Methods to measure apparent diffusion coefficients in compacted bentonite clays and data interpretation

1989 ◽  
Vol 16 (4) ◽  
pp. 434-443 ◽  
Author(s):  
S. C. H. Cheung
Keyword(s):  
Diffusion Coefficient ◽  
Apparent Diffusion Coefficient ◽  
Diffusion Coefficients ◽  
Data Interpretation ◽  
Clay Particles ◽  
Apparent Diffusion Coefficients ◽  
Compacted Bentonite ◽  
Diffusion Parameters ◽  
Apparent Diffusion ◽  
Bentonite Clays

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.

Diffusion of Lead from a Perforated Titanium-Shell Lead-Matrix Container

1991 ◽  
Vol 257 ◽  
Author(s):  
P. Mani Mathew ◽  
Paul A. Krueger ◽  
M. Krause
Keyword(s):  
Diffusion Coefficient ◽  
Apparent Diffusion Coefficient ◽  
Diffusion Coefficients ◽  
Element Model ◽  
Dry Mass ◽  
Silica Sand ◽  
Apparent Diffusion Coefficients ◽  
Apparent Diffusion ◽  
Buffer Mixture ◽  
Source Concentration

ABSTRACTThis paper describes experiments and analyses conducted to determine the range of apparent diffusion coefficients of lead diffusing from an intentionally perforated lead-matrix titanium-shell container into a compacted 1:1 (by dry mass) silica-sand/sodium-bentonite buffer mixture saturated with Standard Canadian Shield Saline Solution at 363 K. Analysis of the experimental data using a single apparent diffusion coefficient could not explain the findings. A possible explanation of the behaviour is presented here. It uses a 2–D finite-element model with six lead species having six different apparent diffusion coefficients. The model can explain the data satisfactorily. Sixty-three percent of the source concentration consisted of slow-moving species, with an apparent diffusion coefficient of 10-15 m2 /s, whereas the fastest species, with an apparent diffusion coefficient of 10-10 m2 /s, constituted only three percent of the source concentration.

scholarly journals Classification of paediatric brain tumours by diffusion weighted imaging and machine learning

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Jan Novak ◽  
Niloufar Zarinabad ◽  
Heather Rose ◽  
Theodoros Arvanitis ◽  
Lesley MacPherson ◽  
...  
Keyword(s):  
Diffusion Coefficient ◽  
Apparent Diffusion Coefficient ◽  
Posterior Fossa ◽  
Brain Tumours ◽  
Diffusion Weighted Imaging ◽  
Regions Of Interest ◽  
Apparent Diffusion Coefficients ◽  
Diffusion Weighted ◽  
Apparent Diffusion ◽  
Paediatric Brain Tumours

AbstractTo determine if apparent diffusion coefficients (ADC) can discriminate between posterior fossa brain tumours on a multicentre basis. A total of 124 paediatric patients with posterior fossa tumours (including 55 Medulloblastomas, 36 Pilocytic Astrocytomas and 26 Ependymomas) were scanned using diffusion weighted imaging across 12 different hospitals using a total of 18 different scanners. Apparent diffusion coefficient maps were produced and histogram data was extracted from tumour regions of interest. Total histograms and histogram metrics (mean, variance, skew, kurtosis and 10th, 20th and 50th quantiles) were used as data input for classifiers with accuracy determined by tenfold cross validation. Mean ADC values from the tumour regions of interest differed between tumour types, (ANOVA P < 0.001). A cut off value for mean ADC between Ependymomas and Medulloblastomas was found to be of 0.984 × 10−3 mm2 s−1 with sensitivity 80.8% and specificity 80.0%. Overall classification for the ADC histogram metrics were 85% using Naïve Bayes and 84% for Random Forest classifiers. The most commonly occurring posterior fossa paediatric brain tumours can be classified using Apparent Diffusion Coefficient histogram values to a high accuracy on a multicentre basis.

A Power-Law Mixing Rule for Predicting Apparent Diffusion Coefficients of Binary Gas Mixtures in Heavy Oil

2017 ◽  
Vol 140 (5) ◽  
Author(s):  
Hyun Woong Jang ◽  
Daoyong Yang ◽  
Huazhou Li
Keyword(s):  
Diffusion Coefficient ◽  
Apparent Diffusion Coefficient ◽  
Heavy Oil ◽  
Diffusion Coefficients ◽  
Gas Mixtures ◽  
Gas Diffusion ◽  
Gas Mixture ◽  
Mixing Rule ◽  
Heavy Oils ◽  
Apparent Diffusion

A power-law mixing rule has been developed to determine apparent diffusion coefficient of a binary gas mixture on the basis of molecular diffusion coefficients for pure gases in heavy oil. Diffusion coefficient of a pure gas under different pressures and different temperatures is predicted on the basis of the Hayduk and Cheng's equation incorporating the principle of corresponding states for one-dimensional gas diffusion in heavy oil such as the diffusion in a pressure–volume–temperature (PVT) cell. Meanwhile, a specific surface area term is added to the generated equation for three-dimensional gas diffusion in heavy oil such as the diffusion in a pendant drop. In this study, the newly developed correlations are used to reproduce the measured diffusion coefficients for pure gases diffusing in three different heavy oils, i.e., two Lloydminster heavy oils and a Cactus Lake heavy oil. Then, such predicted pure gas diffusion coefficients are adjusted based on reduced pressure, reduced temperature, and equilibrium ratio to determine apparent diffusion coefficient for a gas mixture in heavy oil, where the equilibrium ratios for hydrocarbon gases and CO2 are determined by using the equilibrium ratio charts and Standing's equations, respectively. It has been found for various gas mixtures in two different Lloydminster heavy oils that the newly developed empirical mixing rule is able to reproduce the apparent diffusion coefficient for binary gas mixtures in heavy oil with a good accuracy. For the pure gas diffusion in heavy oil, the absolute average relative deviations (AARDs) for diffusion systems with two different Lloydminster heavy oils and a Cactus Lake heavy oil are calculated to be 2.54%, 14.79%, and 6.36%, respectively. Meanwhile, for the binary gas mixture diffusion in heavy oil, the AARDs for diffusion systems with two different Lloydminster heavy oils are found to be 3.56% and 6.86%, respectively.

Study on Retardation Mechanism of 3H, 99Tc, 137Cs, 237Np and 241AM in Compacted Sodium Bentonite

1992 ◽  
Vol 294 ◽  
Author(s):  
H. Sato ◽  
T. Ashida ◽  
Y. Kohara ◽  
M. Yui
Keyword(s):  
Diffusion Coefficient ◽  
Apparent Diffusion Coefficient ◽  
Atmospheric Condition ◽  
Diffusion Method ◽  
Dry Density ◽  
Sodium Bentonite ◽  
Apparent Diffusion Coefficients ◽  
Anion Exclusion ◽  
Apparent Diffusion ◽  
The One

ABSTRACTThe apparent diffusion coefficients were measured at room temperature (about 23°C) under atmospheric condition by the one-dimensional non-steady state diffusion method for 3H, 99Tc, 137Cs, 237Np and 241Am in compacted sodium-bentonite saturated with water. Sodium-bentonite, which is commercially available as KunigelVl®, was used in this study. Experiments were carried out in the density range of 0.4–2.0 (×103kg/m3). Bentonite in the cell was prepared to be saturated with distilled water. The measured apparent diffusion coefficient decreases with increasing dry density of bentonite. That the apparent diffusion coefficient of 3H decreased as a function of dry density of bentonite appears to be the effect of the change of porous structure with dry density of bentonite. 99Tc may be retarded by anion-exclusion because dominant diffusion specie of 99Tc is pertechnetate ion under atmospheric condition. Retardation for 137Cs may be caused by ion-exchange on bentonite. The sorption, anion-exclusion and molecular filtration are considered as a retardation mechanism for 237Np and 241Am because those dominant species are negatively charged and of large ionic size.

Distribution Coefficients and Apparent Diffusion Coefficients of Cesium in Compacted Bentonites

1999 ◽  
Vol 556 ◽  
Author(s):  
Akiko Okamoto ◽  
Kazuya Idemitsu ◽  
Hirotaka Furuya ◽  
Yaohiro Inagaki ◽  
Tatsumi Arima
Keyword(s):  
Diffusion Coefficients ◽  
Distribution Coefficients ◽  
Dry Density ◽  
Apparent Diffusion Coefficients ◽  
Compacted Bentonite ◽  
Apparent Diffusion ◽  
Tracer Solution ◽  
Cesium Concentration ◽  
Penetration Profile ◽  
Very High

AbstractDistribution coefficients and apparent diffusion coefficients of cesium in some compacted bentonites were determined by the penetration profile method. Cylindrical compacted bentonites with the dry density of 0.8 to 1.6 Mg/m3 were contacted with tracer solutions containing 1000, 100 or 10 ppm of cesium. The apparent diffusion coefficients were obtained from the concentration profiles of cesium in compacted bentonites. The distribution coefficients were obtained concurrently by dividing the intercepts of the profiles by the concentration of the tracer solution. The apparent diffusion coefficients of cesium in compacted bentonite were obtained in the range of 0.42 to 9.6· 10−12 m2/s. The apparent diffusion coefficients in the compacted bentonite contacted with three different concentrations of cesium tended to decrease with increasing dry density of the specimen; but, they had no dependence on cesium concentration within a factor of 3 at the same dry density. The distribution coefficient of cesium for the specimens contacted with three different concentrations of cesium were obtained in the range of 0.3 to 90 L/kg and had little dependence on dry density. The distribution coefficients obtained in the compacted bentonites were dependent on pH of the solution rather than concentration of cesium. These distribution coefficients obtained in the compacted bentonites were 10 to 1000 times smaller than those obtained by batch experiments. The data suggest that not all sorption sites for cesium are available in highly compacted bentonite. It is necessary to consider surface diffusion as a significant migration mechanism of cesium through the compacted bentonites at very high pH condition such as 12.

The Dependence of the Diffusion Coefficients of 3H and Cs on Grain Size in Compacted Montmorillonite

1997 ◽  
Vol 506 ◽  
Author(s):  
Mamoru Nakajima ◽  
Tamotsu Kozaki ◽  
Hiroyasu Kato ◽  
Seichi Sato ◽  
Hiroshi Ohashi
Keyword(s):  
Grain Size ◽  
Diffusion Coefficients ◽  
Dry Density ◽  
Formation Factor ◽  
Apparent Diffusion Coefficients ◽  
Compacted Bentonite ◽  
Buffer Material ◽  
Apparent Diffusion ◽  
Different Grain Size ◽  
High Level

ABSTRACTCompacted bentonite is a candidate buffer material in geological disposal of high-level radioactive waste. The transport of radionuclides in compacted bentonite is dominated by diffusion, because of its very low permeability. In this study, we focused on the grain size of clay mineral, which is considered to be closely related to the formation factor in the pore water diffusion model[1,2]. The apparent diffusion coefficients (Da) of HTO and cesium ions in compacted clays were determined using montmorillonite samples with different grain size and dry density, and the effect of the grain size on diffusion behavior was discussed.

Effect of Carbonate on the Migration Behavior of Lanthanides in Compacted Bentonite

MRS Advances ◽  
2018 ◽  
Vol 3 (21) ◽  
pp. 1155-1160 ◽  
Author(s):  
Kazuya Idemitsu ◽  
Kazuyuki Fujii ◽  
Noriyuki Maeda ◽  
Yuki Kakoi ◽  
Noriya Okubo ◽  
...  
Keyword(s):  
Diffusion Coefficient ◽  
Atomic Number ◽  
Diffusion Coefficients ◽  
Chemical Species ◽  
Dry Density ◽  
Migration Behavior ◽  
Bicarbonate Concentration ◽  
Apparent Diffusion Coefficients ◽  
Carbonate Ion ◽  
Apparent Diffusion

ABSTRACTThe apparent diffusion coefficients of La, Nd, Eu, Dy, Er, and Lu in compacted bentonites were investigated at various bicarbonate concentrations. The apparent diffusion coefficients of these lanthanides tended to decrease with increasing dry density. At bicarbonate concentrations below 0.25 M, lanthanum had the largest diffusion coefficient (ca. 10-13 m2/s) at 1.0 Mg/m3, and the diffusion coefficient decreased with increasing atomic number. On the other hand, at bicarbonate concentrations above 0.25 M, lutetium had the largest diffusion coefficient, and the diffusion coefficient decreased with decreasing atomic number. In particular, lanthanum and neodymium had diffusion coefficients below 10-14 m2/s, even at 1.0 Mg/m3. The diffusion coefficient of europium was around 10-13 m2/s at 1.0 Mg/m3 and was influenced less by the bicarbonate concentration. The diffusion coefficient of lutetium increased from 2 × 10-14 to 10-12 m2/s as the bicarbonate concentration was increased to 1.0 M. The concentration of carbonate ion in the pore water of bentonite is estimated to be much lower than that in solutions in contact with bentonite from the viewpoints of solubility and chemical species of lanthanides.

scholarly journals Distinguishing Positional Uncertainty from True Mobility in Single-Molecule Trajectories That Exhibit Multiple Diffusive Modes

2012 ◽  
Vol 18 (4) ◽  
pp. 793-797 ◽  
Author(s):  
Mark Kastantin ◽  
Daniel K. Schwartz
Keyword(s):  
Diffusion Coefficient ◽  
Single Molecule ◽  
Apparent Motion ◽  
Diffusion Coefficients ◽  
Hydrophobic Surface ◽  
Time Interval ◽  
Apparent Diffusion Coefficients ◽  
Positional Uncertainty ◽  
Apparent Diffusion ◽  
Diffusive Modes

AbstractAlthough imperfect spatial localization in single-molecule object tracking experiments has long been recognized to induce apparent motion in an immobile population of molecules, this effect is often ignored or incorrectly analyzed for mobile molecules. In particular, apparent motion due to positional uncertainty is often incorrectly assigned as a distinct diffusive mode. Here we show that, due to both static and dynamic contributions, positional uncertainty does not introduce a new apparent diffusive mode into trajectories, but instead causes a systematic shift of each measured diffusion coefficient. This shift is relatively simple: a factor of σ2/Δt is added to each diffusion coefficient, where σ is the positional uncertainty length scale and Δt is the time interval between observations. Therefore, by calculating the apparent diffusion coefficients as a function of Δt, it is straightforward to separate the true diffusion coefficients from the effective positional uncertainty. As a concrete demonstration, we apply this approach to the diffusion of the protein fibrinogen adsorbed to a hydrophobic surface, a system that exhibits three distinct modes of diffusion.

Effect of pH on Plutonium Migration Behavior in Compacted Bentonite

MRS Advances ◽  
2016 ◽  
Vol 1 (61) ◽  
pp. 4011-4017
Author(s):  
Ryo Hamada ◽  
Noriyuki Maeda ◽  
Kazuya Idemitsu ◽  
Yaohiro Inagaki ◽  
Tatsumi Arima ◽  
...  
Keyword(s):  
Pore Water ◽  
Diffusion Coefficients ◽  
High Level Waste ◽  
Migration Behavior ◽  
Effect Of Ph ◽  
Apparent Diffusion Coefficients ◽  
Compacted Bentonite ◽  
Ph Values ◽  
Apparent Diffusion ◽  
High Level

ABSTRACTIn disposing of high-level radioactive waste, the drop in pH in the repository as the iron overpack corrodes must be considered. Plutonium migration behavior may be affected by the pH of pore water in compacted bentonite barriers in high-level waste repositories. To examine the effect of pH on migration behavior, H-bentonite was prepared by treating Japanese Na-bentonite, Kunipia-F, with hydrochloric acid. Diffusion experiments were performed with mixtures of Na- and H-bentonites. The pH value in the pore water of the water-saturated bentonite mixtures decreased from 8 to 3 as the mixing ratio of H-bentonite increased. Diffusion experiments were carried out by using238Pu then apparent diffusion coefficients were determined from the plutonium distribution in the specimens. The apparent diffusion coefficients were on the order of 10-13to 10-12m2/s at pH values lower than 4, whereas they were less than 10-14m2/s at pH values higher than 6.5. These results indicate that plutonium diffused faster as Pu3+or PuO22+due to disproportionation at lower pH while plutonium could be retarded as Pu(OH)40by sorption on bentonite at higher pH.

scholarly journals Diffusion of Resveratrol in Silica Alcogels

Molecules ◽  
2019 ◽  
Vol 24 (21) ◽  
pp. 3931 ◽  
Author(s):  
Yuxiang Wang ◽  
Zeyu Kao ◽  
Ting Zhang ◽  
Yujun Zhang ◽  
Lili Qin ◽  
...  
Keyword(s):  
Diffusion Coefficient ◽  
Electron Microscope ◽  
Diffusion Coefficients ◽  
Silica Aerogel ◽  
Freeze Drying ◽  
Concentration Data ◽  
Outward Diffusion ◽  
Apparent Diffusion Coefficients ◽  
Apparent Diffusion ◽  
Solvent Replacement

The trans-resveratrol (RSV)-loaded silica aerogel (RLSA) was prepared by the sol-gel method, adding the drug during the aging process, solvent replacement and freeze drying. A series of characterizations showed that RSV stays in the silica aerogel in two ways. First, RSV precipitates due to minimal solubility in water during the solvent replacement process. After freeze drying, the solvent evaporates and the RSV recrystallizes. It can be seen from scanning electron microscope (SEM) and transmission electron microscope (TEM) images that the recrystallized RSV with micron-sized long rod-shaped is integrated with the dense silica network skeleton. Second, from small-angle X-ray scattering (SAXS) results, a portion of the RSV molecules is not crystallized and the size is extremely small. This can be attached to the primary and secondary particles of silica to enhance its network structure and inhibit shrinkage, which is why the volume and pore size of RLSA is larger. In addition, the diffusion of RSV in silica alcogel was studied by a one-dimensional model. The apparent diffusion coefficients of inward diffusion, outward diffusion and internal diffusion were calculated by fitting the time- and position-dependent concentration data. It was found that the outward diffusion coefficient (5.25 × 10−10 m2/s) is larger than the inward (2.93 × 10−10 m2/s), which is probably due to the interface effect. The diffusion coefficients obtained for different concentrations in the same process (inward diffusion) are found to be different. This suggests that the apparent diffusion coefficient obtained is affected by molecular adsorption.

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