Anelastic relaxation due to interstitial solutes diffusion in Nb and Nb-1 wt% Zr

Metals and alloys containing solute atoms dissolved interstitially often show anelastic behavior due to a process know as stress-induced ordering. The application of mechanical spectroscopy measurements to diffusion studies in body-centered cubic metals has been extensively used in the last decades. However the kind of preferential occupation of interstitial solutes in body-centered cubic metals is still controversial. The anelastic properties of the Nb and Nb-1 wt% Zr polycrystalline alloys were determined by internal friction and oscillation frequency measurements using a torsion pendulum inverted performed between 300K and 650K, operating in a frequency oscillation in the hertz bandwidth. The interstitial diffusion coefficients of oxygen and nitrogen in Nb and Nb-1 wt% Zr samples were determined at two distinct conditions: (a) for low concentration of oxygen and (b) for high concentration of oxygen.

Quantifying The Diffusion And Erosion Of Degradable Hydrogels Using A Microfluidic Technique

Hydrogels are composed of cross-linked networks of hydrophilic polymers that are biocompatible due to their high water content. Mass transfer through hydrogels has been suggested as an effective method of drug delivery, specifically in degradable polymers to minimize lasting effects within the body. Diffusion of small molecules in poly (ethylene glycol) diacrylate (PEG-DA) and dextran methacrylate (dex-MA) hydrogels was characterized in a microfluidic device and by complementary techniques. Microfluidic devices were prepared by crosslinking a formulation of hydrogel and photo-initiator, with and without visible dye, using photolithography to define a central microchannel. Channel sizes within the devices were approximately 600 ¿m to simulate vessels within the body. The microfluidic technique allows for both image and effluent analyses. To visualize the diffusive behavior within the dextran hydrogel, methylene blue and sulforhodamine 101 dyes were used in both elution and uptake experiments. Three analysis techniques for measuring diffusion coefficients were used to quantify the diffusion of solute in the hydrogel, including optical microscopy, characterization of device effluent, and NMR analyses. The optical microscopy technique analyzes images of the dye diffusion captured by a stereomicroscope to generate dye concentration v. position profiles. The data was fit to a diffusion model to determine diffusion coefficients and the dye release profile. In a typical elution experiment, aqueous solution is pumped through the microchannel and dye diffuses out of the hydrogel and into the aqueous phase. During elution, images are taken at regular time intervals and the effluent was collected. Analysis of the device effluent was performed using ultraviolet-visible (UV/Vis) spectroscopy to determine the effluent dye concentration and thus a short-time diffusion coefficient. Nuclear magnetic resonance (NMR) was used to determine a free diffusion coefficient of molecules in hydrogel without the effect of a concentration gradient. Diffusion coefficients for methylene blue and sulforhodamine 101 dyes in dex-MA hydrogel calculated using the three analysis methods all agree well. It was determined that utilizing a combination of the three techniques offers greater insight into molecular diffusion in hydrogels than employing each technique individually. The use of the same microfluidic devices used to measure diffusion is explored in the use of studying the degradation of dex-MA hydrogels. By combining what is known about the degradation rate in regards to the effect of pH and crosslinking and the ability to use a dye solution in contrast to establish the hydrogel boundaries could be a novel approach to studying hydrogel degradation.

Diffusion-driven transport in clayrock formations

Clay mineral-rich sedimentary formations are currently under investigation to evaluate their potential use as host formations for installation of deep underground disposal facilities for radioactive waste (e.g. Boom Clay (BE), Opalinus Clay (CH), Callovo-Oxfordian argillite (FR)). The ultimate safety of the corresponding repository concepts depends largely on the capacity of the host formation to limit the flux towards the biosphere of radionuclides (RN) contained in the waste to acceptably low levels. Data for diffusion-driven transfer in these formations shows extreme differences in the measured or modelled behaviour for various radionuclides, e. g. between halogen RN (Cl-36, I-129) and actinides (U-238,U-235, Np-237, Th-232, etc.), which result from major differences between RN of the effects on transport of two phenomena: diffusion and sorption. This paper describes recent research aimed at improving understanding of these two phenomena, focusing on the results of studies carried out during the EC Funmig IP on clayrocks from the above three formations and from the Boda formation (HU). Project results regarding phenomena governing water, cation and anion distribution and mobility in the pore volumes influenced by the negatively-charged surfaces of clay minerals show a convergence of the modelling results for behaviour at the molecular scale and descriptions based on electrical double layer models. Transport models exist which couple ion distribution relative to the clay-solution interface and differentiated diffusive characteristics. These codes are able to reproduce the main trends in behaviour observed experimentally, e.g. D-e(anion) < D-e(HTO) < D-e(cation) and D-e(anion) variations as a function of ionic strength and material density. These trends are also well-explained by models of transport through ideal porous matrices made up of a charged surface material. Experimental validation of these models is good as regards monovalent alkaline cations, in progress for divalent electrostatically-interacting cations (e.g. Sr2+) and still relatively poor for 'strongly sorbing', high K-d cations. Funmig results have clarified understanding of how clayrock mineral composition, and the corresponding organisation of mineral grain assemblages and their associated porosity, can affect mobile solute (anions, HTO) diffusion at different scales (mm to geological formation). In particular, advances made in the capacity to map clayrock mineral grain-porosity organisation at high resolution provide additional elements for understanding diffusion anisotropy and for relating diffusion characteristics measured at different scales. On the other hand, the results of studies focusing on evaluating the potential effects of heterogeneity on mobile species diffusion at the formation scale tend to show that there is a minimal effect when compared to a homogeneous property model. Finally, the results of a natural tracer-based study carried out on the Opalinus Clay formation increase confidence in the use of diffusion parameters measured on laboratory scale samples for predicting diffusion over geological time-space scales. Much effort was placed on improving understanding of coupled sorption-diffusion phenomena for sorbing cations in clayrocks. Results regarding sorption equilibrium in dispersed and compacted materials for weakly to moderately sorbing cations (Sr2+, Cs+, Co2+) tend to show that the same sorption model probably holds in both systems. It was not possible to demonstrate this for highly sorbing elements such as Eu(III) because of the extremely long times needed to reach equilibrium conditions, but there does not seem to be any clear reason why such elements should not have similar behaviour. Diffusion experiments carried out with Sr2+, Cs+ and Eu(III) on all of the clayrocks gave mixed results and tend to show that coupled diffusion-sorption migration is much more complex than expected, leading generally to greater mobility than that predicted by coupling a batch-determined K-d and Ficks law based on the diffusion behaviour of HTO. If the K-d measured on equivalent dispersed systems holds as was shown to be the case for Sr, Cs (and probably Co) for Opalinus Clay, these results indicate that these cations have a D-e value higher than HTO (up to a factor of 10 for Cs+). Results are as yet very limited for very moderate to strongly sorbing species (e.g. Co(II), Eu(III), Cu(II)) because of their very slow transfer characteristics. (C) 2011 Elsevier Ltd. All rights reserved.

Solute transport in crystalline rocks at Äspö — I: Geological basis and model calibration

Water-conducting faults and fractures were studied in the granite-hosted A¨ spo¨ Hard Rock Laboratory (SE Sweden). On a scale of decametres and larger, steeply dipping faults dominate and contain a variety of different fault rocks (mylonites, cataclasites, fault gouges). On a smaller scale, somewhat less regular fracture patterns were found. Conceptual models of the fault and fracture geometries and of the properties of rock types adjacent to fractures were derived and used as input for the modelling of in situ dipole tracer tests that were conducted in the framework of the Tracer Retention Understanding Experiment (TRUE-1) on a scale of metres. After the identification of all relevant transport and retardation processes, blind predictions of the breakthroughs of conservative to moderately sorbing tracers were calculated and then compared with the experimental data. This paper provides the geological basis and model calibration, while the predictive and inverse modelling work is the topic of the companion paper [J. Contam. Hydrol. 61 (2003) 175]. The TRUE-1 experimental volume is highly fractured and contains the same types of fault rocks and alterations as on the decametric scale. The experimental flow field was modelled on the basis of a 2D-streamtube formalism with an underlying homogeneous and isotropic transmissivity field. Tracer transport was modelled using the dual porosity medium approach, which is linked to the flow model by the flow porosity. Given the substantial pumping rates in the extraction borehole, the transport domain has a maximum width of a few centimetres only. It is concluded that both the uncertainty with regard to the length of individual fractures and the detailed geometry of the network along the flowpath between injection and extraction boreholes are not critical because flow is largely one-dimensional, whether through a single fracture or a network. Process identification and model calibration were based on a single uranine breakthrough (test PDT3), which clearly showed that matrix diffusion had to be included in the model even over the short experimental time scales, evidenced by a characteristic shape of the trailing edge of the breakthrough curve. Using the geological information and therefore considering limited matrix diffusion into a thin fault gouge horizon resulted in a good fit to the experiment. On the other hand, fresh granite was found not to interact noticeably with the tracers over the time scales of the experiments. While fracture-filling gouge materials are very efficient in retarding tracers over short periods of time (hours–days), their volume is very small and, with time progressing, retardation will be dominated by altered wall rock and, finally, by fresh granite. In such rocks, both porosity (and therefore the effective diffusion coefficient) and sorption Kds are more than one order of magnitude smaller compared to fault gouge, thus indicating that long-term retardation is expected to occur but to be less pronounced.

Solute transport in crystalline rocks at Äspö — II: Blind predictions, inverse modelling and lessons learnt from test STT1

Based on the results from detailed structural and petrological characterisation and on up-scaled laboratory values for sorption and diffusion, blind predictions were made for the STT1 dipole tracer test performed in the Swedish A¨ spo¨ Hard Rock Laboratory. The tracers used were nonsorbing, such as uranine and tritiated water, weakly sorbing 22Na+, 85Sr2 +, 47Ca2 +and more strongly sorbing 86Rb+, 133Ba2 +, 137Cs+. Our model consists of two parts: (1) a flow part based on a 2D-streamtube formalism accounting for the natural background flow field and with an underlying homogeneous and isotropic transmissivity field and (2) a transport part in terms of the dual porosity medium approach which is linked to the flow part by the flow porosity. The calibration of the model was done using the data from one single uranine breakthrough (PDT3). The study clearly showed that matrix diffusion into a highly porous material, fault gouge, had to be included in our model evidenced by the characteristic shape of the breakthrough curve and in line with geological observations. After the disclosure of the measurements, it turned out that, in spite of the simplicity of our model, the prediction for the nonsorbing and weakly sorbing tracers was fairly good. The blind prediction for the more strongly sorbing tracers was in general less accurate. The reason for the good predictions is deemed to be the result of the choice of a model structure strongly based on geological observation. The breakthrough curves were inversely modelled to determine in situ values for the transport parameters and to draw consequences on the model structure applied. For good fits, only one additional fracture family in contact with cataclasite had to be taken into account, but no new transport mechanisms had to be invoked. The in situ values for the effective diffusion coefficient for fault gouge are a factor of 2–15 larger than the laboratory data. For cataclasite, both data sets have values comparable to laboratory data. The extracted Kd values for the weakly sorbing tracers are larger than Swedish laboratory data by a factor of 25–60, but agree within a factor of 3–5 for the more strongly sorbing nuclides. The reason for the inconsistency concerning Kds is the use of fresh granite in the laboratory studies, whereas tracers in the field experiments interact only with fracture fault gouge and to a lesser extent with cataclasite both being mineralogically very different (e.g. clay-bearing) from the intact wall rock.

Mixing-cell boundary conditions and apparent mass balance errors for advective-dispersive solute transport

In many field or laboratory situations, well-mixed reservoirs like, for instance, injection or detection wells and gas distribution or sampling chambers define boundaries of transport domains. Exchange of solutes or gases across such boundaries can occur through advective or diffusive processes. First we analyzed situations, where the inlet region consists of a well-mixed reservoir, in a systematic way by interpreting them in terms of injection type. Second, we discussed the mass balance errors that seem to appear in case of resident injections. Mixing cells (MC) can be coupled mathematically in different ways to a domain where advective-dispersive transport occurs: by assuming a continuous solute flux at the interface (flux injection, MC-FI), or by assuming a continuous resident concentration (resident injection). In the latter case, the flux leaving the mixing cell can be defined in two ways: either as the value when the interface is approached from the mixing-cell side (MC-RT -), or as the value when it is approached from the column side (MC-RT +). Solutions of these injection types with constant or-in one case-distance-dependent transport parameters were compared to each other as well as to a solution of a two-layer system, where the first layer was characterized by a large dispersion coefficient. These solutions differ mainly at small Peclet numbers. For most real situations, the model for resident injection MC-RI + is considered to be relevant. This type of injection was modeled with a constant or with an exponentially varying dispersion coefficient within the porous medium. A constant dispersion coefficient will be appropriate for gases because of the Eulerian nature of the usually dominating gaseous diffusion coefficient, whereas the asymptotically growing dispersion coefficient will be more appropriate for solutes due to the Lagrangian nature of mechanical dispersion, which evolves only with the fluid flow. Assuming a continuous resident concentration at the interface between a mixing cell and a column, as in case of the MC-RI + model, entails a flux discontinuity. This flux discontinuity arises inherently from the definition of a mixing cell: the mixing process is included in the balance equation, but does not appear in the description of the flux through the mixing cell. There, only convection appears because of the homogeneous concentration within the mixing cell. Thus, the solute flux through a mixing cell in close contact with a transport domain is generally underestimated. This leads to (apparent) mass balance errors, which are often reported for similar situations and erroneously used to judge the validity of such models. Finally, the mixing cell model MC-RI + defines a universal basis regarding the type of solute injection at a boundary. Depending on the mixing cell parameters, it represents, in its limits, flux as well as resident injections. (C) 1998 Elsevier Science B.V. All rights reserved.

Diffusion modeling of percutaneous absorption kinetics: 3. Variable diffusion and partition coefficients, consequences for stratum corneum depth profiles and desorption kinetics

Stratum corneum (SC) desorption experiments have yielded higher calculated steady-state fluxes than those obtained by epidermal penetration studies. A possible explanation of this result is a variable diffusion or partition coefficient across the SC. We therefore developed the diffusion model for percutaneous penetration and desorption to study the effects of either a variable diffusion coefficient or variable partition coefficient in the SC over the diffusion path length. Steady-state flux, lag time, and mean desorption time were obtained from Laplace domain solutions. Numerical inversion of the Laplace domain solutions was used for simulations of solute concentration-distance and amount penetrated (desorbed)-time profiles. Diffusion and partition coefficients heterogeneity were examined using six different models. The effect of heterogeneity on predicted flux from desorption studies was compared with that obtained in permeation studies. Partition coefficient heterogeneity had a more profound effect on predicted fluxes than diffusion coefficient heterogeneity. Concentration-distance profiles show even larger dependence on heterogeneity, which is consistent with experimental tape-stripping data reported for clobetasol propionate and other solutes. The clobetasol propionate tape-stripping data were most consistent with the partition coefficient decreasing exponentially for half the SC and then becoming a constant for the remaining SC. (C) 2004 Wiley-Liss, Inc.

Mass uptake study of the diffusion of water and SBF into poly(2-hydroxyethyl methacrylate-co-tetrahydrofurfuryI methacrylate) containing aspirin or vitamin B-12

The ingress of water and Kokubo simulated body fluid (SBF) into poly (2-hydroxyethyl methacrylate) (PHEMA), and its co-polymers with tetrahydrofurduryl methacrylate (THFMA), loaded with either one of two model drugs, vitamin 1312 or aspirin, was studied by mass uptake over the temperature range 298-318 K. The polymers were studied as cylinders and were loaded with either 5 wt% or 10 wt% of the drugs. From DSC studies it was observed that vitamin B-12 behaved as a physical cross-linker restricting chain segmental mobility, and so had a small anti-plasticisation effect on PHEMA and the co-polymers rich in HEMA, but almost no effect on the T-g of co-polymers rich in THFMA. On the other hand, aspirin exhibited a plasticising effect on PHEMA and the copolymers. All of the polymers were found to absorb water and SBF according to a Fickian diffusion mechanism. The polymers were all found to swell to a greater extent in SBF than in water, which was attributed to the presence of Tris buffer in the SBF. The sorptions of the two penetrants were found to follow Fickian kinetics in all cases and the diffusion coefficients at 310 K for SBF were found to be smaller than those for water, except for the polymers containing aspirin where the diffusion coefficients were higher than for the other systems. For example, for sorption into PHEMA the diffusion coefficient for water was 1.41 X 10(-11) m(2)/s and for SBF was 0.79 x 10-11 m(2)/s, but in the presence of 5 wt% aspirin the corresponding values were 1.27 x 10(-1)1 m(2)/s and 1.25 x 10(-11) m(2)/s, respectively. The corresponding values for PHEMA loaded with 5 wt% B-12 were 1.25 x 10(-11) m(2)/s and 0.74 x 10(-11) m(2)/s, respectively.

Matrix-assisted diffusion-ordered spectroscopy:application of surfactant solutions to the resolution of isomer spectra

The component spectra of a mixture of isomers with nearly identical diffusion coefficients cannot normally be distinguished in a standard diffusion-ordered spectroscopy (DOSY) experiment but can often be easily resolved using matrix-assisted DOSY, in which diffusion behaviour is manipulated by the addition of a co-solute such as a surfactant. Relatively little is currently known about the conditions required for such a separation, for example, how the choice between normal and reverse micelles affects separation or how the isomer structures themselves affect the resolution. The aim of this study was to explore the application of sodium dodecyl sulfate (SDS) normal micelles in aqueous solution and sodium 1,4-bis(2-ethylhexyl)sulfosuccinate (AOT) aggregates in chloroform, at a range of concentrations, to the diffusion resolution of some simple model sets of isomers such as monomethoxyphenols and short chain alcohols. It is shown that SDS micelles offer better resolution where these isomers differ in the position of a hydroxyl group, whereas AOT aggregates are more effective for isomers differing in the position of a methyl group. For both the normal SDS micelles and the less well-defined AOT aggregates, differences in the resolution of the isomers can in part be rationalised in terms of differing degrees of hydrophobicity, amphiphilicity and steric effects. Copyright © 2012 John Wiley & Sons, Ltd.

Matrix-assisted diffusion-ordered spectroscopy:mixture resolution by NMR using SDSmicelles

Diffusion-ordered spectroscopy (DOSY) is a powerful technique for mixture analysis, but in its basic form it cannot separate the component spectra for species with very similar diffusion coefficients. It has been recently demonstrated that the component spectra of a mixture of isomers with nearly identical diffusion coefficients (the three dihydroxybenzenes) can be resolved using matrix-assisted DOSY (MAD), in which diffusion is perturbed by the addition of a co-solute such as a surfactant [R. Evans, S. Haiber, M. Nilsson, G. A. Morris, Anal. Chem. 2009, 81, 4548-4550]. However, little is known about the conditions required for such a separation, for example, the concentrations and concentration ratios of surfactant and solutes. The aim of this study was to explore the concentration range over whichmatrix-assisted DOSY using the surfactant SDS can achieve diffusion resolution of a simple model set of isomers, the monomethoxyphenols. The results show that the separation is remarkably robust with respect to both the concentrations and the concentration ratios of surfactant and solutes, supporting the idea that MAD may become a valuable tool formixture analysis. © 2010 John Wiley & Sons, Ltd.

Matrix-assisted diffusion-ordered spectroscopy

Diffusion NMR is a potentially routine tool in the analysis of mixtures, from industrial and synthetic outputs to natural products. However, the technique struggles to resolve species of similar size. Matrix-assisted DOSY offers a flexible approach to resolving such ambiguities on the basis of the chemical structures involved and on their interactions with a larger co-solute or matrix. The use of chromatographic supports, surfactants and polymers, in particular, is illustrated. The resolution of a wide range of different analyte mixtures, on the basis of differences in chemical structure and in stereochemistry, is demonstrated.

Lattice Boltzmann modeling of fluid flow and solute transport in karst aquifers

A novel modeling approach is applied to karst hydrology. Long-standing problems in karst hydrology and solute transport are addressed using Lattice Boltzmann methods (LBMs). These methods contrast with other modeling approaches that have been applied to karst hydrology. The motivation of this dissertation is to develop new computational models for solving ground water hydraulics and transport problems in karst aquifers, which are widespread around the globe. This research tests the viability of the LBM as a robust alternative numerical technique for solving large-scale hydrological problems. The LB models applied in this research are briefly reviewed and there is a discussion of implementation issues. The dissertation focuses on testing the LB models. The LBM is tested for two different types of inlet boundary conditions for solute transport in finite and effectively semi-infinite domains. The LBM solutions are verified against analytical solutions. Zero-diffusion transport and Taylor dispersion in slits are also simulated and compared against analytical solutions. These results demonstrate the LBM’s flexibility as a solute transport solver. The LBM is applied to simulate solute transport and fluid flow in porous media traversed by larger conduits. A LBM-based macroscopic flow solver (Darcy’s law-based) is linked with an anisotropic dispersion solver. Spatial breakthrough curves in one and two dimensions are fitted against the available analytical solutions. This provides a steady flow model with capabilities routinely found in ground water flow and transport models (e.g., the combination of MODFLOW and MT3D). However the new LBM-based model retains the ability to solve inertial flows that are characteristic of karst aquifer conduits. Transient flows in a confined aquifer are solved using two different LBM approaches. The analogy between Fick’s second law (diffusion equation) and the transient ground water flow equation is used to solve the transient head distribution. An altered-velocity flow solver with source/sink term is applied to simulate a drawdown curve. Hydraulic parameters like transmissivity and storage coefficient are linked with LB parameters. These capabilities complete the LBM’s effective treatment of the types of processes that are simulated by standard ground water models. The LB model is verified against field data for drawdown in a confined aquifer.

Lattice Boltzmann Modeling of Fluid Flow and Solute Transport in Karst Aquifers

A novel modeling approach is applied to karst hydrology. Long-standing problems in karst hydrology and solute transport are addressed using Lattice Boltzmann methods (LBMs). These methods contrast with other modeling approaches that have been applied to karst hydrology. The motivation of this dissertation is to develop new computational models for solving ground water hydraulics and transport problems in karst aquifers, which are widespread around the globe. This research tests the viability of the LBM as a robust alternative numerical technique for solving large-scale hydrological problems. The LB models applied in this research are briefly reviewed and there is a discussion of implementation issues. The dissertation focuses on testing the LB models. The LBM is tested for two different types of inlet boundary conditions for solute transport in finite and effectively semi-infinite domains. The LBM solutions are verified against analytical solutions. Zero-diffusion transport and Taylor dispersion in slits are also simulated and compared against analytical solutions. These results demonstrate the LBM’s flexibility as a solute transport solver. The LBM is applied to simulate solute transport and fluid flow in porous media traversed by larger conduits. A LBM-based macroscopic flow solver (Darcy’s law-based) is linked with an anisotropic dispersion solver. Spatial breakthrough curves in one and two dimensions are fitted against the available analytical solutions. This provides a steady flow model with capabilities routinely found in ground water flow and transport models (e.g., the combination of MODFLOW and MT3D). However the new LBM-based model retains the ability to solve inertial flows that are characteristic of karst aquifer conduits. Transient flows in a confined aquifer are solved using two different LBM approaches. The analogy between Fick’s second law (diffusion equation) and the transient ground water flow equation is used to solve the transient head distribution. An altered-velocity flow solver with source/sink term is applied to simulate a drawdown curve. Hydraulic parameters like transmissivity and storage coefficient are linked with LB parameters. These capabilities complete the LBM’s effective treatment of the types of processes that are simulated by standard ground water models. The LB model is verified against field data for drawdown in a confined aquifer.

Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.