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1
Itto, Yuichi. "Entropy production rate of diffusivity fluctuations under diffusing diffusivity equation." Journal of Physics: Conference Series 1391 (November 2019): 012054. http://dx.doi.org/10.1088/1742-6596/1391/1/012054.
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Jain, Rohit, and K. L. Sebastian. "Diffusing diffusivity: Rotational diffusion in two and three dimensions." Journal of Chemical Physics 146, no. 21 (June 1, 2017): 214102. http://dx.doi.org/10.1063/1.4984085.
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Sposini, Vittoria, Aleksei Chechkin, and Ralf Metzler. "First passage statistics for diffusing diffusivity." Journal of Physics A: Mathematical and Theoretical 52, no. 4 (December 28, 2018): 04LT01. http://dx.doi.org/10.1088/1751-8121/aaf6ff.
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Cheung, S. C. H. "Methods to measure apparent diffusion coefficients in compacted bentonite clays and data interpretation." Canadian Journal of Civil Engineering 16, no. 4 (August 1, 1989): 434–43. http://dx.doi.org/10.1139/l89-073.
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The methods used to determine apparent diffusion coefficients and the appropriate parameters for modelling diffusion through compacted bentonite–water systems are assessed and discussed. The measured apparent diffusion coefficient can vary between methods. The discrepancies are shown to be due to heterogeneous diffusivities arising from the proximity of the surface of clay particles. Two different diffusivity pathways are identified and the diffusive flux is shown to be dictated by the charge of diffusing species, diffusion time, and soil fabric. Key words: apparent diffusion coefficient, methods, compacted bentonite, heterogeneous diffusion, parameters, pathways.
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Lawley, Sean D., and Christopher E. Miles. "Diffusive Search for Diffusing Targets with Fluctuating Diffusivity and Gating." Journal of Nonlinear Science 29, no. 6 (July 10, 2019): 2955–85. http://dx.doi.org/10.1007/s00332-019-09564-1.
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Singh, Rohit R., Ashok S. Sangani, Susan Daniel, and Donald L. Koch. "The combined hydrodynamic and thermodynamic effects of immobilized proteins on the diffusion of mobile transmembrane proteins." Journal of Fluid Mechanics 877 (August 27, 2019): 648–81. http://dx.doi.org/10.1017/jfm.2019.592.
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The plasma membranes of cells are thin viscous sheets in which some transmembrane proteins have two-dimensional mobility and some are immobilized. Previous studies have shown that immobile proteins retard the short-time diffusivity of mobile particles through hydrodynamic interactions and that steric effects of immobile proteins reduce the long-time diffusivity in a model that neglects hydrodynamic interactions. We present a rigorous derivation of the long-time diffusivity of a single mobile protein interacting hydrodynamically and thermodynamically with an array of immobile proteins subject to periodic boundary conditions. This method is based on a finite element method (FEM) solution of the probability density of the mobile protein diffusing with a position-dependent mobility determined through a multipole solution of Stokes equations. The simulated long-time diffusivity in square arrays decreases as the spacing in the array approaches the particle size in a manner consistent with a lubrication analysis. In random arrays, steric effects lead to a percolation threshold volume fraction above which long-time diffusion is arrested. The FEM/multipole approach is used to compute the long-time diffusivity far away from this threshold. An approximate analysis of mobile protein diffusion through a network of pores connected by bonds with resistances determined by the FEM/multipole calculations is then used to explore higher immobile area fractions and to evaluate the finite simulation cell size scaling behaviour of diffusion near the percolation threshold. Surprisingly, the ratio of the long-time diffusivity to the spatially averaged short-time diffusivity in these two-dimensional fixed arrays is higher in the presence of hydrodynamic interactions than in their absence. Finally, the implications of this work are discussed, including the possibility of using the methods developed here to investigate more complex diffusive phenomena observed in cell membranes.
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Kissinger, G., J. Dabrowski, Andreas Sattler, Timo Müller, and Wilfried von Ammon. "Two Paths of Oxide Precipitate Nucleation in Silicon." Solid State Phenomena 131-133 (October 2007): 293–302. http://dx.doi.org/10.4028/www.scientific.net/ssp.131-133.293.
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The coherent agglomeration of interstitial oxygen into single-plane and double-plane plates can explain the two peaks in the M-shaped nucleation curves in Czochralski silicon. The density of nucleation sites for the double-plane plates corresponds to the VO2 concentration. Ab initio calculations have shown that the agglomeration of oxygen atoms in single-plane and doubleplane plates is energetically favorable. These plates are under compressive strain. VO2 agglomeration plays only a minor role for modeling the M-shaped nucleation curves because of prior homogenization treatments. It is of much higher impact if as-grown wafers are subjected to nucleation anneals because of the higher vacancy concentration which was frozen in during crystal cooling. This results in higher nucleation rates at higher temperatures. Because the oxygen diffusivity below 700 °C is important for the nucleation rate and many controversial results about the diffusivity in this temperature range were published, we have analyzed the data from literature. We have demonstrated that the effective diffusivity of oxygen at temperatures below 700 °C which corresponds to the quasi equilibrium dimer concentration is very similar to the extrapolation from oxygen diffusivity at high temperature. The high effective diffusivities from out-diffusion and precipitation experiments, and the somewhat lower effective diffusivities from dislocation locking experiments are the result of an ongoing formation of fast diffusing dimers because the equilibrium is disturbed as the result of the strongly increasing difference in the diffusion length between interstitial oxygen and the fast diffusing dimer with decreasing temperature.
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Leaist, Derek G. "Coupled diffusion of butanol solubilized in aqueous sodium dodecylsulfate micelles." Canadian Journal of Chemistry 68, no. 1 (January 1, 1990): 33–35. http://dx.doi.org/10.1139/v90-008.
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Ternary interdiffusion coefficients have been measured for ten compositions of the system sodium dodecylsulfate (NaDS) + 1-butanol (BuOH) + water at 25 °C. The diffusivity of BuOH in this system is lower than in pure water because about one half of the alcohol is solubilized in the slowly-diffusing NaDS micelles. Yet, surprisingly, diffusion of the NaDS component transports only minor amounts of BuOH. Diffusion of the BuOH component, however, produces a substantial coupled flow of NaDS. Although added BuOH increases the solution viscosity and the size of the micelles, the diffusivity of the NaDS component does not change significantly. The Harned restricted diffusion method for the determination of electrolyte diffusivities is extended to electrolyte + nonelectrolyte solutes. Keywords: micelles, ionic; solubilization; diffusion, coupled.
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De Leo, Cinzia, Domenica Paoletti, and Dario Ambrosini. "Effect of noise on measurements of diffusivity in transparent liquid mixtures by digital speckle photography." European Physical Journal Applied Physics 82, no. 3 (June 2018): 30501. http://dx.doi.org/10.1051/epjap/2018180115.
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Interfacing two liquid mixtures in a diffusion cell induces noise in the initial state of the diffusing system, which produces a gap between the diffusion boundary and the ideally boundary assumed in the theory. Measured diffusivity values systematically drift with time and they are often corrected by using a linear shift of the zero-time of the process after sufficiently long time when the system reaches the free one-dimensional diffusion regime. In data analysis methods which involve optical correlation between pairs of successive digital images of the cell, it is not easy to establish how long the transient lasts. We show that when the initial perturbation between solution and solvent relaxes slowly toward the diffusive regime no simple zero-time correction can be applied.
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Nakashima, Y. "Self- diffusion of H2O in stevensite gel: effects of temperature and clay fraction." Clay Minerals 37, no. 1 (March 2002): 83–91. http://dx.doi.org/10.1180/0009855023710019.
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AbstractSelf-diffusion coefficients of water molecules (1H2O) in Na-stevensite gel were measured by pulsed-gradient spin-echo (PGSE) proton nuclear magnetic resonance (NMR). The effects of clay fraction (0.00 37.7 wt.%) and temperature (20.0 60.3°C) were studied. The results show: (1) phenomenologically, the H2O self-diffusivity in the clay gel, D, is expressed by D/D0 = exp( 0.0198w) where D0 is the H2O self-diffusivity in bulk water of the temperature and wis the clay weight fraction (wt.%). (2) The activation energy of the diffusivity in the stevensite gel is nearly equal to that in bulk water. Thus, the normalized diffusivity, D/D0, obeys a temperature-independent master curve. (3) The exponential dependence of D/D0 on wfor w <25 wt.% (≈ 12 vol.%) can be explained by a random walk model, in which unbound H2O molecules diffuse in the geometrically tortuous pore structure of randomly scattered clay mineral grains. (4) The measured diffusivity can also be explained by a model of unbound H2O diffusing in a polymer network with a specific meshsize or characteristic interval of the crosslinkage.
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Voronkov, Vladimir V., and Robert Falster. "Fast and Slow Vacancies in Silicon." Solid State Phenomena 205-206 (October 2013): 157–62. http://dx.doi.org/10.4028/www.scientific.net/ssp.205-206.157.
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Vacancies (and probably also self-interstitials) in silicon appear to exist in several forms (atomic configurations) some of them being fast diffusers and other slow diffusers. The data on enhanced self-diffusivity under proton irradiation, on vacancy and oxide precipitate profiles installed by Rapid Thermal Annealing, and on the self-diffusivity under equilibrium conditions suggest that there are at least two kinds of vacancy: 1) Vw- a fast-diffusing localized vacancy manifested in electron irradiated samples (Watkins vacancy), 2) Vs- a slow-diffusing extended vacancy manifested under hot proton irradiation. In RTA experiments, these two species behave as one equilibrated subsystem of a moderate effective diffusivity intermediate between those of Vwand Vs. There is also strong evidence in favor of a third kind of vacancy: Vfa fast extended species, which controls the grown-in voids in silicon crystals.
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Cattaneo, F., and S. M. Tobias. "On the measurement of turbulent magnetic diffusivities: the three-dimensional case." Journal of Fluid Mechanics 735 (October 24, 2013): 457–72. http://dx.doi.org/10.1017/jfm.2013.506.
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AbstractIt has been shown that it is possible to measure the turbulent diffusivity of a magnetic field by a method involving oscillatory sources. So far the method has only been tried in the special case of two-dimensional fields and flows. Here we extend the method to three dimensions and consider the case where the flow is thermally driven convection in a large-aspect-ratio domain. We demonstrate that if the diffusing field is horizontal the method is successful even if the underlying flow can sustain dynamo action. We show that the resulting turbulent diffusivity is comparable with, although not exactly the same as, that of a passive scalar. We were not able to measure unambiguously the diffusivity if the diffusing field is vertical, but argue that such a measurement is possible if enough resources are utilized on the problem.
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Čížek, Jakub, František Lukáč, Marián Vlček, Ivan Procházka, Franziska Traeger, Detlef Rogalla, and Hans Werner Becker. "Diffusivity of Hydrogen in ZnO Single Crystal." Defect and Diffusion Forum 326-328 (April 2012): 459–64. http://dx.doi.org/10.4028/www.scientific.net/ddf.326-328.459.
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Hydrogen diffusivity in ZnO (0001) single crystal was investigated using electrical resistometry and nuclear reaction analysis (NRA). ZnO crystals were covered with a thin Pd over-layer and electrochemically charged with hydrogen. The net concentration of hydrogen determined by NRA was found to be in a reasonable agreement with the value estimated from the transported charge using the Faradays law. The hydrogen diffusion coefficient in ZnO was estimated from in-situ electrical resistivity measurements. Moreover, NRA investigations revealed existence of a subsurface layer with very high concentration of hydrogen (up to 40 at.%). Typical surface modification observed on hydrogen loaded crystal by light microscope indicates hydrogen-induced plastic deformation realized by a slip in the c-direction. Open-volume defects introduced by hydrogen-induced plastic deformation trap diffusing hydrogen and cause an enhancement of hydrogen concentration in the deformed subsurface layer.
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Dong, Hui Long, Bo Yu Zheng, and Fei Fan Chen. "Peak Diffusing Measurement Method for Estimating Thermal Diffusivity of Thin Films." Advanced Materials Research 1035 (October 2014): 166–72. http://dx.doi.org/10.4028/www.scientific.net/amr.1035.166.
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A novel peak diffusing measurement method is reported. In this method, a pulsed Gaussian heat source is focused on the material’s surface, and a thermal camera is utilized for detecting the temperature evolution. Specially, the peak temperature timetmaxat different distance from the heat source center is extracted using the Singular Spectrum Analysis (SSA). Thermal diffusivity is then calculated by fitting multiple sets of extractedtmaxinto the derived regression equation. The advantage of this method is that it does not require the high precision time synchronization between the excitation source and detector. Also, the calculation process is very simple, which achieves an efficient in situ measurement of the thermal diffusivity. The measured radial thermal diffusivity of samples prepared from Ti and Ni is in good agreement with the reference data with a 1.8% and a 3.9% error bound.
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Beke, Dezső L., A. Lakatos, G. Erdélyi, A. Makovecz, G. A. Langer, Lajos Daróczi, K. Vad, and A. Csik. "Investigation of Grain Boundary Diffusion in Thin Films by SNMS Technique." Defect and Diffusion Forum 312-315 (April 2011): 1208–15. http://dx.doi.org/10.4028/www.scientific.net/ddf.312-315.1208.
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It was shown more recently in our Laboratory [1,2,3] that having a substrate/diffusant/thin-film/cap-layer structure (the thin film was typically several 10 nm thick, with the same order of magnitude of grain size; the refractory metal cap layer was used just to avoid the oxidation), first the diffusant atoms migrated very fast across the thin film and segregated at the film/cap-layer interface. The accumulated atoms at the film/cap layer interface form a secondary diffusion reservoir and atoms diffuse back to the layer. Later on, the thin film was gradually filled up with the diffusing atoms and composition depth profiles, determined by Secondary Neutral Mass Spectroscopy (SNMS), showed a maximum at the cap layer-thin film interface. The accumulated atoms at this interface formed a secondary diffusion reservoir and atoms diffused back to the layer. These observations can be interpreted supposing a bimodal grain boundary structure with different (fast and low) diffusivities. The observed grain boundary diffusion phenomena can be classified as C-type diffusion. The appearance of the peak observed at the cap layer interface can be used as a tool to determine the grain boundary diffusivity along the fast boundaries. Because the fast boundaries were saturated in the first stage of the process, this back-diffusion took place along the low-diffusivity boundaries only. Thus the SNMS depth-profiling is a good method to determine grain boundary diffusivities in a bimodal structure. In addition, from the overall impurity content inside the film the segregation can also be estimated, if the bulk solubility is low and the GB density is known. Numerical simulations of C-type GB diffusion in thin films with a bimodal structure confirmed that the interpretation of the result depicted above is reasonable [4]. In order to estimate roughly the GB diffusion data we determined the fast diffusivity using the first appearance method. The lower diffusivity was determined from the time evolution of the broadening of the diffusant/thin film interface. In addition both (slow and fast) diffusivities were also estimated from fitting numerical solutions obtained in [4] too.
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Feisel, Yves, Jonathan M. Castro, and Donald B. Dingwell. "Diffusion of F and Cl in dry rhyodacitic melt." American Mineralogist 104, no. 11 (November 1, 2019): 1689–99. http://dx.doi.org/10.2138/am-2019-7095.
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Abstract Chemical diffusion of F and Cl has been experimentally determined in a rhyodacitic melt obtained from remelting a sample of Hekla pumice (Iceland). Diffusion couple experiments were conducted in a vertical tube furnace over a temperature range of 750–950 °C and in air for durations of 1 to 35 days. Concentration profiles of F and Cl were obtained for the quenched samples using an electron microprobe. Fluorine and chlorine exhibit Arrhenian behavior over the range of temperature investigated here. The pre-exponential factors of F and Cl are D0(F) = 4.3 × 10−4 and D0(Cl) = 1.6 × 10−5 m2/s. Fluorine diffusion coefficients vary in the order of 1 × 10−15 to 1 × 10−13 m2/s, whereas Cl diffusivity is up to two orders of magnitude slower. The activation energies for F and Cl diffusivities are equal within error at 223 ± 31 and 229 ± 52 kJ/mol, respectively. The difference in diffusivity between F and Cl is particularly pronounced in the melt of our study, compared to results obtained for other magmatic melt compositions. This means that the potential for diffusive fractionation exists and may occur especially under conditions of magma ascent and bubble growth, as this would favor partitioning of the relatively fast-diffusing halogens into growing bubbles, due to H2O exsolution. A dependence of diffusivity on atomic radius observed here is enhanced over that observed in more basic, less viscous melts, indicating that diffusive fractionation is more likely to be pronounced in more silicic, more viscous systems. A proper parameterization and modeling of diffusive fractionation of halogens in actively degassing volcanic systems thus holds the potential of serving as a tool for quantifying the processes responsible for volcanic unrest.
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Ahamad, Nabi, and Pallavi Debnath. "Rouse model in crowded environment modeled by “diffusing diffusivity”." Physica A: Statistical Mechanics and its Applications 549 (July 2020): 124335. http://dx.doi.org/10.1016/j.physa.2020.124335.
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Jain, Rohit, and K. L. Sebastian. "Diffusing diffusivity: a new derivation and comparison with simulations." Journal of Chemical Sciences 129, no. 7 (June 13, 2017): 929–37. http://dx.doi.org/10.1007/s12039-017-1308-0.
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Kapoor, Rajat, and S. T. Oyama. "Measurement of solid state diffusion coefficients by a temperature-programmed method." Journal of Materials Research 12, no. 2 (February 1997): 467–73. http://dx.doi.org/10.1557/jmr.1997.0068.
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This paper presents a method for determining diffusivities in solids where the diffusing species desorbs or reacts at the external surfaces, and where the diffusivity does not vary appreciably with concentration. The method involves measuring the flux of the diffusive species out of the solid under the influence of a temperature program. A general model is developed, based on nonisothermal Fickian diffusion, which is applicable to solid particles with slab or spherical geometry. The solution is presented both as an analytical expression and as correlation charts of experimentally observable quantities. These charts are contour diagrams of the temperatures of peak diffusion rate with ln(E/R) and ln(D0/h2) as the axes, where E and D0 are the activation energy and pre-exponential terms of the diffusivity expression D = D0 exp(−E/RT), where R is the gas constant, and h the size of the particles. This paper deals exclusively with the case of oxygen diffusion in the vanadium oxide system. In this case, vanadium oxide was reduced in a reactive ammonia stream at conditions in which the surface reaction was fast compared to the diffusive transport process. Using this method the diffusion parameters were found to be D0 = 1.9 × 10−5 cm2 s−1 and E = 101 kJ/mol. The method was checked by varying the crystallite size of the vanadium oxide sample in the range 2h = 0.14−0.29 μm.
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Kotnurkar, Asha S., Joonabi Beleri, Irfan Anjum Badruddin, Sarfaraz Kamangar, and Nandalur Ameer Ahammad. "Peristaltic Transport of Carreau Nanofluid in Presence of Triple Diffusion in an Asymmetric Channel by Multi-Step Differential Transformation Method." Mathematics 10, no. 5 (March 3, 2022): 807. http://dx.doi.org/10.3390/math10050807.
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The present work investigates the influence of triple diffusion on Carreau nanoliquid in peristaltic flow through an asymmetric channel. By using appropriate non-dimensional parameters, governing equations are transformed to conventional non-linear partial differential equations. The Ms-DTM is used to find solutions to developing equations. Because of the buoyancy force that prevails inside the boundary layer, velocity is impacted by the buoyancy ratio. The current investigation found that as the varied values of the modified Dufour parameter were increased, the temperature profile increased. The thermal conductivity increases as thermal diffusivity increases. It has also been discovered that the existence of triple-diffusing components with low diffusivity might alter the type of convection in the system. Graphs depict the influence of several parameters on velocity, salt1 and salt2 concentrations, solute concentration, and temperature.
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Hidalgo-Soria, M., E. Barkai, and S. Burov. "Cusp of Non-Gaussian Density of Particles for a Diffusing Diffusivity Model." Entropy 23, no. 2 (February 17, 2021): 231. http://dx.doi.org/10.3390/e23020231.
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We study a two state “jumping diffusivity” model for a Brownian process alternating between two different diffusion constants, D+>D−, with random waiting times in both states whose distribution is rather general. In the limit of long measurement times, Gaussian behavior with an effective diffusion coefficient is recovered. We show that, for equilibrium initial conditions and when the limit of the diffusion coefficient D−⟶0 is taken, the short time behavior leads to a cusp, namely a non-analytical behavior, in the distribution of the displacements P(x,t) for x⟶0. Visually this cusp, or tent-like shape, resembles similar behavior found in many experiments of diffusing particles in disordered environments, such as glassy systems and intracellular media. This general result depends only on the existence of finite mean values of the waiting times at the different states of the model. Gaussian statistics in the long time limit is achieved due to ergodicity and convergence of the distribution of the temporal occupation fraction in state D+ to a δ-function. The short time behavior of the same quantity converges to a uniform distribution, which leads to the non-analyticity in P(x,t). We demonstrate how super-statistical framework is a zeroth order short time expansion of P(x,t), in the number of transitions, that does not yield the cusp like shape. The latter, considered as the key feature of experiments in the field, is found with the first correction in perturbation theory.
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Mishra, Manoranjan, A. De Wit, and Kirti Chandra Sahu. "Double diffusive effects on pressure-driven miscible displacement flows in a channel." Journal of Fluid Mechanics 712 (October 9, 2012): 579–97. http://dx.doi.org/10.1017/jfm.2012.439.
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AbstractThe pressure-driven miscible displacement of a less viscous fluid by a more viscous one in a horizontal channel is studied. This is a classically stable system if the more viscous solution is the displacing one. However, we show by numerical simulations based on the finite-volume approach that, in this system, double diffusive effects can be destabilizing. Such effects can appear if the fluid consists of a solvent containing two solutes both influencing the viscosity of the solution and diffusing at different rates. The continuity and Navier–Stokes equations coupled to two convection–diffusion equations for the evolution of the solute concentrations are solved. The viscosity is assumed to depend on the concentrations of both solutes, while density contrast is neglected. The results demonstrate the development of various instability patterns of the miscible ‘interface’ separating the fluids provided the two solutes diffuse at different rates. The intensity of the instability increases when increasing the diffusivity ratio between the faster-diffusing and the slower-diffusing solutes. This brings about fluid mixing and accelerates the displacement of the fluid originally filling the channel. The effects of varying dimensionless parameters, such as the Reynolds number and Schmidt number, on the development of the ‘interfacial’ instability pattern are also studied. The double diffusive instability appears after the moment when the invading fluid penetrates inside the channel. This is attributed to the presence of inertia in the problem.
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Dobosz, Romuald, and Krzysztof Jan Kurzydlowski. "Diffusion in Condensed Matter by Finite Element Method." Diffusion Foundations 12 (September 2017): 127–45. http://dx.doi.org/10.4028/www.scientific.net/df.12.127.
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In this Chapter, the finite element simulations of diffusion processes in homogeneous and polycrystalline materials are presented as well as some analytical solutions and implementations of basic diffusion relations. For the homogeneous materials the presented examples show the changes in time of the concentration of diffusing matter within the semi-infinite system and simulation of anisotropic nature of diffusion processes.The polycrystalline materials have been analysed for three cases, namely influence of average grain size and the homogeneity of grain size on the macroscopic diffusivity as well as simulation of the diffusion strains. The homogenisation technique has been used to estimate the diffusion property of grains aggregates.
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Handa, Y. Paul, and Zhiyi Zhang. "Sorption, Diffusion, and Dilation in Linear and Branched Polycarbonate–CO2 Systems in Relation to Solid State Processing of Microcellular Foams." Cellular Polymers 21, no. 4 (July 2002): 221–35. http://dx.doi.org/10.1177/026248930202100401.
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The sorption and diffusion of CO2 in linear and branched polycarbonates were investigated using a high-temperature, high-pressure gravimetric technique. The branched structure does not affect gas solubility, but affects the gas diffusivity in the sub-Tg region, with CO2 diffusing faster through the branched structure than the linear one. Both solubility and diffusivity depend linearly on pressure at temperatures above Tg, but demonstrate complicated pressure dependence at temperatures below Tg. In the sub-Tg region, volume change of the polymer matrix accompanying the gas dissolution was measured using a dilatometer. The plasticized Tgs obtained from dilation and solubility measurements agreed with those obtained directly by high-pressure DSC. In addition, a plasticization related densification phenomenon was observed in the sub-Tg region. The competing effects of dilation and densification suggest significant implications in terms of solid state processing of microcellular foams.
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Shukla, Prakhar, Nabi Ahamad, and Pallavi Debnath. "Diffusing Diffusivity in Dynamics of Unentangled Polymer Melts." Macromolecular Theory and Simulations 31, no. 2 (October 31, 2021): 2100056. http://dx.doi.org/10.1002/mats.202100056.
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Jain, Rohit, and Kizhakeyil L. Sebastian. "Diffusing Diffusivity: Survival in a Crowded Rearranging and Bounded Domain." Journal of Physical Chemistry B 120, no. 34 (August 11, 2016): 9215–22. http://dx.doi.org/10.1021/acs.jpcb.6b06094.
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Koch, Donald L., and John F. Brady. "Dispersion in fixed beds." Journal of Fluid Mechanics 154 (May 1985): 399–427. http://dx.doi.org/10.1017/s0022112085001598.
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A macroscopic equation of mass conservation is obtained by ensemble-averaging the basic conservation laws in a porous medium. In the long-time limit this ‘macro-transport’ equation takes the form of a macroscopic Fick's law with a constant effective diffusivity tensor. An asymptotic analysis in low volume fraction of the effective diffusivity in a bed of fixed spheres is carried out for all values of the Péclet number ℙ = Ua/Df, where U is the average velocity through the bed. a is the particle radius and Df is the molecular diffusivity of the solute in the fluid. Several physical mechanisms causing dispersion are revealed by this analysis. The stochastic velocity fluctuations induced in the fluid by the randomly positioned bed particles give rise to a convectively driven contribution to dispersion. At high Péclet numbers, this convective dispersion mechanism is purely mechanical, and the resulting effective diffusivities are independent of molecular diffusion and grow linearly with ℙ. The region of zero velocity in and near the bed particles gives rise to non-mechanical dispersion mechanisms that dominate the longitudinal diffusivity at very high Péclet numbers. One such mechanism involves the retention of the diffusing species in permeable particles, from which it can escape only by molecular diffusion, leading to a diffusion coefficient that grows as ℙ2. Even if the bed particles are impermeable, non-mechanical contributions that grow as ℙ ln ℙ and ℙ2 at high ℙ arise from a diffusive boundary layer near the solid surfaces and from regions of closed streamlines respectively. The results for the longitudinal and transverse effective diffusivities as functions of the Péclet number are summarized in tabular form in §6. Because the same physical mechanisms promote dispersion in dilute and dense fixed beds, the predicted Péclet-number dependences of the effective diffusivities are applicable to all porous media. The theoretical predictions are compared with experiments in densely packed beds of impermeable particles, and the agreement is shown to be remarkably good.
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Covington, Leroy, Kamalesh Munirathinam, Akand Islam, and Kenneth Roberts. "Synthesis and characterization of nanostructured molybdenum & tungsten carbide materials, and study of diffusion model." Polish Journal of Chemical Technology 14, no. 1 (January 1, 2012): 28–34. http://dx.doi.org/10.2478/v10026-012-0055-8.
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Synthesis and characterization of nanostructured molybdenum & tungsten carbide materials, and study of diffusion model Powders of two molybdenum carbides (Mo2C and MoC1-x) and tungsten carbide (WC) were prepared by means of temperature programmed reaction (TPR) method. Mo2C and MoC1-x were synthesized by reacting MoO3 with a preselected molar ratio of methane/hydrogen and carbon monoxide/hydrogen gas mixtures respectively. WC was prepared using tungsten oxide (WO3) and a methane/hydrogen gas mixture. These carbides were ultrasonically dispersed in de-ionized water. Samples were characterized using room temperature x-ray diffraction and scanning microscopy. A kinetic diffusion model is also studied to determine diffusivities in solids where the diffusing species desorbs or reacts at the external surfaces, and where the diffusivity does not vary appreciably with concentrations. The method involves measuring the flux of the diffusive species into the solid under the influence of a temperature program.
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Sahu, Kirti Chandra. "Double-diffusive instability in core–annular pipe flow." Journal of Fluid Mechanics 789 (January 27, 2016): 830–55. http://dx.doi.org/10.1017/jfm.2015.760.
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The instability in a pressure-driven core–annular flow of two miscible fluids having the same densities, but different viscosities, in the presence of two scalars diffusing at different rates (double-diffusive effect) is investigated via linear stability analysis and axisymmetric direct numerical simulation. It is found that the double-diffusive flow in a cylindrical pipe exhibits strikingly different stability characteristics compared to the double-diffusive flow in a planar channel and the equivalent single-component flow (wherein viscosity stratification is achieved due to the variation of one scalar) in a cylindrical pipe. The flow which is stable in the context of single-component systems now becomes unstable in the presence of two scalars diffusing at different rates. It is shown that increasing the diffusivity ratio enhances the instability. In contrast to the single fluid flow through a pipe (the Hagen–Poiseuille flow), the faster growing axisymmetric eigenmode is found to be more unstable than the corresponding corkscrew mode for the parameter values considered, for which the equivalent single-component flow is stable to both the axisymmetric and corkscrew modes. Unlike single-component flows of two miscible fluids in a cylindrical pipe, it is shown that the diffusivity and the radial location of the mixed layer have non-monotonic influences on the instability characteristics. An attempt is made to understand the underlying mechanism of this instability by conducting the energy budget and inviscid stability analyses. The investigation of linear instability due to the double-diffusive phenomenon is extended to the nonlinear regime via axisymmetric direct numerical simulations. It is found that in the nonlinear regime the flow becomes unstable in the presence of double-diffusive effect, which is consistent with the predictions of linear stability theory. A new type of instability pattern of an elliptical shape is observed in the nonlinear simulations in the presence of double-diffusive effect.
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GIONA, M., S. CERBELLI, and F. CRETA. "Spectral properties and universal behaviour of advecting–diffusing scalar fields in finite-length channels." Journal of Fluid Mechanics 612 (October 10, 2008): 387–406. http://dx.doi.org/10.1017/s0022112008003042.
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This paper analyses the relaxation towards the steady state of an advecting–diffusing field in a finite-length channel. The dominant eigenvalue, −-ΛF, of the advection–diffusion operator provides the slowest relaxation time scale for achieving steady state in open flow devices. We focus on parallel flows and analyse how ΛF depends on the velocity profile and the molecular diffusivity. As a result of the universal localization features of the eigenfunction associated with ΛF, we find that ΛF can be predicted analytically based on the local behaviour of the velocity profile near the stagnation points. Microfluidic applications of the theory are also addressed.
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Dong, Huilong, Boyu Zheng, and Feifan Chen. "ANNULAR THERMAL-WAVE DIFFUSING MEASUREMENT METHOD FOR LOCAL THERMAL DIFFUSIVITY EVALUATION." Heat Transfer Research 47, no. 1 (2016): 49–69. http://dx.doi.org/10.1615/heattransres.2015009989.
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Grebenkov, Denis S. "A unifying approach to first-passage time distributions in diffusing diffusivity and switching diffusion models." Journal of Physics A: Mathematical and Theoretical 52, no. 17 (March 28, 2019): 174001. http://dx.doi.org/10.1088/1751-8121/ab0dae.
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Voronkov, Vladimir V., G. I. Voronkova, A. V. Batunina, V. N. Golovina, Robert J. Falster, M. Cornara, N. B. Tiurina, and A. S. Guliaeva. "Properties of Fast-Diffusing Oxygen Species in Silicon Deduced from the Generation Kinetics of Thermal Donors." Solid State Phenomena 156-158 (October 2009): 115–22. http://dx.doi.org/10.4028/www.scientific.net/ssp.156-158.115.
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The generation of Thermal Donors in Si is a nucleation process controlled by several mobile On clusters. The rate-limiting transitions are found to be O1 O2 and O4 O5. The individual transition rates G12 and G45, and also G23 and G34 are deduced from the experimental data. From the transient variation of the generation rate G(t), the equilibrium concentration of the dimers is found, and with it the dimeric diffusivity is also defined. In samples pre-treated at high T, the G(t) dependence has a maximum, due to quenched-in fast-diffusing oxygen monomers (FDMs). The concentration and diffusivity of FDMs were determined.
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Linnarsson, Margareta K., and Anders Hallén. "Diffusion of Alkali Metals in SiC." Materials Science Forum 778-780 (February 2014): 297–300. http://dx.doi.org/10.4028/www.scientific.net/msf.778-780.297.
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Diffusion of lithium, sodium and potassium in SiC has been studied by secondary ion mass spectrometry. The alkali metal diffusion sources have been introduced by ion implantation. Subsequent anneals have been carried out in vacuum or in Ar atmosphere in the temperature range 700 °C - 1500 °C for 5 min to 16 h. The bombardment-induced defects in the vicinity of the ion implanted profile are readily decorated by the implanted . In the bulk, the diffusing alkali metals are most likely trapped and detrapped at boron and/or other defects during diffusion. The diffusivity of the studied alkali metals decreases as the mass increases, Li+<Na+<K+, but the sodium mobility in SiC is substantial already at 1100 °C.
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Brady, John F. "The long-time self-diffusivity in concentrated colloidal dispersions." Journal of Fluid Mechanics 272 (August 10, 1994): 109–34. http://dx.doi.org/10.1017/s0022112094004404.
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The long-time self-diffusivity in concentrated colloidal dispersions is determined from a consideration of the temporal decay of density fluctuations. For hydrodynamically interacting Brownian particles the long-time self-diffusivity, Ds∞, is shown to be expressible as the product of the hydrodynamically determined short-time self-diffusivity, Ds(ϕ), and a contribution that depends on the distortion of the equilibrium structure caused by a diffusing particle. An argument is advanced to show that as maximum packing is approached the long-time self-diffusivity scales as Ds∞(ϕ) ∼ Ds0(ϕ)/g(2; ϕ), where g(2; ϕ) is the value of the equilibrium radial-distribution function at contact and ϕ is the volume fraction of interest. This result predicts that the longtime self-diffusivity vanishes quadratically at random close packing, ϕm ≈ 0.63, i.e. Ds∞D0(1-ϕ/ϕm)2 as ϕ→ϕm, where D0 = kT/6πνa is the diffusivity of a single isolated particle of radius a in a fluid of viscosity ν. This scaling occurs because Ds0(ϕ) vanishes linearly at random close packing and the radial-distribution function at contact diverges as (1 -ϕ/ϕm)−1. A model is developed to determine the structural deformation for the entire range of volume fractions, and for hard spheres the longtime self-diffusivity can be represented by: Ds∞(ϕ) = Ds∞(ϕ)/[1 + 2ϕg(2;ϕ)]. This formula is in good agreement with experiment. For particles that interact through hard-spherelike repulsive interparticle forces characterized by a length b(> a), the same formula applies with the short-time self-diffusivity still determined by hydrodynamic interactions at the true or ‘hydrodynamic’ volume fraction ϕ, but the structural deformation and equilibrium radial-distribution function are now determined by the ‘thermodynamic’ volume fraction ϕb based on the length b. When b [Gt ] a, the long-time self-diffusivity vanishes linearly at random close packing based on the ‘thermodynamic’ volume fraction ϕbm. This change in behaviour occurs because the true or ‘hydrodynamic’ volume fraction is so low that the short-time self-diffusivity is given by its infinite-dilution value D0. It is also shown that the temporal transition from short- to long-time diffusive behaviour is inversely proportional to the dynamic viscosity and is a universal function for all volume fractions when time is nondimensionalized by a2/Ds∞(ϕ).
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Dong, Huilong, Boyu Zheng, and Feifan Chen. "EXCITATION PULSE WIDTH IN THE PEAK DIFFUSING METHOD FOR THERMAL DIFFUSIVITY MEASUREMENT." International Journal of Energy for a Clean Environment 16, no. 1-4 (2015): 225–33. http://dx.doi.org/10.1615/interjenercleanenv.2015015411.
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Leaist, Derek G. "The effects of aggregation, counterion binding, and added NaCl on diffusion of aqueous methylene blue." Canadian Journal of Chemistry 66, no. 9 (September 1, 1988): 2452–57. http://dx.doi.org/10.1139/v88-386.
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A simplified version of the Hamed conductimetric technique is used to measure binary diffusion of the self-associating dye methylene blue chloride in water at 25 °C. As the dye concentration is increased from 0.0006 to 0.02 mol dm−3, aggregation of the dye monomers and binding of the chloride counterions cause the dye's binary diffusion coefficient to drop from 0.83 × 10−9 to 0.63 × 10−9 m2 s−1. Ternary diffusion coefficients for aqueous methylene blue chloride +NaCl solutions are also reported. These results show that small amounts of added NaCl (0.005 or 0.01 mol dm−3) sharply reduce the diffusivity of the dye component, and that each mole of diffusing dye cotransports 0.2–0.7 mol NaCl. Diffusion of trace amounts of the dye in the presence of a large excess of an inert supporting electrolyte is discussed briefly.
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Borland, Colin, Fiona Bottrill, Aled Jones, Chris Sparkes, and Alain Vuylsteke. "The significant blood resistance to lung nitric oxide transfer lies within the red cell." Journal of Applied Physiology 116, no. 1 (January 1, 2014): 32–41. http://dx.doi.org/10.1152/japplphysiol.00786.2013.
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The lung nitric oxide (NO) diffusing capacity (DlNO) mainly reflects alveolar-capillary membrane conductance (Dm). However, blood resistance has been shown in vitro and in vivo. To explore whether this resistance lies in the plasma, the red blood cell (RBC) membrane, or in the RBC interior, we measured the NO diffusing capacity (Dno) in a membrane oxygenator circuit containing ∼1 liter of horse or human blood exposed to 14 parts per million NO under physiological conditions on 7 separate days. We compared results across a 1,000-fold change in extracellular diffusivity using dextrans, plasma, and physiological salt solution. We halved RBC surface area by comparing horse and human RBCs. We altered the diffusive resistance of the RBC interior by adding sodium nitrite converting oxyhemoglobin to methemoglobin. Neither increased viscosity nor reduced RBC size reduced Dno. Adding sodium nitrite increased methemoglobin and was associated with a steady fall in Dno ( P < 0.001). Similar results were obtained at NO concentrations found in vivo. The RBC interior appears to be the site of the blood resistance.
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Qin, Zihan, Zhengwei He, Guozheng Wu, Gula Tang, and Qian Wang. "Developing Water-Quality Model for Jingpo Lake Based on EFDC." Water 14, no. 17 (August 23, 2022): 2596. http://dx.doi.org/10.3390/w14172596.
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Water-quality model simulation is the key to understanding hydrological processes and water-quality dynamic(s). In this study, Jingpo Lake, which is the most typical lake in the northern cold region of China, was selected as the research object. A numerical simulation model for transporting and diffusing the chemical oxygen demand (CODMn) and ammonia nitrogen (NH3N) with ice-covered and open-water periods was constructed and calibrated using the Environmental Fluid Dynamics Code (EFDC). Parameters such as the bottom roughness, ice roughness, diffusion coefficient, horizontal momentum diffusivity, molecular eddy viscosity, molecular diffusivity, buoyancy influence coefficient, CODMn decay rate and NH3N decay rate were validated. The research findings show that there were differences in the hydrodynamic water-quality changing process during the ice-covered and open-water periods, as well as for the seasonal ice-covered waterbody. The key parameter decay rates of the CODMn and NH3N in the ice-covered periods were lower than those in the open-water periods due to the water-temperature decline. The R2 of the CODMn and NH3N reached 90.71% and 79.79%, respectively. Thus, it may be concluded that the EFDC model could well reflect changes in the water level of Jingpo Lake, as well as the transport and diffusion of the CODMn and NH3N in Jingpo Lake.
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Rout, Smruti Sourav, Burkhard C. Schmidt, and Gerhard Wörner. "Constraints on non-isothermal diffusion modeling: An experimental analysis and error assessment using halogen diffusion in melts." American Mineralogist 105, no. 2 (February 1, 2020): 227–38. http://dx.doi.org/10.2138/am-2020-7193.
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Abstract Diffusion chronometry on zoned crystals allows constraining duration of magmatic evolution and storage of crystals once temperatures are precisely known. However, non-isothermal diffusion is common in natural samples, and thus timescales may not be determined with confidence while assuming isothermal conditions. The “non-isothermal diffusion incremental step (NIDIS) model” (Petrone et al. 2016) is proposed for such cases for a non-isothermal diffusive analysis. We conducted diffusion experiments with stepwise temperature changes to analyze and test the model, evaluated the associated errors and improved the accuracy by suggesting an alternative algorithm to model diffusion times. We used Cl and F (≤0.4 wt%) as the diffusing elements in nominally anhydrous (H2O ≤ 0.3 wt%) phonolitic melt with composition of Montana Blanca (Tenerife, Spain) in an experimental setup that successively generates multiple diffusive interfaces for different temperatures by adding glass blocks of different Cl and F concentrations. This compound set of two diffusion interfaces represents distinct compositional zones that diffusively interact at different temperatures, which can be taken as an equivalent to non-isothermal diffusion in zoned magmatic crystals. The starting temperature ranged from 975 to 1150 °C, and each set of experiments included a temperature change of 85–150 °C and a total duration of 8–12 h. The experiments were carried out in an internally heated pressure vessel equipped with a rapid quench device at 1 kbar pressure. Cl and F concentration profiles were obtained from the quenched samples by electron microprobe analysis. Although the estimated diffusion times from the NIDIS-model matched well with true experimental values, the errors on estimated timescales, due to errors in curve-fitting and uncertainty in temperature, were ±10–62% (1σ). The errors are much larger at 61–288% (1σ) when the uncertainty in diffusivity parameters is included. We discuss the efficiency and limitations of the model, assess the contribution from different sources of error, and their extent of propagation. A simpler alternative algorithm is proposed that reduces errors on the estimates of diffusion time to 10–32% (1σ) and 60–75% (1σ), with and without including uncertainty in diffusivity parameters, respectively. Using this new algorithm, we recalculated the individual diffusion times for the clinopyroxene crystals analyzed by Petrone et al. (2016) and obtained a significantly reduced error of 26–40% compared to the original error of 61–100%. We also analyzed a sanidine megacryst from Taapaca volcano (N. Chile) as a test case for non-isothermal modeling and obtained diffusion times of 1.5–9.4 ky, which is significantly different from isothermal analyses including a previous study on similar sample. In this analysis, the error estimated by our new method is reduced by 63–70%.
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Balcone-Boissard, Hélène, Don R. Baker, Benoit Villemant, Jean Cauzid, Georges Boudon, and E. Deloule. "Br diffusion in phonolitic melts: Comparison with fluorine and chlorine diffusion." American Mineralogist 105, no. 11 (November 1, 2020): 1639–46. http://dx.doi.org/10.2138/am-2020-7372.
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Abstract Bromine diffusion was measured in two natural phonolitic melts: (1) a K2O-rich (~10 wt%) one synthesized from the white pumice phase of the 79 AD eruption of Vesuvius (Italy), and (2) a Na2O-rich (~10 wt%) one corresponding to the most differentiated melt of the 12 000 BC eruption of the Laacher See (Germany). Experiments were performed at 0.5 and 1.0 GPa, 1250 to 1450 °C, at anhydrous and hydrous (2.65 ± 0.35 wt% of dissolved water) conditions. Experiments conducted with the diffusion-couple technique in the piston cylinder were performed with only bromine diffusing and with the simultaneous diffusion of a halogen mixture (F, Cl, Br) to evaluate the interactions between the halogens during diffusion. The diffusion profiles of Br were measured by X-ray fluorescence using synchrotron radiation microprobe (SYXRF), ID18F, at the European Synchrotron Radiation Facility (ESRF, France). Bromine diffusion displays Arrhenian behavior under anhydrous conditions that is similar when it diffuses alone and when it diffuses with F and Cl. The Br diffusion coefficients range between 2 × 10–12 m2/s at 1250 °C and 1.5 × 10–11 m2/s at 1450 °C for the Na-rich melt and between 3 × 10–12 m2/s at 1250 °C and 2.5 × 10–11 m2/s at 1450 °C for the K-rich melt, at 1.0 GPa. Although Br mobility is independent of F and Cl in anhydrous phonolitic melts, its behavior may be dependent on the dominant alkali in the melt, as previously observed for Cl, but not F. For hydrous experiments, although the data are scattered, the Br diffusivity increases slightly with water and the Na/K ratio seems to influence Br diffusivity. Similarly to noble gases, halogen diffusivity at a given temperature in the phonolitic melts appears related to the ionic porosity of the silicate structure. Compared to basaltic melt, Br diffusivities are approximately one order of magnitude lower in the Na-phonolite melt, because of the difference of the pre-exponential factor. Br mobility appears to be decoupled from melt viscosity, considering the results here.
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Cabrini, Marina, Sergio Lorenzi, Tommaso Pastore, and Diego Pesenti Bucella. "Hydrogen diffusion in low alloy steels under cyclic loading." Corrosion Reviews 37, no. 5 (September 25, 2019): 459–67. http://dx.doi.org/10.1515/corrrev-2019-0008.
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AbstractThe aim of this work is to analyze hydrogen transport in a low alloy steel by applying the electrochemical permeation technique to matrices subject to cyclic loading conditions, up to the yield strength and beyond this limit. The results indicate that, with an increase in the applied maximum stress, a decrease in the apparent diffusivity takes place, along with a marked and instantaneous reduction of diffusing hydrogen in the lattice and an increase in hydrogen solubility. An effect on the permeation current was observed, together with a variation of hydrogen diffusion kinetics ascribable to the activation on new trapping sites, with an appreciable effect under cyclic loading already at 55% of the yield limit, which becomes more relevant in the plastic domain.
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Lacalli, Thurston C., and Lionel G. Harrison. "Turing's model and branching tip growth: relation of time and spatial scales in morphogenesis, with application to Micrasterias." Canadian Journal of Botany 65, no. 7 (July 1, 1987): 1308–19. http://dx.doi.org/10.1139/b87-184.
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Morphogenesis following cell division in Micrasterias rotata is by outgrowth and repeated branching of a series of semicell lobes. Though successive branching events are qualitatively similar, they display changes in time and space scales, and these can be quantitated with the aid of autoradiographic patterns of labelled wall precursors that appear late in morphogenesis but which seem to represent its history. This enables us to consider branching as the conversion of a single centre of growth activity into two and to attempt to locate these centres precisely, in terms of both position and time of establishment. Temporal and spatial scales both decrease, by 75%, through a sequence of five branching events, in linear functional relationship to each other. This correlation points toward kinetic control of morphogenesis, i.e., the involvement of something like a reaction–diffusion mechanism. We analyse this possibility in terms of available reaction–diffusion theory to show how, after various simplifying assumptions, and if the time and space scales of branch formation are known, an effective diffusivity, [Formula: see text], for the patterning mechanism can be estimated. For M. rotata we obtain orders of magnitude: [Formula: see text], with an upper limit on the diffusivity of the faster diffusing of the two morphogenetic substances in the mechanism of ca. 1 × 10−7 cm2/s. These values implicate the cell membrane as the most probable site of pattern formation.
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Bakhouya-Sabbahi, N., J. Bouzon, and J. M. Vergnaud. "Radial Diffusion in a Sphere with Subsequent Change in Dimension. Desorption with a Finite Surface Coefficient of Mass Transfer in an Infinite Volume." Engineering Plastics 2, no. 2 (January 1994): 147823919400200. http://dx.doi.org/10.1177/147823919400200205.
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The liquid located in a polymer evaporates by following a process controlled by diffusion-evaporation. The general case when the desorption is followed by subsequent shrinkage is studied by considering a spherical polymer with a radial diffusion and a finite rate of evaporation. The volume of the surrounding is so large that it can be considered as infinite. The mathematical treatment is achieved, leading to general equations of radial diffusion and evaporation with a following change in dimension of the polymer. These general equations reduce to the Fick's equation when the amount of substance transferred is small enough. These general equations have no analytical solution, and the problem is resolved by using a numerical method with finite differences. The following parameters are of interest: the diffusivity, the coefficient of mass transfer on the surface, the radius of the empty bead, the relative volume expansion of the polymer due to the presence of the diffusing substance.
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Bakhouya-Sabbahi, N., J. Bouzon, and J. M. Vergnaud. "Radial Diffusion in a Sphere with Subsequent Change in Dimension. Desorption with a Finite Surface Coefficient of Mass Transfer in an Infinite Volume." Polymers and Polymer Composites 2, no. 2 (February 1994): 105–13. http://dx.doi.org/10.1177/096739119400200205.
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The liquid located in a polymer evaporates by following a process controlled by diffusion-evaporation. The general case when the desorption is followed by subsequent shrinkage is studied by considering a spherical polymer with a radial diffusion and a finite rate of evaporation. The volume of the surrounding is so large that it can be considered as infinite. The mathematical treatment is achieved, leading to general equations of radial diffusion and evaporation with a following change in dimension of the polymer. These general equations reduce to the Fick's equation when the amount of substance transferred is small enough. These general equations have no analytical solution, and the problem is resolved by using a numerical method with finite differences. The following parameters are of interest: the diffusivity, the coefficient of mass transfer on the surface, the radius of the empty bead, the relative volume expansion of the polymer due to the presence of the diffusing substance.
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Cherniak, D. J., and E. B. Watson. "Ti diffusion in feldspar." American Mineralogist 105, no. 7 (July 1, 2020): 1040–51. http://dx.doi.org/10.2138/am-2020-7272.
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Abstract Chemical diffusion of Ti has been measured in natural K-feldspar and plagioclase. The sources of diffusant used were TiO2 powders or pre-annealed mixtures of TiO2 and Al2O3. Experiments were run in crimped Pt capsules in air or in sealed silica glass capsules with solid buffers (to buffer at NNO). Rutherford backscattering spectrometry (RBS) was used to measure Ti diffusion profiles. From these measurements, the following Arrhenius relations are obtained for diffusion normal to (001):For oligoclase, over the temperature range 750–1050 °C:DOlig=6.67×10-12exp(-207±31kJ/mol/RT)m2s-1For labradorite, over the temperature range 900–1150 °C:DLab=of4.37×10-14exp(-181±57kJ/mol/RT)m2s-1For K-feldspar, over the temperature range 800–1000 °C:DKsp=3.01×10-6exp(-342±47kJ/mol/RT)m2s-1. Diffusivities for experiments buffered at NNO are similar to those run in air, and the presence of hydrous species appears to have little effect on Ti diffusion. Ti diffusion also shows little evidence of anisotropy. In plagioclase, there appears to be a dependence of Ti diffusion on An content of the feldspar, with Ti diffusing more slowly in more calcic plagioclase. This trend is similar to that observed for other cations in plagioclase, including Sr, Pb, Ba, REE, Si, and Mg. In the case of Ti, an increase of 30% in An content would result in an approximate decrease in diffusivity of an order of magnitude. These data indicate that feldspar should be moderately retentive of Ti chemical signatures, depending on feldspar composition. Ti will be more resistant to diffusional alteration than Sr. For example, Ti zoning on a 50 μm scale in oligoclase would be preserved at 600 °C for durations of ~1 million years, with Sr zoning preserved only for ~70 000 yr at this temperature. These new data for a trace impurity that is relatively slow-diffusing and ubiquitous in feldspars (Hoff and Watson 2018) have the potential to extend the scope and applicability of t-T models for crustal rocks based on measurements of trace elements in feldspars.
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Käpylä, P. J., M. Rheinhardt, A. Brandenburg, and M. J. Käpylä. "Turbulent viscosity and magnetic Prandtl number from simulations of isotropically forced turbulence." Astronomy & Astrophysics 636 (April 2020): A93. http://dx.doi.org/10.1051/0004-6361/201935012.
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Context. Turbulent diffusion of large-scale flows and magnetic fields plays a major role in many astrophysical systems, such as stellar convection zones and accretion discs. Aims. Our goal is to compute turbulent viscosity and magnetic diffusivity which are relevant for diffusing large-scale flows and magnetic fields, respectively. We also aim to compute their ratio, which is the turbulent magnetic Prandtl number, Pmt, for isotropically forced homogeneous turbulence. Methods. We used simulations of forced turbulence in fully periodic cubes composed of isothermal gas with an imposed large-scale sinusoidal shear flow. Turbulent viscosity was computed either from the resulting Reynolds stress or from the decay rate of the large-scale flow. Turbulent magnetic diffusivity was computed using the test-field method for a microphysical magnetic Prandtl number of unity. The scale dependence of the coefficients was studied by varying the wavenumber of the imposed sinusoidal shear and test fields. Results. We find that turbulent viscosity and magnetic diffusivity are in general of the same order of magnitude. Furthermore, the turbulent viscosity depends on the fluid Reynolds number (Re) and scale separation ratio of turbulence. The scale dependence of the turbulent viscosity is found to be well approximated by a Lorentzian. These results are similar to those obtained earlier for the turbulent magnetic diffusivity. The results for the turbulent transport coefficients appear to converge at sufficiently high values of Re and the scale separation ratio. However, a weak trend is found even at the largest values of Re, suggesting that the turbulence is not in the fully developed regime. The turbulent magnetic Prandtl number converges to a value that is slightly below unity for large Re. For small Re we find values between 0.5 and 0.6 but the data are insufficient to draw conclusions regarding asymptotics. We demonstrate that our results are independent of the correlation time of the forcing function. Conclusions. The turbulent magnetic diffusivity is, in general, consistently higher than the turbulent viscosity, which is in qualitative agreement with analytic theories. However, the actual value of Pmt found from the simulations (≈0.9−0.95) at large Re and large scale separation ratio is higher than any of the analytic predictions (0.4−0.8).
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Voronkov, Vladimir V., Robert J. Falster, and Semih Senkader. "Anomalous Out-Diffusion Profiles of Nitrogen in Silicon." Solid State Phenomena 156-158 (October 2009): 149–54. http://dx.doi.org/10.4028/www.scientific.net/ssp.156-158.149.
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Out-diffusion nitrogen profiles measured by SIMS after annealing at 850 and 800oC, have a peculiar minimum at a depth of about 5 m. The profiles are well reproduced by simulations assuming that there is a considerable fraction of nitrogen stored in substitutional clusters VN4. Upon annealing, these clusters lose nitrogen and convert into a stable high-temperature form VN1. This reaction involves a preliminary attachment of a fast-diffusing interstitial trimer, N3. Accordingly, the conversion occurs only in the bulk but not at the surface (due to out-diffusion loss of N3), and the substitutional component decreases from the surface towards the bulk. By fitting the profiles, the two basic parameters of the N2/N1 transport are deduced: P = D1K1/2 (a combination of the monomeric diffusivity D1 and the dissociation constant of dimers, K), and the dissociation time of dimers. With these data, D1(T) and K(T) are specified.
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Kytikova, O. Yu, M. V. Antonyuk, T. A. Gvozdenko, and T. P. Novgorodtseva. "Diffusing capacity of lungs in chronic obstructive pulmonary disease: gender, age, and race aspects." Bulletin Physiology and Pathology of Respiration, no. 85 (September 23, 2022): 116–30. http://dx.doi.org/10.36604/1998-5029-2022-85-116-130.
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Introduction. Diffusion capacity of lungs is the second most important respiratory test after spirometry. The importance of assessing lung diffusion capacity in chronic obstructive pulmonary disease (COPD) is not given due attention, although this parameter reflects changes in functional lung volume and gas transport through the alveolar-capillary membrane, thereby providing more information about respiratory physiology than spirometry results. Diffusing capacity of the lung for carbon monoxide (DLCO) measurement is the standard in pulmonology, however, in recent years, close attention has been given to the determination of lung diffusion capacity for nitric oxide (DLNO), which gives better explanation of gas transport through the alveolar-capillary membrane compared to DLCO. Recent literature is actively discussing the inclusion of age, race, and gender aspects in spirometric reference equations that are used to assess spirometric parameters and lung diffusion capacity.Aim. To analyze the literature over the past five years, reflecting the views of modern researchers on methods for diagnosing lung diffusion capacity, as well as the contribution of age, race, and gender aspects to the assessment of this parameter in COPD.Materials and methods. The PubMed database was searched for information for the period 2017-2022 according to the selected inclusion criteria. Information requests included the following set of keywords: “diffusion capacity”, “chronic obstructive pulmonary disease”, “gender”, “age”, “race”, “DLNO”, “DLCO”. 123 articles were analyzed.Results. Recent evidence highlights the importance of including lung diffusivity in COPD prognostic programs. Determining the diffusion capacity of the lungs for nitric oxide may be a promising area of research soon. Gender and age considerations play an important role in the interpretation of spirometry data and lung diffusion capacity. The issue of including a racial trait in the assessment of the diffusing capacity of the lungs in COPD is in doubt.
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Uematsu, Masashi, Kenzo Ibano, and Kohei M. Itoh. "Effect of the SiO2/Si Interface on Self-Diffusion in SiO2 Upon Oxidation." Defect and Diffusion Forum 273-276 (February 2008): 685–92. http://dx.doi.org/10.4028/www.scientific.net/ddf.273-276.685.
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The effect of the SiO2/Si interface on Si self-diffusion in SiO2 during thermal oxidation was investigated using silicon isotopes. Samples with natSiO2/28Si heterostructures were oxidized at 1150 ~ 1250 °C and the 30Si diffusion in 28SiO2 during the thermal oxidation was investigated by secondary ion mass spectrometry (SIMS) measurements. Near the SiO2/Si interface, a significant profile broadening of the 30Si isotope from natSiO2 toward the newly grown 28SiO2 was observed. This 30Si self-diffusivity sharply decreases with oxidation time and hence with increasing distance between 30Si diffusion region and the interface. This distance-dependent 30Si self-diffusion was simulated taking into account the effect of Si species generated at the interface upon oxidation and diffusing into SiO2 to enhance Si self-diffusion. The simulation fits the SIMS profiles and these results indicate that Si species, most likely SiO, are emitted from the SiO2/Si interface upon Si thermal oxidation to release the oxidation-induced stress, as has been predicted by recent theoretical studies. Furthermore, combined with our recent results on O self-diffusion, the diffusion behavior of the emitted SiO near the SiO2/Si interface is discussed.