Partial Diffusion Coefficients Research Articles

Dynamics of an EIS spatially heterogeneous rabies model

This paper is devoted to the study of population dynamics of an EIS epidemic reaction-diffusion model in spatially heterogeneous environments, where the rates of disease-induced mortality and disease transmission are space dependent. For such a class of systems, we provide clear pictures on the global dynamics in terms of the basic reproduction number R0, which improves the local dynamics proposed in Wang and Zhao (2012) [20]. When R0≤1, the disease-free steady state is globally asymptotically stable. Different from earlier works for many epidemic models, we obtain the positive steady states by using bifurcation theory for R0>1, which can be easily generalized to the case where the reaction-diffusion system involves partial diffusion coefficients of zero.

Numerical calculation of interstitial dumbbell-mediated transport coefficients in dilute crystalline systems with non-truncated correlations

ABSTRACT Interstitial dumbbell-mediated diffusion can affect segregation and precipitation properties of solutes in alloys under irradiated conditions. Accurate computation of transport coefficients for dumbbell-mediated diffusion thus becomes essential for modelling solute segregation under irradiation. In this work, we extend the Green's function approach, a general numerical approach, to compute accurate transport coefficients for interstitial dumbbell-mediated mechanisms in the dilute limit for arbitrary crystalline systems with non-truncated correlations in atomic diffusion. We also present results of tracer correlation factors, solute drag ratios and partial diffusion coefficient ratios in iron and nickel-based alloys computed with our approach, compare our results with existing results in the literature, and discuss some aspects of correlated solute-dumbbell motion.

Effect of Al2O3 on the molten slag microstructure information by molecular dynamics simulation and experimental analysis

The metallurgical properties of blast furnace slag changed when high alumina iron ore was used extensively due to the resulting changes of the molten slag microstructure. In the study, based on typical CaO–MgO–SiO2–Al2O3 slag systems with different w(Al2O3) content, molecular dynamics simulation was used to calculate the microstructural properties of particles in the high-temperature slag system, such as bond length, partial radial distribution function, coordination numbers, and diffusion coefficient. In addition, X-ray diffraction (XRD), Fourier transform infrared (FTIR) spectroscopy, and 27Al solid-state magic angle spinning nuclear magnetic resonance (27Al SS MAS NMR) were used to detect and analyze the samples. The comprehensive calculations and experimental results show that increasing w(Al2O3) can enhance the structural stability of each ion pair, and the strength of the structural stability is such that Si–O > Al–O > Mg–O > Ca–O. The self-diffusion coefficients are as follows: Mg2+ > Ca2+ > Al3+ > Si4+, which leads to the transformation of the [SiO4]4−(Q0), [Si2O7]6−(Q1) and [Si2O6]4−(Q2) structural units to [Si2O5]2−(Q3). The degree of polymerization of slag increased as well as the stability of the structural units. Moreover, the coordination of Al will change from the [AlO6]9−octahedral structure of six-coordinated Al to the [AlO5]7−pentahedral structure of five-coordinated Al and the [AlO4]5−tetrahedral structure of four-coordinated Al. It was also found that the content of non-bridge oxygen in the whole slag system decreased continuously, leading to the increasing degree of polymerization of slag, and the experimental results were consistent with the molecular dynamics calculation.

Calphad-based phase-field study of the interplay between spheroidal graphite growth and chemical segregation in ductile cast iron

Spheroidal graphite in ductile cast irons forms in a divorced eutectic solidification, controlled by interstitial diffusion of carbon through the enveloping austenitic shell. As technical cast irons are multicomponent alloys, carbon diffusion can strongly be affected by content and chemical gradient of other solute elements. During growth of a eutectic cell, all solute elements are partitioned at the austenite/liquid interface. Substitutional diffusion within the austenite is almost negligible, but expansion-induced spatial displacement of the iron-rich matrix and solute atoms during graphite growth significantly complicates multidimensional numerical simulation. A recently developed volumetric multi-phase-field approach, implemented in the Micress software, now accounts for the volume expansion and related matter and solute transport. In the present case study, this approach is applied to investigate the evolving chemical gradients and their potential effect on carbon diffusion during growth of a three-dimensional eutectic cast iron cell. Phase and concentration dependent thermodynamic data, partial molar volumes and diffusion coefficients are evaluated from linked Calphad-databases. The interface properties of the polycrystalline spheroidal graphite nodule are modelled based on a dedicated effective multi-facetted anisotropy function. A special target is to investigate whether increase in Si content may result in a significant reduction of the carbon flux, eventually favoring graphite degeneration and chunky growth.

Combined effects of partial slip and variable diffusion coefficient on mass and heat transfer subjected to chemical reaction

This article is a generalization of already published work and investigates the combined effects of chemical reaction, partial slip, temperature and concentration, jumps on the transport of heat energy and solute of variable mass conductance in a fluid of temperature dependent viscosity and thermal conductivity. Publish benchmark (Hayat et al 2015 Partial slip effects in flow over nonlinear stretching surface Appl. Math. Mech. 36 1513–26) is the special case of present work. It is also important to highlight that partial slip effects in the presence of variable diffusion coefficients are investigated first time. It is found that the distractive chemical reaction accelerates the rate of diffusion of solute. However, diffusion rate is decelerated by constructive chemical reaction. The concentration of solute in the liquid regime increases as the mass diffusion increases due to the rise in temperature. It is also observed that the diffusion of momentum of wall in fluid of constant viscosity is faster than the diffusion of momentum fluid of viscosity varying under rise in temperature. Further, an increase in thermal conductivity due to rise in temperature causes an enhancement in rate of heat conduction from wall into the fluid. Eventually, temperature of fluid rises.

Fabrication of composite membranes for pervaporation of tetrahydrofuran-water: Optimization of intrinsic property by response surface methodology and studies on vulcanization mechanism by density functional theory

Response surface methodology (RSM) optimized accelerator-to-sulfur (A/S) ratio was used to synthesize semi efficiently vulcanized styrene butadiene rubber (SBRSEV0) membrane possessing optimum balance between tensile strength (TS) and elongation at break (EAB). In addition, composite membranes, such as SBRSEV8, SBRSEV12 and SBRSEV24, were fabricated via incorporating 8, 12 and 24 wt% carbon black filler (CBF), respectively. The changes in physicochemical properties, as a result of crosslinking and CBF loading, were determined by analyzing CP MAS 13C-NMR, FTIR, TGA, DSC, XRD, FESEM-EDX and crosslink densities. Several bi-/poly-sulfidic products, formed by crosslinking precursors of SBR in accelerated sulfur vulcanization, were examined to ascertain the unambiguous reaction mechanism. In this regard, an extensive density functional theory (DFT) based optimization was conducted to apprehend the relative variation in stabilities of several mono-/poly-crosslinked configurations by measuring dipole moments and ground state energies. Moreover, intrinsic membrane properties, such as partial permeabilities and diffusion coefficients, were measured at varying conditions. RSM was employed to optimize membrane efficiency resulting from individual and/or interactive effects of input variables. For the first time, systematic three-stage RSM based optimization (i.e., TS/EAB, total flux (TF)/separation factor (SF) and partial permeabilities) was used to ensure excellent balance between TS/EAB (5.78 MPa/499.008% at 2.32 and 3.29 wt% of A and S, respectively), minimum TF/maximum SF (36.90 g m–2 h–1/202.46 at 35 °C, 0.97 wt% tetrahydrofuran (THF) and 24 wt% CBF) and minimum/maximum partial permeabilities of water/THF (2.94×10–8/4.64×10–8 Barrer at 35 °C, 0.97 wt% THF and 11.49 wt% CBF).

INFLUENCE OF THE TWO-STAGE SINTERING MODE ON STRUCTURE FORMATION AND PROPERTIES OF POWDERED ALL-PRESSED BIMETALLIC IRON-BASED MATERIALS

The paper justifies the urgency and efficiency of obtaining bimetallic iron-based materials by two-step isothermal sintering to enable forming the structure of the product bases at the first stage and activating diffusion processes in the wear-resistant layer only at the second stage to eliminate any high-porosity areas and brittle inclusions at interlayer boundaries typical for powder materials doped with carbides, nitrides and borides. The analysis of equation solutions for diffusion in two-component heterogeneous powder systems made it possible to propose an option for determining the time and temperature of homogenizing sintering of bimetallic materials taking into account grain-size distribution of powders, concentration and partial diffusion coefficients of components, charge bulk density, initial and final porosity of the products. Experiments proved that bimetallic materials containing 15– 20 wt.% of chromium carbide, 20–25 wt.% of ferrochromium and iron as the rest component in the wear-resistant layer charge have the best combination of hardness, wear resistance and radial compression strength after sintering in a chamber furnace in protective medium at 1150–1180 °C with a holding time of 1,5–2,0 hours at the first stage, and in an induction furnace at 1350– 1370 °C for 25–35 s with a heating rate of 450–470 °C/s at the second stage. Structure formation peculiarities of the interlayer boundaries and wear-resistant layer during two-step sintering of all-pressed bimetallic materials are shown. It is found that for high-temperature sintering by high-frequency (8 or 16 kHz) heating at the second stage, the depth of chromium diffusion from the wear-resistant layer to the matrix is 120–130 μm, and Cr concentration in various points of interlayer and interparticle boundaries varies between 1 and 30 wt.% thus allowing formation of a transition layer with a structure consisting of a ferritic-austenitic matrix with martensitic colonies and dispersed particles of (Cr,Fe)23C6, (Cr,Fe)7C3 and (Cr,Fe)3C2 ferrochromium carbides uniformly distributed over the volume.

Influence of the structure and morphology of ultrathin poly(3-hydroxybutyrate) fibers on the diffusion kinetics and transport of drugs

Ultrathin fibers of a biodegradable polymer poly(3-hydroxybutyrate) with an encapsulated drug (dipyridamole, 0–5% of poly(3-hydroxybutyrate) mass) are obtained by electrospinning. Introduction of the drug substantially affects the geometric shape and crystallinity of individual filaments as well as the total porosity of the fibrillar film on their basis. As follows from the SEM data, in the absence of the drug or at its low concentration (<3%), poly(3-hydroxybutyrate) fibers appear as ellipse-like fragments alternating with cylindrical ones. At a higher content of the drug (3–5%), the abnormal ellipse-like structures are practically absent and the fiber acquires the cylindrical shape. A set of morphological and crystallinity characteristics of the fibers determines the absorption of water and the rate of the diffusion transport of the drug as well as the corresponding profiles of its controlled release. A simplified model of drug desorption from the fibrillar film is advanced which considers two sequential stages of the process: (i) diffusion of the drug in the polymer fiber with coefficient D f ~ 10–12 cm2/s and dimeter φf ~ 2–4 μm and (ii) transport of the drug in the interfibrillar porous space filled by solvent with diffusion coefficient D w = 5.5 × 10–6 cm2/s. Using the characteristics of porosity, crystallinity, and geometry of the fibers and diffusion effective coefficients D eff calculated from the profile of drug release, it is shown that the limiting stage of the transport of the drug is its diffusion in the volume of the cylindrical fiber. The model makes it possible to turn from the experimental values of D eff to partial diffusion coefficients D f and to calculate the kinetic profile of drug release with allowance made for the above-listed factors.

Separation of tetrahydrofuran using RSM optimized accelerator-sulfur-filler of rubber membranes: Systematic optimization and comprehensive mechanistic study

Response surface methodology (RSM) optimized, semi efficiently vulcanized (SEV) and filled organophilic composite natural rubber (NR) membranes of varying physichochemical interactions were reported for sorption-diffusion-permeation based separation of tetrahydrofuran (THF) from binary aqueous mixtures. RSM was used to obtain optimum accelerator/sulfur (A/S) ratio required for crosslinking of nine membranes to find excellent balance of mechanical properties. These membranes were characterized by FESEM, AFM, EDX, XRD, DTG, TGA, DSC and FTIR. Vulcanized products formed from several crosslinking precursors of NR via radical and/or ionic paths were incorporated to impart an unambiguous reaction mechanism. RSM was also used to obtain optimum conditions (temperature/concentration/filler) for total flux (TF) and separation factor (SF). Membrane intrinsic properties, like partial permeabilities (PPs), selectivities and diffusion coefficients (DCs) were also studied. NRSEV12 membrane showed excellent balance of TF (24.01±0.7 g m−2 h−1) and SF (118.8±4.16) at 0.97 wt% of THF in feed and 35 °C.

Introduction of vacancy drag effect to first-principles-based rate theory model for irradiation-induced grain-boundary phosphorus segregation

In order to examine the vacancy drag effect on phosphorus segregation at grain-boundaries, we estimated partial diffusion coefficients by kinetic Monte Carlo simulations considering atomic transitions for all the binding states of a phosphorus atom and a vacancy, and incorporated them into a rate theory model to simulate grain-boundary phosphorus coverage in neutron-irradiated reactor pressure vessel steels. As a result, it was confirmed that phosphorus atoms are transported to grain-boundaries by the vacancy drag effect. We found that the vacancy drag effect occurs even when only the first-nearest-neighbor binding states are considered, though it does not occur if the partial diffusion coefficients are obtained through the expression derived by theoretical analysis [Ebihara, et al., J. Nucl. Mater. 414 (2011) 328–335]. In addition, we found that grain-boundary phosphorus segregation is suppressed by the vacancy mechanism of phosphorus transport regardless of the vacancy drag effect.

Water diffusivity suppression and ethanol-over-water diffusion selectivity enhancement for ethanol/water mixtures in polydimethylsiloxane–zeolite membranes

Abstract The diffusion behavior of ethanol solutions in polydimethylsiloxane (PDMS) and zeolite-filled PDMS membranes at 298 K was investigated. The partial effective diffusion coefficients of the ethanol and water permeants were determined experimentally using the gravimetric method in conjunction with concentration determination on remaining mixtures. The time-resolved sorption levels of ethanol/water binary mixtures in the membranes were measured and partitioned into individual solvent uptakes. These data were used to determine the diffusion coefficients of the individual solvents from the ethanol/water mixtures (10−95% ethanol concentrations). In the PDMS films, the faster-moving water molecules were slowed down and the ethanol diffusivity was accelerated. Both permeants exhibited similar diffusion coefficients (3−4×10 −10 m 2 /s), indicating a significant diffusion coupling effect of the co-permeants in the PDMS. In a PDMS–(30%) zeolite composite membrane, both permeant diffusivities for the binary mixtures decreased as compared to those in the PDMS. Meanwhile, the ethanol diffused faster than the water co-penetrant by a factor of 2.4−3.5 due to the suppression of water diffusion. Water molecules demonstrated a non-Fickian diffusion behavior, implying different transport mechanisms for the water diffusion process. The PDMS–zeolite membrane exhibited higher ethanol-over-water diffusion selectivities than those in the pristine PDMS membrane.

Biophysical investigations of complement receptor 2 (CR2, CD21) ligand interactions reveal specific amino acid contacts unique to each receptor–ligand pair

Complement receptor II (CD21) is the receptor for C3d fragments on immune complexes. It also serves as a receptor for Epstein–Barr virus (EBV) and on B-lymphocytes CD21 amplifies signalling through the B cell receptor. CD21 is shed from the surface of the cell and is found circulating in plasma. There, soluble CD21 (sCD21) binds to CD23 and complement fragments, thereby modulating the immune response. sCD21 activates monocytes through binding to membrane CD23. The clinical significance of sCD21 is shown by the increased levels found in the sera of patients with B lymphomas, EBV infections and other lymphoblastoid tumors. In this paper, we report the isolation of soluble CD21 from human plasma using affinity chromatography and density gradient centrifugation. sCD21 was found to be a single 126 kDa molecular species. By determining the sedimentation coefficient, we have calculated the partial specific volume, diffusion coefficient and frictional coefficient of the protein. These values show that the sCD21 isolated from human plasma is an elongated rod-shaped molecule.

Unipolar transient carrier transport in a semiconductor heterostructure with two subbands

The effective diffusivity in a multi-component ensemble is not only determined by the partial diffusion coefficients of the constituents, but also by different diagonal and off-diagonal elements of the velocity matrix. Different velocities of the respective subbands give rise to a positive excess contribution to the effective diffusion coefficient. However, a reduction of diffusivity can arise, when the off-diagonal elements of the velocity tensor differ from each other. In this case, the cross correlation between subbands favors the tendency towards phase separation that manifests itself in a qualitative change of the transient carrier transport. Under this condition, memory effects have a profound influence on the transport properties.

Simulation of thermally induced processes of diffusion and phase formation in layered binary metallic systems

Results of the simulation of thermally induced processes of diffusion and phase formation in model and experimentally investigated layered binary metallic systems are presented. The physical model is based on the Darken phenomenological theory and on the mechanism of interdiffusion of components along the continuous diffusion channels of phases in the two-phase regions of the system. The simulation of processes in the model systems showed that the thermally stabilized concentration profiles in two-layer binary metallic systems are virtually independent of the partial diffusion coefficients; for the systems with the average concentration of components that is the same over the sample depth, the time of the thermal stabilization of the structural and phase state inhomogeneous over the depth grows according to a power law with increasing thickness of the system in such a manner that the thicknesses of the surface layers grow, while the thickness of the intermediate layer approaches a constant value. The results of the simulation of the processes of diffusion and phase formation in experimentally investigated layered binary systems Fe-Ti and Cu-Be upon sequential isothermal and isochronous annealings agree well with the experimental data.

SPECTRAL-CORRELATION ANALYSIS OF COUPLED CHAOTIC SELF-SUSTAINED OSCILLATORS

Spectra and autocorrelation functions are studied in a system of two coupled self-sustained chaotic oscillators. We show that spectral and correlation characteristics are connected with partial effective phase diffusion coefficients. The evolution of spectra and diffusion coefficients are considered from the asynchronous regime to the regime of synchronous chaos. We draw the analogy between spectral characteristics of coupled chaotic oscillators and noisy coupled periodic oscillators.

Analysis of the effect of interatomic interaction energy in V-Fe alloys with different iron concentrations on segregation and swelling processes after ion irradiation

Comparative analysis of iron segregation profiles near the free surfaces of V-(2, 5, 7) at % Fe alloys irradiated with 50-keV V+ ions at temperatures 30–40°C with doses from 1 × 1019 to 1 × 1021 ions/m2 has been performed. Data on the change in the moduli of normal elasticity and the values of swelling of these alloys with a change in Fe concentration in them are reported. A correlation between the character of the concentration dependence of the degree of Fe segregation, partial diffusion coefficients of the alloy components, the Young moduli, and the preference factors for vacancies and interstitials between dislocations and voids in these alloys is established.

Influence of difference in the atomic volumes of the components on the mutual diffusion in liquid binary alloys

Expressions relating the partial diffusion coefficients, macroscopic flow velocity, and mutual diffusion coefficient are obtained. Unlike the known Darken relations, the relations obtained take into account the difference in the atomic volumes of the solution components. The influence of the volume factor is more pronounced when the component concentrations are significantly different.

Kinetic formulation for the Graetz–Nusselt ultra-parabolic equation

The well-posedness of the Cauchy problems for a quasilinear ultra-parabolic equation with partial diffusion and discontinuous convection coefficients is established for both entropy and kinetic formulations. The kinetic formulation is set up and solved by means of studying of the Young measures, associated with sequences of solutions of parabolic approximations. The kinetic equation appears as the linear scalar equation, which describes the evolution of the distribution functions of the Young measures in time and space, and which involves an additional ‘kinetic’ variable. The proofs of the principal results of the paper are based on the originally constructed renormalization procedure for the kinetic equation.

Metastable phase state during mechanical alloying

The interstitial mechanism of interdiffusion is effective under the conditions of powder treatment in high-energy ball mills. The major arguments to support this point of view are the following: (1) intermetallic phases are formed in sequences strictly determined by the asymmetry of the partial diffusion coefficients, the first to emerge being an intermetallic phase based on the low-mobile component; (2) the experimental evidence demonstrating the similarity of diffusion mechanisms in Mechanical Alloying (MA) and Solid State Reactions (SSR) in the course of annealing of diffusional pairs. The asymmetry of partial diffusion coefficients and the interstitial diffusion mechanism during annealing are determined by thermal activation, while in MA, the same is due to mechanical activation. Finally (3), our approach is based on the theory of Indenbom and Orlov explaining the plasticity mechanisms by the generation and movement of interstitial atoms under large or impact strains at low temperatures. The formation of certain phases during MA can be delayed due to the lack or insufficiency of vacancy mobility, if the thermodynamic driving force is much too low to be able to overcome the energy barriers for nucleation and growth. In the Cr-Ti -system, formation of stable Laves- phase and amorphization occur during post -MA annealing.

Diffusion and Kirkendall effect in PbSe–EuS multilayer

Epitaxial PbSe–EuS multilayer subjected to diffusion annealing was examined by low-angle X-ray diffraction and Bragg X-ray diffraction. Multilayer profile change in the course of diffusion intermixing was determined by simulation of X-ray diffraction on the model multilayer profile and comparison of calculated patterns with experimental ones. The systematic shift of the average Bragg peak found at diffusion shows the presence of Kirkendall effect in the specimen. Matano procedure was applied to calculate the partial diffusion coefficients of the multilayer components.