Tracer Diffusion Research Articles

Theory of tracer diffusion in concentrated hard-sphere suspensions

A phenomenological theory of diffusion and cross-diffusion of tracer particles in concentrated hard-sphere suspensions is developed. Expressions for the diffusion coefficients as functions of the host particle volume fraction are obtained up to the close-packing limit. In concentrated systems the tracer diffusivity decreases because of the reduced pore space available for diffusion. The tracer diffusivity can be modelled by a Stokes–Einstein equation with an effective viscosity that depends on the pore size. Tracer diffusion and segregation during sedimentation cease at a critical trapping volume fraction corresponding to a tracer glass transition. The tracer cross-diffusion coefficient, however, increases near the glass transition and diverges in the close-packed limit.

The theory of diffusion in a binary mixture of molecules coadsorbed on a two-dimensional lattice

The diffusion in the binary mixture of molecules coadsorbed on a square lattice is investigated by a theoretical approach and the Monte Carlo simulations. Using a lattice gas model I have derived a system of equations describing the diffusion of the molecules in the Fickian and Onsager representations. Also, I have obtained the analytical expressions for the Fickian diffusion coefficients. These expressions are derived taking into account the lateral interactions between the molecules and the interactions of the activated molecules in the saddle points of the lattice potential relief with their surroundings. The diffusion equations in the Fickian representation coincide with the corresponding classical counterparts, but the Onsager-like equations differ significantly from their standard lore – the cross terms are absent. It occures that the new transport coefficients describing the diffusion in the new Onsager representation are expressed in a rather nontrivial way via the phenomenological coefficients entering the classical equations. The Monte Carlo simulations have been used to test the correctness of the new expressions. There is a very good coincidence between the thermodynamic and kinetic data in the whole coverage region and in the wide range of the lateral interactions. The interactions substantially influence on the behavior of the thermodynamic quantities and the tracer and Fick diffusivities. These results demonstrate that the classical description of the molecule diffusion in the Onsager representation is not universal and may be not applied for some lattice gas systems.

Motional and Spin Dynamics of Individual Neutral Impurities in an Ultracold Gas

Recent studies on the dynamics of single, neutral impurities immersed in an ultracold gas are reviewed. This paradigmatic model system is realized by the controlled doping of single Caesium atoms into an ultracold Rubidium gas. Interaction between the impurity and the gas in both the motional and internal degrees of freedom is studied for a broad range of bath temperatures in the thermal and quantum‐degenerate regime. Tracing single‐atom diffusion it is found that, even for a granular bath, where the assumption of a continuous medium is not fulfilled, a modified Langevin equation yields excellent predictions for tracer diffusion. Numerical modeling of impurity dynamics in a three‐dimensional superfluid bath shows the emergence of a prethermalized state for intermediate times due to the existence of a superfluid critical momentum, while for lower dimensions the effect of thermal phonons dominates and obstructs the formation of such nonthermal states. Finally, unleashing the quasi‐spin degree of freedom, the authors observe and control spin‐exchange dynamics between individual impurities and the bath. Moreover, a regime of sympathetic impurity cooling is realized, where the internal‐state coherence of the impurity is preserved. In the future, control over the motional and spin‐degree of freedom will enable using individual impurities as thermalized, localized, minimally invasive quantum probes for a quantum fluid.

Anomalous tracer diffusion in the presence of extended obstacles on a triangular lattice

Proteins diffuse to their sites of action within cells in a crowded, strongly interacting environment of nucleic acids and other macromolecules. An interesting question is how the highly crowded environment of biological cells affects the dynamic properties of passively diffusing particles. The Lorentz model is a generic model covering many of the aspects of transport in a heterogeneous environment. We investigate biologically relevant situations of immobile obstacles of various shapes and sizes. The Monte Carlo simulations for the diffusion of a tracer particle are carried out on a two-dimensional triangular lattice. Obstacles are represented by non-overlapping lattice shapes that are randomly placed on the lattice. Our simulation results indicate that the mean-square displacement displays anomalous transport for all obstacle shapes, which extends to infinite times at the corresponding percolation thresholds. In the vicinity of this critical density the diffusion coefficient vanishes according to a power law, with the same conductivity exponent for all obstacle shapes. At the fixed density of obstacles, we observe that the diffusion coefficient is higher for the smaller obstacles if the object size is defined as the highest projection of the object on one of the six directions on the triangular lattice. The dynamic exponent, which describes the anomalous transport at the critical density, is the same for all the obstacle shapes. Here we show that the values of critical exponents estimated for all disordered environments do not depend on the microscopic details of the present model, such as obstacle shape, and agree with the predicted values for the underlying percolation problem. We also provide the evidence for a divergent non-Gaussian parameter close to the percolation transition for all obstacle shapes.

Models of infiltration into homogeneous and fractal porous media with localized sources.

We study a random-walk infiltration (RWI) model, in homogeneous and in fractal media, with small localized sources at their boundaries. In this model, particles released at a source, maintained at a constant density value, execute unbiased random walks over a lattice; a model that represents solute infiltration by diffusion into a medium in contact with a reservoir of fixed concentration. A scaling approach shows that the infiltrated length, area, or volume evolves in time as the number of distinct sites visited by a single random walker in the same medium. This is consistent with numerical simulations of the lattice model and exact and numerical solutions of the corresponding diffusion equation. In a Sierpinski carpet, the infiltrated area is expected to evolve as t^{D_{F}/D_{W}} (Alexander-Orbach relation), where D_{F} is the fractal dimension of the medium and D_{W} is the random-walk dimension; the numerical integration of the diffusion equation supports this result with very good accuracy and improves results of lattice random-walk simulations. In a Menger sponge in which D_{F}>D_{W} (i.e., a fractal with a dimension close to 3), a linear time increase of the infiltrated volume is theoretically predicted and confirmed numerically. Thus, no evidence of fractality can be observed in measurements of infiltrated volumes or masses in media where random walks are not recurrent, although the tracer diffusion is anomalous. We compare our findings with results for a fluid infiltration model in which the pressure head is constant at the source and the front displacement is driven by the local gradient of that head. Exact solutions in two and three dimensions and numerical results in a carpet show that this type of fluid infiltration is in the same universality class of RWI, with an equivalence between the head and the particle concentration. These results set a relation between different infiltration processes with localized sources and the recurrence properties of random walks in the same media.

On diffusion behaviors in face centered cubic phase of Al-Co-Cr-Fe-Ni-Ti high-entropy superalloys

Owning the excellent high temperature properties, low cost and density, Al-Co-Cr-Fe-Ni-Ti high-entropy superalloys (HESAs) represent a potential substitute for Ni-based superalloys. In this paper, the composition-dependent interdiffusivity matrices of face centered cubic (fcc) Al-Co-Cr-Fe-Ni-Ti HESAs at 1473 K were first determined via a combination of diffusion multiple technique and HitDIC software based on the numerical inverse method. The correlations between the main interdiffusivities and the components suggest that alloying elements play great impact on diffusion in HESAs. After that, comprehensive comparisons of the interdiffusivities and tracer diffusivities in present fcc HESAs with the literature data in fcc-based pure elements, lower-order alloys and traditional high-entropy alloys were conducted. The results indicate that the sluggish diffusion effect exists for only some of the components in the present HESAs. Moreover, comparisons of the diffusion coefficients between the HESAs and traditional Ni-based superalloys with refractory elements show that the interdiffusivities in the present HESAs are lower than the Ni-based superalloys with most refractory elements, but higher than those with Ir, Re and Os. Furthermore, it is also found that refractory elements need to be added in order to further improve the creep resistance of the HESAs.

Airflow analysis of Pyeongtaek St Mary's Hospital during hospitalization of the first Middle East respiratory syndrome patient in Korea.

Middle East respiratory syndrome (MERS) is known to be transmitted through close contact. However, epidemiological surveys of MERS in Korea indicated that some secondary patients were infected without close contact. Therefore, the possibility of other transmission routes must be identified. In this study, the possibility of MERS spreading through airflow was investigated on the eighth floor of Pyeongtaek St Mary's Hospital. Computational fluid dynamics was used to analyse the indoor airflow and passive tracer diffusion during the index patient's stay. Six cases were simulated for different outdoor wind directions and indoor mechanical ventilation operations. When a passive tracer was released in ward 8104, where the index patient was hospitalized, the passive tracer spread through the indoor airflow, which was created by the outdoor airflow. Ward 8109, which had the largest number of infected cases and was far distant from ward 8104, showed passive tracer concentration in all cases. This result indicates that MERS may have spread through airflow. The study results do not imply that the infection pathway of MERS is airborne. However, the results show the possibility of MERS spreading through airflow in specific environments such as poor ventilation environments.

Diffusion Rates of Components in Metal-Silicides Depending on Atomic Number of Refractory Metal Component

Interdiffusion studies conducted in group IVB, VB and VIB metal-silicon systems are discussed in detail to show a pattern in the change of diffusion coefficients with the change in atomic number of the refractory metal (M) component. MSi2and M5Si3phases are considered for these discussions. It is shown that integrated diffusion coefficients increase with the increase in atomic number of the refractory component when the data are plotted with respect to the melting point normalized annealing temperature. This indicates the increase in overall defect concentration facilitating the diffusion of components. This is found to be true in both the phases. Additionally, the estimated ratios of tracer diffusion coefficients indicate the change in concentration of antisite defects in certain manner with the change in atomic number of the refractory components.

Fractional Brownian motion in a finite interval: correlations effect depletion or accretion zones of particles near boundaries

Fractional Brownian motion (FBM) is a Gaussian stochastic process with stationary, long-time correlated increments and is frequently used to model anomalous diffusion processes. We study numerically FBM confined to a finite interval with reflecting boundary conditions. The probability density function of this reflected FBM at long times converges to a stationary distribution showing distinct deviations from the fully flat distribution of amplitude 1/L in an interval of length L found for reflected normal Brownian motion. While for superdiffusion, corresponding to a mean squared displacement (MSD) with 1 < α < 2, the probability density function is lowered in the centre of the interval and rises towards the boundaries, for subdiffusion (0 < α < 1) this behaviour is reversed and the particle density is depleted close to the boundaries. The MSD in these cases at long times converges to a stationary value, which is, remarkably, monotonically increasing with the anomalous diffusion exponent α. Our a priori surprising results may have interesting consequences for the application of FBM for processes such as molecule or tracer diffusion in the confines of living biological cells or organelles, or other viscoelastic environments such as dense liquids in microfluidic chambers.

Cation Diffusion in Compacted Clay: A Pore-Scale View.

Cation diffusion through compacted clays is of great interest due to its potential for buffer materials for waste disposal. The importance of the electrokinetic effect on cationic tracer diffusion is investigated by using pore-scale simulations to consider the influence from the electrokinetic properties and topology of clays. It is indicated that the normalized volume charge density has a significant impact on the cationic diffusion. In clays with a large normalized volume charge density, the electrical double layer has the major impact on cationic diffusion. When the ion strength of the pore solution is constant, the flux from the electromigration term can be negligible. However, once an ion strength gradient is added, the electromigration process should be considered carefully due to its non-negligible role to balance the alteration of total flux. The present study could help improve the understanding of the transport mechanism of simple cationic tracers in compacted clays.

Oxygen diffusion in amorphous and partially crystalline gallium oxide.

Oxygen transport in amorphous (a-GaO1.5) and partially crystalline (a/c-GaO1.5) gallium oxide was studied by means of 18O/16O isotope exchange experiments and time-of-flight secondary ion mass spectrometry (ToF-SIMS). Thin films of a-GaO1.5 were deposited by pulsed laser deposition (PLD) on alumina substrates at room temperature in an oxygen atmosphere. Oxygen tracer diffusion coefficients D* and oxygen surface exchange coefficients k* were determined as a function of temperature, 300 ≤ T/°C ≤ 370, and as a function of oxygen partial pressure, 2 ≤ p(O2)/mbar ≤ 500 at a temperature of T = 330 °C. The activation energy of oxygen tracer diffusion in amorphous gallium oxide was found to be EA = 0.8 eV. In addition, the time-temperature-transformation (TTT) diagram of crystallisation of amorphous gallium oxide was determined.

Demystifying the sluggish diffusion effect in high entropy alloys

Interdiffusion studies in Co-Cr-Fe-Mn-Ni, Co-Fe-Mn-Ni, Co-Cr-Fe-Ni, and Co-Cr-Mn-Ni, as well as a reevaluation of the previous results obtained for Al-Co-Cr-Fe-Ni, were conducted. In the experimental part, diffusion couples were annealed at four different temperatures: 1230, 1270, 1310 and 1350 K for each system. Then, the results were evaluated with use of the optimization-based technique, combined with the Miedema's thermodynamic description, what allowed obtaining of tracer diffusion coefficients for all elements in all considered systems. The correctness of the applied approach was tested on the example of Co-Cr-Fe-Mn-Ni system, showing very good agreement of determined tracer diffusivities with the values obtained by other authors. Obtained values of diffusivities were compared with the available data for a number of conventional binary and ternary systems. No signs of diffusion retardation were observed in the absolute temperature scale. In the case of temperature scale normalized with respect to the melting point, an abnormal behavior, previously attributed to the HEAs' sluggish diffusion effect was observed. However, it occurred only for alloys with prominent manganese content and was completely independent of the number of components, being just as likely to occur in binary systems as in HEAs. Therefore, the alleged sluggishness of diffusion in HEAs should be treated just as a result of specific compositions of the previously studied alloys and cannot be generalized for all high entropy systems.

Concentration-dependent atomic mobilities in FCC CoCrFeMnNi high-entropy alloys

The diffusion kinetics in a CoCrFeMnNi high entropy alloy is investigated by a combined radiotracer–interdiffusion experiment applied to a pseudo-binary Co15Cr20Fe20Mn20Ni25/Co25Cr20Fe20Mn20Ni15 couple. As a result, the composition-dependent tracer diffusion coefficients of Co, Cr, Fe and Mn are determined. The elements are characterized by significantly different diffusion rates, with Mn being the fastest element and Co being the slowest one. The elements having originally equiatomic concentration through the diffusion couple are found to reveal up-hill diffusion, especially Cr and Mn. The atomic mobility of Co seems to follow a S-shaped concentration dependence along the diffusion path. The experimentally measured kinetic data are checked against the existing CALPHAD-type databases.In order to ensure a consistent treatment of tracer and chemical diffusion a generalized symmetrized continuum approach for multi-component interdiffusion is proposed. Both, tracer and chemical diffusion concentration profiles are simulated and compared to the measurements. By using the measured tracer diffusion coefficients the chemical profiles can be described, almost perfectly, including up-hill diffusion.

Reconsidering the Analysis of Refractive-Index-Matched Polymer/Polymer/Solvent Tracer Diffusion Experiments

A method for analyzing quasielastic light-scattering (QELS) data from compatible polymer–polymer–solvent systems, in which the refractive index increment for one polymer species relative to the solvent is close to zero while the other is present in dilute quantities, is explained. Specifically, the technique makes use of the fact that for such systems the scattered intensity at wave vector q can be equally well expressed in terms of the tracer polymer’s molecular-weight distribution or in terms of a distribution of decay rates obtained from the inverse Laplace transform of the autocorrelation function. Appropriate integrations over these two distributions result in one-to-one mappings of individual tracer molecular weights in the tracer’s molecular-weight distribution to individual decay rates (and thus, tracer diffusivities) in the decay rate/tracer diffusivity distribution. Thus polydispersity in the molecular-weight distribution of the tracer polymer becomes advantageous. Employing this technique, a s...

The scale invariance criterion for geophysical fluids

Abstract The scale invariance of geophysical fluids is investigated in terms of a scale invariance criterion. It was developed by Schaefer-Rolffs et al. (2015) based on the implication that each scale invariant subrange shall have its own criterion. Two particular cases are considered, namely the synoptic scales where the Coriolis term is significant, and the smaller scales where the anelastic approximation is valid. The first case is characterized by a constant enstrophy cascade rather than an energy cascade, leading to a significant restatement of the invariance criterion. In the second case, small-scale fluctuations of density, pressure, and temperature are taken into account that have to be included into the known scale invariance criterion as specific scaling relations. It is further shown that the scaling of Billant and Chomaz (2001) is a special case of the present anelastic scaling relations. In both cases, the respective scale invariance criteria are applied to the turbulent nonlinear harmonic, the k -model, and the passive tracer diffusion. It is demonstrated that, in analogy to previous work, only the dynamic approaches are scale invariant. In addition, it is shown that for the anelastic approximation the scaling ratio of stratified turbulence has to be applied to the vertical length scale instead of the vertical mixing length.

Atomistic modelling of the diffusion of C in Fe[sbnd]Cr alloys

The diffusion of C in FeCr solid solutions is modelled and compared to experimental data. A set of binding energies and migration barriers for C diffusion in different local chemical environments are first calculated using density functional theory. A pair interaction model is developed in order to reproduce these data and predict the migration barriers in other environments. The diffusion model is then implemented in a kinetic Monte Carlo method to simulate tracer diffusion experiments, using a standard procedure, and internal friction experiments, using a novel method. Simulations of internal friction show a unique Snoek peak in the whole concentration range, between pure iron and pure chromium. The average migration barrier for C diffusion in FeCr alloys is found to increase progressively with the Cr concentration, with a small rate below 6 %Cr. In Cr-rich alloys, the effective migration barrier for C diffusion is found to be larger in tracer diffusion than in the internal friction simulations. We conclude that the effective migration barrier extracted from tracer diffusion is closely related to trapping effects of C atoms in Fe-rich local environments, whereas the migration barrier associated with internal friction is mainly controlled by the migration barriers of the most probable configurations, as it is clearly shown in the Cr-rich domain.

Active microrheology in corrugated channels.

We analyze the dynamics of a tracer particle embedded in a bath of hard spheres confined in a channel of varying section. By means of Brownian dynamics simulations, we apply a constant force on the tracer particle and discuss the dependence of its mobility on the relative magnitude of the external force with respect to the entropic force induced by the confinement. A simple theoretical one-dimensional model is also derived, where the contribution from particle-particle and particle-wall interactions is taken from simulations with no external force. Our results show that the mobility of the tracer is strongly affected by the confinement. The tracer velocity in the force direction has a maximum close to the neck of the channel, in agreement with the theory for small forces. Upon increasing the external force, the tracer is effectively confined to the central part of the channel and the velocity modulation decreases, which cannot be reproduced by the theory. This deviation marks the regime of validity of linear response. Surprisingly, when the channel section is not constant, the effective friction coefficient is reduced as compared to the case of a plane channel. The transversal velocity, which cannot be studied with our model, follows qualitatively the derivative of the channel section, in agreement with previous theoretical calculations for the tracer diffusivity in equilibrium.

Diffusion and its Application in NiMnGa Alloys

Heusler NiMnGa alloys are often categorized as ferromagnetic shape memory alloys or magnetocaloric materials, which are important for both practical applications and fundamental research. The NiMnGa alloys undergo a series of diffusion and diffusionless transformation from high temperature to low temperature. Among these transformation, martensitic transformation from austenitic phase to martensitic phase is critical in determining the properties of the alloys. Although martensitic transformation is considered diffusionless, diffusion also has important applications in the research of NiMnGa alloysDiffusion couples along with equilibrium alloys have been used to determine the ternary phase diagrams in NiMnGa alloys. Phase diagrams are important in selecting NiMnGa alloys, in particular two-phase NiMnGa alloys for practical applications. Furthermore, the diffusion couples effectively assist in the determination of compositions that exhibit martensitic transformation temperature near room temperature. Diffusion coefficients have been assessed for NiMnGa alloys. Tracer diffusivity of Ni, Mn and Ga was reported in a wide temperature range and followed Arrhenius behavior. Two different activation energies were obtained, corresponding to B2 and L21 crystal structure, respectively. Interdiffusion coefficients for NiMnGa alloys with B2 crystal structure are measured, which showed that Ni diffuses the fastest, followed by Mn then Ga. The diffusion coefficients provide useful information for fabricating NiMnGa alloys through diffusional process.A combinatorial approach involving diffusion couples and advance characterization has been developed to investigate the mechanical properties, microstructure and crystallography of NiMnGa alloys rapidly and systematically over a large compositional range. The composition-dependent modulus and hardness for NiMnGa alloys was extracted from the diffusion couples with the help of nanoindentation. Martensitic phases with non-modulated and various modulated crystal structures, and austenitic phase were identified in the interdiffusion zones by transmission electron microscopy. The results demonstrate the capability of using diffusion couples to speed up the discovery of new NiMnGa alloys or other similar alloys showing martensitic transformation.

Monte Carlo Simulation of Correlation Effects in a Random SC Alloy via Interstitialcy Mechanisms

In this paper some recent progress in the area of Monte Carlo simulation of diffusion via the interstitialcy mechanism in a randomly ordered binary alloy is reviewed. Topics discussed include the calculation of tracer correlation factorsfA and fBas a function of composition and jump frequency ratiowA/wBand interstitialcy correlation factors fI; which play a crucial role in the interpretation of ion-conductivity data. The percolation behavior of fI when wA ≪ wB is analysed in detail and limits of the tracer diffusivity ratios bD A/bD B for alloy compositions below thepercolation threshold are presented. Allowance for non-collinear jumps (partly) replacing concurrent collinear site exchanges leads to a reduction of diffusion correlation effects.This goes along with a shift of the diffusion percolation threshold to lower concentrations of the (more) mobile component B. Even stronger changes of mass and charge transport compared to an exclusively collinear interstitialcy scheme are observed for additional contributions of direct interstitial jumps. It is remarkable that for both extensions of interstitialcy-mediated diffusion the Haven ratio appears to be greater than unity in certain compositionranges poor in B.

Flux Correction and Overturning Stability: Insights from a Dynamical Box Model

AbstractA recent paper suggested that the global climate models used to project future climate changes may significantly overestimate the stability of the Atlantic meridional overturning circulation under anthropogenic global warming. It further asserted that “flux adjusting” the models (adding offsets to heat and freshwater fluxes to reproduce the observed density field) may reduce model stability. However, temperature, salinity, and density fields in climate models likely deviate from observations because of biases in model physics as well as inaccuracies in fluxes. In such cases it is unclear whether adjusting the fluxes to produce a more realistic density field will result in a model with more realistic stability properties, as flux correction may be compensating for other inaccuracies in model formulation. We investigate this question using a simplified dynamical box model, in which we can flux correct one version of the model to match density gradients within another version of the model. We show that flux adjustment can realistically compensate for biases in stability associated with some processes, such as uncertainty in the value of the vertical diffusivity, but not other processes, such as inaccurate simulation of the relationship between density structure and overturning or the isopycnal tracer diffusivity coefficient. An ability to compensate for biases when the overturning shuts off does not imply an ability to compensate for biases in when it reestablishes itself, and vice versa.