Multicomponent Diffusion Effects Research Articles

Effect of multicomponent Tb-Cu films diffusion on the magnetic properties and thermal stability of sintered Nd-Fe-B magnets

In order to improve the diffusion characteristics of heavy rare earth in the grain boundary, effects of the diffusion process as well as the ratio of Tb and Cu (RTb/Cu) during the layered deposition process on the magnetic properties of Tb-Cu diffused Nd-Fe-B magnets were systematically investigated. The coercivity of the diffused magnet with RTb/Cu = 4:1 was enhanced most, which increased from 10.86 kOe to 21.80 kOe. Cu greatly improved the composition homogenization of diffused magnets. For the present designed diffused magnet, the highest utilization efficiency of Tb reached 43.96 kOe/wt%. Moreover, the reduced demagnetization risk of sintered Nd-Fe-B magnets was verified by using finite element method based on the experimentally obtained temperature characteristics of the magnet.

Colloidal transport of heavy metals in low‐advective‐velocity environmental systems: Reactive transport model on biogeochemical and hydrodynamic impacts

AbstractIn this study, the impact of colloid facilitated transport of heavy metals on the overall biogeochemical processes is demonstrated in example Lake Coeurd'Alene sediments. Release and transport of heavy metals (Pb and Zn) on initially sorbed colloidal Fe (hydr)oxide minerals are compared with immobile surfaces under various advective flow velocities. The reactive transport model integrates a coupled biotic reaction network with multiple terminal electron acceptors, including multicomponent diffusion and electrostatic double layer (EDL) treatment effects, illustrating the impact of colloidal transport under competing biogeochemical reaction dynamics for the first time to the authors’ knowledge. The model results illustrate the sensitivity of the results under low‐flow‐velocity conditions. Although enhanced Fe reduction prevails with immobile Fe (hydr)oxide mineral surfaces, the desorbed metal ions with aqueous sulfide complexes are rather “washed out” from the system along with advective transport of solutes, whereas the reductive dissolution of colloidal Fe (hydr)oxides from freshly coming colloidal surfaces results in the accumulation of metal and sulfide ions in the system. The results show that when the potential transport of sorbed contaminants with colloidal particles are ignored, the contaminant concentrations might be underestimated under low‐flow‐velocity conditions, especially around 10−8 or 10−9 m s−1, where the underestimation for the worst case scenario at the lowest bound of low‐flow‐velocity conditions may reach around 90% with depth. On the other hand, this impact may be less significant under cases of higher flow velocity, even around higher limits of low‐velocity environments around 10−7 m s−1, as well as in pure diffusive transport cases.

Light scattering from mixtures of interacting, nonionic micelles with hydrophobic solutes.

Model equations for the Rayleigh ratio and the electric field autocorrelation function are derived using thermodynamic fluctuation theory applied to crowded solute-containing micellar solutions and microemulsions with negligible molecular species and polydispersity. This theory invokes non-equilibrium thermodynamics and enforces local equilibrium between molecular solute, surfactant, and the various micellar species, in order to elucidate the influence of self-assembly on light scattering correlation functions. We find that self-assembly driven variations in the average micelle radius and aggregation number along gradients in concentration, which were previously shown to drive strong multicomponent diffusion effects expressed via the ternary diffusivity matrix [D], do not affect the scattering functions in the limit of zero local polydispersity. Hence, theoretical predictions for the Rayleigh ratio and the field autocorrelation function for ternary mixtures of solute-containing, locally monodisperse micellar solutions are identical to those developed for binary mixtures of monodisperse, colloidal hard spheres. However, self-assembly driven multicomponent diffusion phenomena are predicted to influence the thermodynamic driving forces for diffusion in these mixtures. In support of our theoretical results, measurements for the Rayleigh ratio and the field autocorrelation function for ternary aqueous solutions of decaethylene glycol monododecyl ether (C12E10) with either decane or limonene solute were performed for several molar ratios and volume fractions up to ϕ ≈ 0.25, and for binary mixtures of C12E10/water up to ϕ ≈ 0.5. Excellent agreement between our light scattering theory and experimental data is achieved for low to moderate volume fractions (ϕ < 0.3), and at higher concentrations when our theoretical results are corrected to account for micelle dehydration.

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.

Biogeochemical cycling of heavy metals in lake sediments: impact of multispecies diffusion and electrostatic effects

Fate and transport of heavy metals is controlled by the biogeochemical processes in the environment. Reactive transport modeling is particularly important for capturing the complex interplay between the microbial community dynamics and redox-stratified environments. The focus of this study is to investigate the impacts of (i) multicomponent diffusion (MCD) and (ii) electrical double layer (EDL) on reactive diffusive transport of heavy metals at Lake Coeur d’Alene (LCdA) sediments. The solute benthic fluxes at LCdA sediments are controlled by diffusion, and therefore, the biogeochemical model is focused purely on diffusive transport. In diffusive transport-dominated multicomponent systems, species-specific multicomponent diffusion (i.e., Nernst-Planck representation of diffusion) and the explicit treatment of electrostatic effects can play an important role on the overall dynamics of biogeochemical cycling of metals in the system. The results of this study demonstrate that the use of single uniform diffusion coefficient for all species in purely diffusion-dominated sediments may underestimate the mobility of heavy metals undergoing complex reaction network. This outcome is further signified when explicit treatment of EDL effects is considered in addition to MCD. The simulation results also illustrate the importance of aqueous metal (bi)sulfide complexes, especially when MCD and EDL effects are implemented in reactive transport simulations, impacting the solubility and dynamics of heavy metals in diffusion-dominated systems. The competitive effects of Fe-reducing bacteria FRB and sulfate reducing bacteria SRB activities on pH and overall biogeochemical processes are also demonstrated with multispecies diffusion and explicit treatment of electrostatic effects in the system.

A slip-flow model for multi-component shale gas transport in organic nanopores

With the rapid development of shale gas resources, the accurate simulation of shale gas development process is becoming more and more important. Shale gas transport through nanopores of shale formation is the basic of shale gas development simulation. At present, the effect of impurities on methane transport through nanopores is neglected. In this paper, a novel model is presented for simulating multi-component shale gas transport through nanopores of shale formation. The effects of multi-component, slippage flow, and Knudsen diffusion are considered in the model. Results show that when the shale gas in nanopores is very thin, the Knudsen diffusion plays the dominant role over wide range of nanopore radius. While the effect of multi-component on Knudsen number and contribution degree can be neglected, both of the slippage flow rate and the Knudsen diffusion rate increase with increasing of CO2 content. Under medium pressure condition, there exists two turning points where the slippage flow and Knudsen diffusion take turns in charge of the shale gas transmission. Under high pressure condition, the slippage flow is the dominant factor over wide range of nanopore sizes. While the conductivities increase with decreasing methane content, the effect of multi-component on contribution degrees of slippage and Knudsen diffusion can be neglected.

Experiments, modeling and scaling-up of membrane reactors for hydrogen production via steam methane reforming

Steam methane reforming (SMR), which is endothermic and equilibrium-limited, is an important reaction in syngas production and in hydrogen generation for hydrogen economy. To improve SMR, a process intensification concept using membrane walled reactors is explored in detail here. The simultaneous removal of hydrogen shifts the equilibrium, allowing higher conversion to be realized than in traditional mode without product removal. The paper provides experimental data on kinetics using Ni/Al2O3 catalyst and kinetic models. The membrane permeability is also measured and fitted with Sievert’s law. Using these data, we develop three-dimensional models in the COMSOL Multiphysics platform which include momentum and energy balances, along with multicomponent diffusion effects. Using these detailed models, the paper proposes scale-up strategies. A monolith arrangement with provision for simultaneous heat supply and hydrogen removal is suggested and modeled in detail. The optimum geometric arrangement for the suggested design is examined, and recommendations are made for the proposed reactor design. The design providing the best effectiveness of membrane utilization has a surface area-to-reactor volume ratio of 255 m2/m3—which can be shown to be related to the product of Damkohler and Peclet numbers being close to unity, indicating that the hydrogen production rate matches to permeation.

Numerical solution of the parabolic multicomponent convection–diffusion mass transfer equations by a splitting method

ABSTRACTThe splitting method used in a previous study for the numerical solution of mass transfer equations in ternary systems is generalized to mixtures with n-components. The diffusion coefficients are considered constant. Theoretical results about the stability of the method are presented, as well as numerical simulations for mixtures with n = 4, 5, and 6. The numerical experiments confirmed the theoretical results and show good numerical performances. Moreover, multicomponent diffusion effects without an imposed concentration gradient are investigated for mixtures with n = 4, 5, and 6 components.

Multicomponent diffusion in aluminosilicate garnet: coupling effects due to charge compensation

ABSTRACTThree kinds of multicomponent diffusion effects, arising from three distinct physical mechanisms, are evident in stranded diffusion profiles at the rims of partially resorbed garnets from the contact aureole of the Makhavinekh Lake Pluton, northern Labrador. Profiles that display a subtle maximum in Ca concentration are explained by the prevailing ideal mean-field theory of multicomponent diffusion, but models implementing that theory cannot replicate inverted profiles for Li and internal maxima for Nd, Sm, and Eu. The anomalous profiles are quantitatively reproduced, however, by numerical simulations employing a model based on coupled movement of charge-compensating groups during diffusional transport of yttrium and the rare-earth elements (Y+REEs). An alkali-type charge-compensation mechanism for the heterovalent substitution of Y+REEs on dodecahedral sites in garnet produces direct charge coupling between Li+ and (Y+REE)3+ and leads to co-diffusion of Li+-(Y+REE)3+ pairs, with the result that Li profiles closely mimic those for Y+REEs. A menzerite-type charge-compensation mechanism produces indirect charge coupling among all Y+REE components, with the result that the fluxes of low-abundance REEs become partly dependent on the fluxes of Y+REEs present in higher abundance. These findings have implications for the robustness of Li profiles in garnet as monitors of fluid–rock interaction, for geochronology based on the Sm–Nd and Lu–Hf systems, and for future experimental attempts to quantify rates of diffusion in garnet.

Morphological instability of a solid sphere of dilute ternary alloy growing by diffusion from its melt

The diffusion-limited growth of an initially spherical particle of dilute ternary alloy in contact with its melt has been studied from a theoretical point of view and the effects of interface kinetics and multicomponent diffusion have been characterized on the development of a shape perturbation of the sphere. When both concentrations of the diffusing species are imposed in the far-field, the different radii related to the absolute and relative stability of the particle with respect to the development of spherical harmonics have been determined when a linear kinetics law is considered for the solid/liquid interface. The development of the shape fluctuations of the sphere has been also characterized when the flux of both species are set in the far-field.

Decontamination of VX from Silicone: Characterization of Multicomponent Diffusion Effects

A continuum model of the transport and reaction processes occurring during decontamination of the chemical warfare agent (CWA) [2-(diisopropylamino)ethyl]-O-ethyl methylphosphonothioate (VX) absorbed in a silicone elastomer using solutions of sodium hydroxide in water, methanol, and mixtures thereof is presented. This model is based on the Maxwell-Stefan formulation of multicomponent diffusion along with the Flory-Huggins model of thermodynamic equilibrium in the polymer. It was found that, as methanol from the decontaminant absorbs into the silicone, the diffusivity of VX increases, accelerating its flux from the polymer phase to the decontaminant liquid phase. This composition dependence of the diffusivity was accurately described by the Vignes equation. Although the decontamination kinetics were slower for the methanol-based decontaminant in a well-stirred liquid-phase reactor, the overall performance was superior compared to the aqueous-based decontaminant due to the enhanced extraction rate from the polymer. These findings highlight the need to consider extraction dynamics on equal footing with reaction kinetics when formulating decontaminants intended for use on absorbing polymer materials.

Chemical zonation in olivine-hosted melt inclusions

Significant zonation in major, minor, trace, and volatile elements has been documented in naturally glassy olivine-hosted melt inclusions from the Siqueiros Fracture Zone and the Galapagos Islands. Components with a higher concentration in the host olivine than in the melt (e.g., MgO, FeO, Cr2O3, and MnO) are depleted at the edges of the zoned melt inclusions relative to their centers, whereas except for CaO, H2O, and F, components with a lower concentration in the host olivine than in the melt (e.g., Al2O3, SiO2, Na2O, K2O, TiO2, S, and Cl) are enriched near the melt inclusion edges. This zonation is due to formation of an olivine-depleted boundary layer in the adjacent melt in response to cooling and crystallization of olivine on the walls of the melt inclusions, concurrent with diffusive propagation of the boundary layer toward the inclusion center. Concentration profiles of some components in the melt inclusions exhibit multicomponent diffusion effects such as uphill diffusion (CaO, FeO) or slowing of the diffusion of typically rapidly diffusing components (Na2O, K2O) by coupling to slow diffusing components such as SiO2 and Al2O3. Concentrations of H2O and F decrease toward the edges of some of the Siqueiros melt inclusions, suggesting either that these components have been lost from the inclusions into the host olivine late in their cooling histories and/or that these components are exhibiting multicomponent diffusion effects. A model has been developed of the time-dependent evolution of MgO concentration profiles in melt inclusions due to simultaneous depletion of MgO at the inclusion walls due to olivine growth and diffusion of MgO in the melt inclusions in response to this depletion. Observed concentration profiles were fit to this model to constrain their thermal histories. Cooling rates determined by a single-stage linear cooling model are 150–13,000 °C h−1 from the liquidus down to ~1,000 °C, consistent with previously determined cooling rates for basaltic glasses; compositional trends with melt inclusion size observed in the Siqueiros melt inclusions are described well by this simple single-stage linear cooling model. Despite the overall success of the modeling of MgO concentration profiles using a single-stage cooling history, MgO concentration profiles in some melt inclusions are better fit by a two-stage cooling history with a slower-cooling first stage followed by a faster-cooling second stage; the inferred total duration of cooling from the liquidus down to ~1,000 °C ranges from 40 s to just over 1 h. Based on our observations and models, compositions of zoned melt inclusions (even if measured at the centers of the inclusions) will typically have been diffusively fractionated relative to the initially trapped melt; for such inclusions, the initial composition cannot be simply reconstructed based on olivine-addition calculations, so caution should be exercised in application of such reconstructions to correct for post-entrapment crystallization of olivine on inclusion walls. Off-center analyses of a melt inclusion can also give results significantly fractionated relative to simple olivine crystallization. All melt inclusions from the Siqueiros and Galapagos sample suites exhibit zoning profiles, and this feature may be nearly universal in glassy, olivine-hosted inclusions. If so, zoning profiles in melt inclusions could be widely useful to constrain late-stage syneruptive processes and as natural diffusion experiments.

Transient evaporation of moving water droplets in steam–hydrogen–air environment

During a severe loss of coolant accident in a nuclear reactor, steam and hydrogen are produced by the oxidation of reactor core and get distributed in the containment. A water spray system is employed to cool the mixture as well as to enhance the mixing of the gases to avoid hydrogen accumulation. This paper presents two-phase numerical simulations of transient vaporization of a moving spherical water droplet. The numerical model considers the variation of thermo-physical properties in both liquid- and vapor-phases, as functions of temperature and species concentrations. Multi-component diffusion and surface tension effects are also considered. The model has been validated using experimental results available in literature for hydrocarbon fuel droplet evaporation. Validated model is used to study the evaporation characteristics of moving water droplets under conditions typically observed in nuclear reactor during a loss of coolant accident. The effects of ambient temperature and hydrogen concentration on the vaporization characteristics are studied thoroughly.

Two-phase modeling of evaporation characteristics of blended methanol–ethanol droplets

The paper presents a two-phase numerical model to simulate transient vaporization of a spherical two-component liquid fuel droplet. The model considers variation of thermo-physical properties in both liquid- and vapor-phases, as functions of temperature and species concentrations. Multi-component diffusion and surface tension effects are also considered. The model has been validated using the experimental data available in literature. The validated model is used to study the vaporization characteristics of both suspended and moving methanol–ethanol blended droplets in an atmospheric pressure environment. Relative strengths of forced convection and Marangoni convection are studied and compared for both suspended and moving droplets. Results in terms of streamlines, isotherms and isopleths at different time instants are reported and discussed. For low relative velocities, solutal Marangoni effects are seen to be important.

Propagation and stability characteristics of laminar lifted diffusion flame base

Numerical calculations of the flame propagation speed and the Damköhler number (Da) at laminar lifted flame base were carried out. The results are intended for further understanding the propagation and the Damköhler mechanisms for flame stabilization, with the former based on a tribrachial flame propagating against the local flow velocity and the latter based on the competition between the reaction time and local residence time of the peak reaction zone. Propane fuel without and with dilution (40% helium and argon, by volume) was used, while the reaction scheme adopted was the one-step irreversible Arrhenius kinetics (see Li et al., Combust. Flame 157 (2010) 1484–1495) which proved successful in predicting the flame lift-off height and effects of thermal expansion and multi-component diffusion. The results reported in this paper show that the flame base propagation speed is up to approximately four times of the one-dimensional stoichiometric flame speed of the fuels used, depending on where the propagation front is defined. These results are compared with previously published experimental and theoretical results from laminar and turbulent diffusion flames. It is found that the flame base propagation speed (Vp) increases in the downstream direction as a result of increasing jet velocity (Vo) under most flame conditions, providing a stabilizing mechanism. However, there exist conditions where Vp decreases while the flame stabilizes. The flame base Damköhler number (Da) always increases as the flame liftoff height increases (resulting from increasing jet velocity). Da is here defined as ratio of peak reaction rate of the reaction kernel (RR) to the flame stretch rate (k) determined at the intersection of the reaction kernel (approximately coinciding with the 2000K isotherm) and the stoichiometric contour. The value of Da appears to be of the order of 10−3 for the three fuels studied, and the increasing trend of Da with the lift-off height also helps to explain the flame stabilization.

“Reprint of Numerical simulation of multi-component mass transfer in rigid or circulating drops: Multi-component effects even in the presence of weak coupling”

Numerical simulation results of mass transfer to and from drops with applications to liquid–liquid extraction processes are considered. Multiple solute components (specifically 2 solute components) are assumed to be present in the drop. The system is described using the theory of multi-component mass transfer, in which a flux of one component can be coupled to a concentration gradient in the other. The nominal strength of this coupling is determined by the off-diagonal elements of a diffusivity matrix. Naively it might be thought that, if the off-diagonal matrix elements are small compared to the diagonal ones, then the influence of coupling between components is essentially negligible. It is shown however that this is not always the case. Particular focus is given to the case where one solute component has an imposed concentration difference between the drop interior and the drop surface, whilst the other solute has no such difference imposed. Mass transfer is still observed for the latter component, which is a clear indication of coupling due to multi-component diffusion effects. The mass fraction of the component with no imposed concentration difference evolves first by deviating from its initial value, but later returns back to this initial value. It is possible to place a bound on the extent of this deviation in terms of the elements of the diffusivity matrix and any concentration difference imposed on the other component. Circulation flow, if present within the drop, is found only to have a weak influence on the maximum extent of the aforementioned deviation. It has however a role in speeding up the rates of deviation and subsequent return of component mass fraction compared to a non-circulating rigid drop case. Circulation also determines the order in which individual pointwise locations in the drop experience this deviation and subsequent return: only points near the drop surface experience a rapid evolution in the absence of circulation, whereas points either near the surface or near the axis evolve rapidly in the presence of circulation.

Experimental investigation of characteristics of cavitation in gasoline

Cavitation processes in gasoline were experimentally investigated with an objective of gathering measurement data for developing an appropriate numerical model with an intention of simulating flows in automotive fuel pumps. An experimental setup was manufactured to examine bubble growth and collapse processes in gasoline under different circumstances. Bubbles were found to collapse at only a considerably higher pressure than the one they were produced at resulting in a hysteresis in the bubble volume - absolute pressure diagram. According to the results a time-dependent deterministic model might be developed for the contraction phase in spite of nucleation being a stochastic phenomenon. Investigating the response of the system to small disturbances the experienced characteristics were very similar to those of heat conduction and diffusion equations leading to the conclusion that size changes of bubbles seem to be controlled by the heat and mass transport processes undergoing in their vicinity and the multico mponent diffusion effects can be responsible for the observed hysteresis. The experimental results established a good starting point for numerical model development.

Numerical simulation of multi-component mass transfer in rigid or circulating drops: Multi-component effects even in the presence of weak coupling

Numerical simulation results of mass transfer to and from drops with applications to liquid–liquid extraction processes are considered. Multiple solute components (specifically 2 solute components) are assumed to be present in the drop. The system is described using the theory of multi-component mass transfer, in which a flux of one component can be coupled to a concentration gradient in the other. The nominal strength of this coupling is determined by the off-diagonal elements of a diffusivity matrix. Naively it might be thought that, if the off-diagonal matrix elements are small compared to the diagonal ones, then the influence of coupling between components is essentially negligible. It is shown however that this is not always the case. Particular focus is given to the case where one solute component has an imposed concentration difference between the drop interior and the drop surface, whilst the other solute has no such difference imposed. Mass transfer is still observed for the latter component, which is a clear indication of coupling due to multi-component diffusion effects. The mass fraction of the component with no imposed concentration difference evolves first by deviating from its initial value, but later returns back to this initial value. It is possible to place a bound on the extent of this deviation in terms of the elements of the diffusivity matrix and any concentration difference imposed on the other component. Circulation flow, if present within the drop, is found only to have a weak influence on the maximum extent of the aforementioned deviation. It has however a role in speeding up the rates of deviation and subsequent return of component mass fraction compared to a non-circulating rigid drop case. Circulation also determines the order in which individual pointwise locations in the drop experience this deviation and subsequent return: only points near the drop surface experience a rapid evolution in the absence of circulation, whereas points either near the surface or near the axis evolve rapidly in the presence of circulation.

The effect of multicomponent diffusion on supersonic flow of carbon dioxide past bodies

Different approaches are considered to the inclusion of multicomponent diffusion into numerical analysis of supersonic flow of carbon dioxide past blunt-nosed bodies. Calculation results are given, which illustrate the effect of diffusion processes on heat transfer to the surface of a space vehicle moving in the atmosphere of Mars.

The Soret effect in naturally propagating, premixed, lean, hydrogen–air flames

Comparatively little attention has been given to multicomponent diffusion effects in lean hydrogen–air flames, in spite of the importance of these flames in safety and their potential importance to future energy technologies. Prior direct numerical simulations either have considered only the mixture-averaged transport model, or have been limited to stabilized flames that do not exhibit the thermo-diffusive instability. The so-called full, multicomponent transport model with cross-diffusion is found to predict hotter, significantly faster flames with much faster extinction and division of cellular structures.