Concentration-dependent Diffusion Research Articles

Modeling of conductivity relaxation in oxide ceramics taking account of concentration dependent chemical diffusivities and surface exchange coefficients

Conductivity relaxation of disk-shaped ceramic samples upon a sudden change of the oxygen partial pressure of the surrounding gas phase has been simulated by application of a three-dimensional finite element model. The geometry is based on a homogeneous cylindrical specimen with a diameter of 10mm and a thickness of 0.1mm, where four peripheral line contacts are attached to the sample in accordance with the van der Pauw method. Both the chemical diffusion coefficient and the chemical surface exchange coefficient are assumed to vary with the oxygen non-stoichiometry during the oxygen exchange reaction (oxidation or reduction). The alteration of the oxygen non-stoichiometry as well as the relaxation of the electrical conductivity are calculated simultaneously. The modeling of conductivity relaxation curves is applied to the SOFC cathode material La0.4Sr0.6FeO3−δ (LSF) at 900°C. The simulation of conductivity relaxation curves can be performed for arbitrary oxygen partial pressure changes. The present modeling approach allows the interpretation of significant differences between oxidation and reduction steps owing to the concentration (non-stoichiometry) dependence of the kinetic parameters.

Effect of Current on Diffusivity in Metal Hexaborides: A Spark Plasma Sintering Study.

We present the effect of pulsed direct current on metal ion diffusion in CaB6-SrB6 diffusion couples, showing that the diffusivity of Ca2+ and Sr2+ across the diffusion couple interface is higher toward the positive electrode when subjected to a current flow of 2.2 kA at a temperature of 2007 K. We attribute this enhanced mobility to the movement of negatively charged metal vacancies toward the positive electrode in the system. Energy-dispersive spectroscopy is used to map the concentration of Ca2+ and Sr2+ in the region near the interface, and diffusion profiles are fitted with error functions. The concentration curves display concentration-dependent Boltzmann-Matano diffusivity. Total dopant values (Q) have been used to numerically compare the differences between Ca2+ diffusion in SrB6 and Sr2+ diffusion in CaB6. We determine an enhancement of 3.8× for Ca2+ into SrB6 versus an enhancement of 1.8× for Sr2+ into CaB6. No new phases are formed at the interface between CaB6 and SrB6, since hexaboride compounds readily form solid solutions. The results elucidate the role of pulsed direct current on the diffusion of metal ions in hexaboride compounds.

The effect of applied compressive stress on the diffusion of carbon in carbon supersaturated S-phase layer

In this study, hydrostatic compressive stresses are applied on the prior-carburized samples of 316 ASS to discover the relationship between interstitial diffusion process and the applied stresses. Carbon diffusion profiles are compared and concentration dependent diffusion coefficients are discussed to further advance scientific understanding of diffusion process in supersaturated S-phase. The experimental results demonstrate that the applied compressive stress can retard the fast diffusion process comparing to the unstressed one. Based on theoretical modelling, the effect of the applied hydrostatic compressive stresses on the diffusion of carbon in carbon supersaturated 316 austenitic stainless steel is discussed.

Miscible displacements with concentration-dependent diffusion and velocity-induced dispersion in porous media

Diffusion and dispersion play significant roles in miscible displacements. In the present study, the frontal instabilities in miscible displacements incorporating both concentration-dependent diffusion coefficient (CDDC) and velocity-induced dispersion (VID) are investigated in homogeneous porous media through nonlinear numerical simulation. Special characteristics have been presented and analyzed for such CDDC-VID case by examining the frontal instabilities. In particular, the VID has more important influence on stabilizing displacements than CDDC. While with CDDC considered, the displacements are more unstable compared with the ConstD-VID case with constant diffusion coefficient (ConstD) and velocity-induced dispersion (VID). Parametric analysis is conducted to study the effects of longitudinal dispersion strength, transverse dispersion, mobility ratio, and Peclet number for the CDDC-VID case. They all affect the development of frontal instabilities, while their roles are different with those of ConstD-VID case. Furthermore, the relative importance of these parameters is analyzed. It is found that the same parameter plays different roles in affecting breakthrough time and sweep efficiency. The correlated equations are obtained to predict breakthrough time and sweep efficiency which agree quite well with the simulated values. It is therefore capable of predicting breakthrough time and sweep efficiency with high accuracy for the CDDC-VID cases in miscible displacements.

Generalized model for the diffusion of solvents in glassy polymers: From Fickian to Super Case II.

The diffusion of small solvent molecules in glassy polymers may take on a variety of different forms. Fickian, anomalous, Case II and Super Case II diffusion have all been observed, and theoretical models exist that describe each specific type of behavior. Here we present a single generalized kinetic model capable of yielding all these different types of diffusion on the basis of just two parameters. The principal determinant of the type of diffusion is observed to be a dimensionless parameter, γ, that describes the influence of solvent-induced swelling in lowering the potential barriers separating available solvent sites. A second parameter, η, which characterizes the effect of the solvent in reducing the potential energy of a solvent molecule when at rest at an available site, only influences the type of diffusion to a lesser extent. The theoretical analysis does not include any effects that are explicitly non-local in time, an example of which is the inclusion of polymer viscosity in the Thomas-Windle model; it thus represents a variant of Fick's second law utilizing a concentration-dependent diffusivity when η is small. To check the significance of time-delayed swelling, a simulation of a modified model was performed that contained a history-dependent term. The results were found to be very similar to those in the time-local model.

Numerical modeling of bronze coating formation using concentration-dependent diffusivity

The engineering of a component’s surface is of remarkable importance; it allows applications that surpass what is achievable by the substrate alone by improving surface properties such as hardness, wear, and corrosion resistance and even aesthetic value. In this work, formation of bronze coatings through the diffusion of electrodeposited tin on copper via heat treatment was studied. Specifically, the single phase α was targeted due to its attractive properties. Determining the correct heat treatment parameters is crucial since only a specific range of composition leads to the formation of the desired microstructure and, consequently, properties. The diffusion behavior of tin-copper for the formation of a single phase α is elucidated and a numerical model is developed to predict the composition profile after heat treatment, which agrees with experimental observations.

Nonlinear simulation of miscible displacements with concentration-dependent diffusion coefficient in homogeneous porous media

The nonlinear dynamics of miscible flow displacements in homogeneous porous media are examined for the special case of concentration-dependent diffusion coefficient (CDDC) models. Highly accurate numerical methods are used to simulate the time evolution of fingering with both mobility and diffusion coefficient contrasts of two components in a fully miscible solution system. The simulations revealed that, when compared with a constant diffusion coefficient (CDC), the CDDC models show drastically different viscous fingering structures and mixing of the two components. In particular, for a pure diffusion process with a stable front, using a CDDC results in less mixing, with a non-symmetric concentration gradient. While for the unstable displacements with relatively large mobility contrasts, it is found that using a CDDC tends to trigger fingers at the very beginning of the displacements. The diffusion-dominated period is therefore very short and can nearly be neglected. Moreover, the fingers reach the downstream boundary much earlier with fingering structures about 2–4 times more complex than the CDC case. Quantitative analysis indicates that the exponential CDDC models can enhance the mixing by shortening the diffusive regime but not change the growth rate of mixing in the convective regime. In addition, in contrast with the CDC case, the time required for the appearance of fingers for the CDDC seems to be independent of Peclet number Pe at a relatively large log mobility ratios R. As Pe increases for the CDDC cases, more complex dynamics of the fingers are observed, which can only be found at very high Pe and R values for the CDC case. In addition, a small increase in R is able to significantly enhance the instabilities since it can result in not only larger mobility contrast but also a steeper diffusion gradient.

Concentration dependent diffusivities of model solvents in heavy oil

Concentration dependent diffusivities of model solvents in heavy oil

Effect of the universal acid-base indicator on the formation of the concentration-dependent diffusion instability

The effect of the universal acid-base indicator on the pattern formation and mass transfer in a two-layer system composed of two reactive miscible liquids in a vertical Hele-Shaw cell is studied experimentally. The reaction we study is a neutralization one. It turns out that the presence of the indicator leads to a change in the spatio-temporal characteristics of the system and even in the mass transfer mechanism near the reaction front—from diffusive to convective. The conditions, where the universal indicator does not affect the reaction and can be used as a visualizing mean, are reported.

Water-enhanced interdiffusion of major elements between natural shoshonite and high-K rhyolite melts

The interdiffusion of six major elements (Si, Ti, Fe, Mg, Ca, K) between natural shoshonite and a high-K rhyolite (Vulcano island, Aeolian archipelago, Italy) has been experimentally measured by the diffusion couple technique at 1200°C, pressures from 50 to 500MPa and water contents from 0.3 (‘nominally dry’) to 2wt%. The experiments were carried out in an internally heated pressure vessel, and major element profiles were later acquired by electron probe microanalysis. The concentration-distance profiles are evaluated using a concentration-dependent diffusivity approach. Effective binary diffusion coefficients for four intermediate silica contents are obtained by the Sauer-Freise modified Boltzmann-Matano method. At the experimental temperature and pressures, the diffusivity of all studied elements notably increases with dissolved H2O content. Particularly, diffusion is up to 1.4 orders of magnitude faster in a melt containing 2wt% H2O than in nominally dry melts. This effect is slightly enhanced in the more mafic compositions. Uphill diffusion was observed for Al, while all other elements can be described by the concept of effective binary interdiffusion. Ti is the slowest diffusing element through all experimental conditions and compositions, followed by Si. Fe, Mg, Ca and K diffuse at similar rates but always more rapidly than Si and Ti. This trend suggests a strong coupling between melt components. Since effects of composition (including water content) are dominant, a pressure effect on diffusion cannot be clearly resolved in the experimental pressure range.

Effect of block copolymer morphology on crystallization and water transport

The effect of block copolymer morphology on polymer crystallization and water sorption was investigated using two amphiphilic block copolymers with minority hydrophilic phase. Such polymers have many potential membrane applications, including CO2 capture and water purification. A model block copolymer chemistry comprising polystyrene and poly(ethylene oxide) (PEO) is used in this work. Both block copolymers have strongly phase-separated order, one with lamellar morphology and another with cylindrical morphology. In addition to the block copolymer structure, the PEO phase is semicrystalline at room temperature. The block copolymer structure has dramatic consequences for the degree of PEO crystallinity even in the absence of water. Furthermore, the crystallinity is affected by water sorption. PEO melting and degree of crystallinity were determined as a function of water content. Water solubility was measured between 35 and 75 °C. Interestingly, water sorption properties are dictated almost exclusively by the amorphous PEO volume fraction, being low in the semicrystalline state (below 55 °C) and higher in the amorphous state (above 55 °C). At 55 °C, crystallite dissolution is observed with increasing water solubility. Water diffusion coefficient was also measured; it decreases monotonically with increasing water content. This concentration dependence of diffusion is explained by water clustering, which increases with increasing water content. In addition to block copolymer morphology playing a major role in PEO crystallinity, it has a significant effect on water diffusion in the amorphous polymers and is of practical importance as investigations at elevated temperature are not possible with homopolymer PEO.

Diffusion in quaternary polymer solutions—Model development and validation

Multicomponent diffusion in polymer solutions is a complex and not yet completely understood phenomenon. Available studies are so far almost exclusively limited to ternary systems containing a polymer and two solvents. In this work measurement data in form of isothermal drying curves in quaternary systems, consisting of the polymer poly(vinyl acetate) (PVAC) and the solvents dichloromethane, methanol and toluene obtained by inverse micro-Raman spectroscopy (IMRS) is presented. The measurements show that the diffusive behaviour is a function of the overall composition of the mixture, as additional solvents accelerate diffusion. Since no numerical model for such systems has been validated in literature, a framework for the simulation of mass transfer processes in quaternary systems has been developed. The shrinking of the film due to evaporation is taken into account by a transformation of the frame of reference. The concentration-dependent diffusion coefficients are calculated by an expression only requiring binary data, previously only tested in ternary systems, enabling predictions in uncharacterized multicomponent systems. Cross-term diffusion is neglected. The numerical model, validated by the measurement data, is able to predict the experimental results reliably for varying initial conditions.

Quantitative and mechanistic analysis of impact of novel cassava-assisted improved processing on fluid transport phenomenon in humidity-temperature-stressed bio-derived films

Bio-derived films’ realistic performance integrity is ascertained by their resilience in highly-stressful storage conditions, a function of its ability to respond timely and manages fluid barrier appropriately. Bio-derived films’ moisture and temperature sensitivity often posed mass transport challenges, thus decreasing their lifespan. Quantifying bio-derived film mass transport behaviour has been limited to mass transfer representations, which can be imperfect to understand fully mass transport phenomenon. This study reported quantitative and mechanistic analysis of fluid-phase mass transport phenomenon in Simultaneous Release Recovery Cyanogenesis-produced intact bitter cassava (IBC) bio-derived films under stressful conditions. Films were tested for solvent solubility, swelling ratio, sorption and permeability to water vapour and oxygen at 10–40°C and 10–95% RH. Film’s structural alterations were characterised by their thermal and chemical properties. Modified-BET, Peleg, Oswin models best described sorption data. Temperature-dependence of film water vapour permeability was simulated best by Arrhenius model, while oxygen permeability was influenced highly by crystallinity and RH. Non-organic and organic film-solvent diffusion followed case II and Fickian diffusional patterns respectively. Solvents induced structural changes in IBC films with concentration-dependent diffusion. Cassava bio-derived films’ integrity will depend on the host environment, thus maximum care should be ensured to minimise environment impact during applications. Nonetheless, IBC films hold potential as biomaterials for broad range product use.

Electrochemical Reactions in Li-Ion Battery Electrodes and Their Interaction with Mechanical Stresses: Size Effects, Phase Segregation, and Crack Propagation

Since their introduction 25 years ago, lithium-ion batteries have risen to become the primary power source for mobile devices such as electric tooth brushes and razors, but also for cellphones and tablet PCs. They have a high potential for wider application, e.g. in (hybrid) electric vehicles or for the storage of renewable energy. This is currently hindered by the gradual capacity fade over cycle lifetime. Main factors for this degradation are electrochemical side-effects such as SEI formation and mechanical damage. The cyclic insertion and extraction of Li ions results in high stress levels in and large deformation of the electrodes, leading to delamination of the electrode structure and to fracture of individual particles, respectively. The freshly cracked surface is then exposed to further chemical reactions. Experimental evidence however suggests, that nanostructured electrodes exhibit a higher resilience against this diffusion-induced mechanical degradation.In this talk, we report on our efforts towards modeling the chemo-mechanical processes taking place in free-standing electrode particles at the micro- and the nano-scale. In particular, we describe two models used to study the interaction of phase segregation and crack growth, as well as the interaction of chemical reactions and surface tension in nanoparticles. Both models feature a direct coupling between diffusion and elasticity as well as concentration-dependent diffusivity. In particular, the Butler-Volmer relation for the description of electrochemical surface reactions has been modified to account for the effects of mechanical stress and phase formation.We show that surface tension provides mechanical stabilization in nanoparticles, allowing, in principle, for higher charge/discharge rates. This effect is size-and shape-dependent. Due to surface tension, however, the usable capacity of a particle shrinks with its size. Regarding phase segregation, we demonstrate how the rate of surface reactions can determine the separation behavior, and that the evolution of the phase interface can drive the propagation of pre-existing cracks in an electrode particle.

Estimation of the non-linear diffusion coefficient with Marcov Chain Monte Carlo method based on the integral information

PurposeThis paper aims to present development and application of the Bayesian inverse approach for retrieving parameters of non-linear diffusion coefficient based on the integral information.Design/methodology/approachThe Bayes formula was used to construct posterior distribution of the unknown parameters of non-linear diffusion coefficient. The resulting aposteriori distribution of sought parameters was integrated using Markov Chain Monte Carlo method to obtain expected values of estimated diffusivity parameters as well as their confidence intervals. Unsteady non-linear diffusion equation was discretised with the Global Radial Basis Function Collocation method and solved in time using Crank–Nicholson technique.FindingsA number of manufactured analytical solutions of the non-linear diffusion problem was used to verify accuracy of the developed inverse approach. Reasonably good agreement, even for highly correlated parameters, was obtained. Therefore, the technique was used to compute concentration dependent diffusion coefficient of water in paper.Originality/valueAn original inverse technique, which couples efficiently meshless solution of the diffusion problem with the Bayesian inverse methodology, is presented in the paper. This methodology was extensively verified and applied to the real-life problem.

Thermal stability of low-temperature-carburized austenitic stainless steel

To study the thermal stability of the “case” (hard layer) that forms on AISI-316L austenitic stainless steel by low-temperature carburization, we exposed carburized specimens to temperatures between 573 K and 648 K (300 and 375 °C) in air for 20.7 Ms (8 months). In spite of a colossal supersaturation with carbon, the austenite does not precipitate carbides. No carbon is lost to the ambient. Carbon diffuses deeper into the alloy, resulting in a flatter carbon-fraction–depth profile. This is realistically simulated assuming temperature- and concentration-dependent carbon diffusion. Exposing to 648 K for 20.7 Ms about doubles the average carbon depth. The near-surface carbon fraction decreases only moderately, particularly as the material appears to assimilate carbon from the ambient. Accordingly, the beneficial effects of low-temperature carburization on mechanical properties and corrosion resistance are retained throughout such long-term heat exposure, implying corresponding service life of low-temperature-carburized parts at temperatures below 650 K.

Determination of Transport Parameters in Liquid Binary Lithium Ion Battery Electrolytes

Various numerical methods for the simulation of ion-transport in concentrated binary electrolyte solutions can be found in the literature, whereas the corresponding transport parameters are rarely discussed. In this contribution, a polarization cell consisting of two electrodes separated by a porous separator is proposed to determine the concentration dependent binary diffusion coefficient of non-aqueous electrolyte solutions. Therefore, two different electrochemical methods are extended so that they can be applied to electrolyte solutions in a porous medium. Additionally, the different methods are compared with each other by means of numerical simulations. The proposed experimental setup is used to determine the concentration dependent binary diffusion coefficient of an exemplary electrolyte, lithium perchlorate dissolved in a mixture of ethylene carbonate and diethyl carbonate, and the data are compared to those available in the literature. It will be shown that the most reliable method to determine concentration dependent binary diffusion coefficients are long-term relaxation experiments in a two-electrode cell using a porous separator.

Управление перемешиванием в проточном микрореакторе с варьируемым зазором

Continuous-flow microreactors are at the center of the revolution that occurs in chemical engineering technology. The advantages of these new reactor types are: the quick and effective mixing of the reagents, very small reagent quantities used for the synthesis, the regulation of the main reaction parameters, i.e. flow rate, residence time, pressure and so on with very high accuracy. In this paper, a Hele-Shaw cell with a variable gap width is theoretically analyzed as the main element of the flow reactor of more advanced type. As a test reaction, we consider the reaction of neutralization of nitric acid with sodium hydroxide occurring in water, which leads, as it was previously demonstrated, to convective instability in the gravity field due to the effect of concentration-dependent diffusion (CDD instability). We show that the equations of motion are, in general, analogous to the fluid filtration equations in a porous medium (Darcy problem) with the variable permeability. We demonstrate numerically that the prototyping the spatially-distributed shape of the reactor zone can successfully separate the incoming and outgoing flows of reagents, control the intensity of the mixing processes locally, increase or decrease the value of the product of the outlet. The possibility of controlling the chemo-hydrodynamic flows in a reactor in real time through a local change in the width of the gap is also discussed.

Convective instability in a two-layer system of reacting fluids with concentration-dependent diffusion

The development of convective instability in a two-layer system of miscible fluids placed in a narrow vertical gap has been studied theoretically and experimentally. The upper and lower layers are formed with aqueous solutions of acid and base, respectively. When the layers are brought into contact, the frontal neutralization reaction begins. We have found experimentally a new type of convective instability, which is characterized by the spatial localization and the periodicity of the structure observed for the first time in the miscible systems. We have tested a number of different acid–base systems and have found a similar patterning there. In our opinion, it may indicate that the discovered effect is of a general nature and should be taken into account in reaction–diffusion–convection problems as another tool with which the reaction can govern the movement of the reacting fluids. We have shown that, at least in one case (aqueous solutions of nitric acid and sodium hydroxide), a new type of instability called as the concentration-dependent diffusion convection is responsible for the onset of the fluid flow. It arises when the diffusion coefficients of species are different and depend on their concentrations. This type of instability can be attributed to a variety of double-diffusion convection. A mathematical model of the new phenomenon has been developed using the system of reaction–diffusion–convection equations written in the Hele–Shaw approximation. It is shown that the instability can be reproduced in the numerical experiment if only one takes into account the concentration dependence of the diffusion coefficients of the reagents. The dynamics of the base state, its linear stability and nonlinear development of the instability are presented. It is also shown that by varying the concentration of acid in the upper layer one can achieve the occurrence of chemo-convective solitary cell in the bulk of an almost immobile fluid. Good agreement between the experimental data and the results of numerical simulations is observed.

The Modeling of Nitrogen Mass Transport in CoCr Alloys

Abstract The kinetics of plasma nitriding of CoCr alloy below temperatures of nitrides formation and mechanisms of nitrogen penetration are analyzed by proposed kinetic modeling in this article. Proposed nitrogen diffusion model is based on the trapping – detrapping (TD) model and developed taking into account the effect of the concentration dependent diffusivity of nitrogen, nitrogen adsorption on the surface of alloy and surface swelling process. The model indicates the influence of chromium atoms to nitrogen atoms diffusivity. The model consists of time and depth dependent diffusion, which is described by a partial differential equation, and it is solved by using Crank – Nicolson finite difference method. By fitting of experimental nitrogen depth profiles, it is shown that nitrogen diffusion coefficient varies with nitrogen concentration according to Einstein-Smoluchowski relation. Nitrogen depth profiles in plasma nitrided medical grade CoCr alloy (ISO 5831 – 12) at T = 400 °C for 1, 4 and 20 hours calculated on the basis of this model are in good agreement with experimental nitrogen profiles. Furthermore, the swelling process is showed and analyzed, derived the dependency of swelling rate on nitriding duration – the swelling rate is inversely proportional to the square root of nitriding duration. The obtained diffusion coefficient value and the swelling process rates satisfy the experimental data form Ref. The derived model explains physical processes during plasma nitriding and allows obtaining nitrogen depth profiles for any requisite nitriding duration.