mass Spectrometry. Over the entire investigated temperature range the Na self-diffusion coefficient is by a factor of ge 500 higher than the K self-diffusion coefficient. Diffusion mediated by binary ^{39}K–^{41}K exchange is required for obtaining satisfactory fits of the model curves to the experimental data, and the respective kinetic coefficient is well constrained.

Concentration of unconventional methane resources using microporous membranes: Process assessment and scale-up

Unconventional methane resources are usually diluted in air, which prevents their use as feedstock in chemical or thermal processes. Some of them (e.g. coal mine ventilation air or diluted landfill biogas) are emitted directly to the atmosphere without harnessing, increasing the contribution of methane to global warming. Gas permeation membranes offer an alternative for the concentration of these methane resources, increasing considerably their harnessing possibilities. Microporous materials, such as carbon molecular sieve, zeolite or metal organic frameworks, have emerged as alternative to polymeric materials for the preparation of these membranes.The present work is based on simulations of the separation of methane and nitrogen mixtures, using SAPO-34 and carbon molecular sieve membranes. Mass transfer has been modelled in two scales: the membrane material (modelled using the Maxwell-Stefan multicomponent surface diffusion model) and the membrane module (based on the plug flow model). A sensitivity analysis of the influence of the main operating variables on the membrane performance has revealed that the most important ones are transmembrane pressure difference, methane feed concentration and membrane loading. It has been found that SAPO-34 membranes are more suited to concentrate methane in lean mixtures, while the carbon membrane perform better with rich mixtures.The membrane process has been scaled-up for a feed gas flow rate of 1000 m3/h n.t.p. with target methane recovery of 70% for two cases: lean (1%) and rich (50%) methane feed mixtures.

Experimental method for determination of shrinkage direction during holographic recording in Bayfol HX photopolymer

Subject of Research. The paper presents experimental determination of the main shrinkage direction caused by photopolymerization during holographic recording in Bayfol HX material. Method. The determination method for the main shrinkage direction is based on registration of the change in volume holograms characteristics (period, the orientation of isophase planes relative to material surfaces and hologram thickness) caused by the shrinkage. For the implementation of this method a 2D-model is presented which describes shrinkage as a vector. The effect of the shrinkage on characteristics of holograms is evaluated based on geometrical laws. We performed modeling of the shrinkage with different directions and determined its effect on a variety of arbitrarily oriented holograms-gratings. Namely, the cases of isotropic shrinkage, as well as shrinkage in the direction of the material surfaces, the lattice vector and the isophase planes were considered. The experiment is carried out involving a simultaneous recording of two total internal reflection holograms in a photopolymerizable Bayfol HX composite. The changes of their characteristics make it possible to determine clearly the main shrinkage direction. Main Results. The main shrinkage direction has been determined along the less side of the material (considering thickness). However, the experiment has demonstrated a deviation of this direction along the lattice vector as well. Practical Relevance. The developed model and the experimental method allow for taking into account the shrinkage in Bayfol HX while modeling of photopolymerization and multicomponent diffusion in this material. The studied technique also facilitates predictions of hologram characteristics after the shrinkage aimed at its compensation.