Measurement Of Effective Diffusion Coefficients Research Articles

Water Effective Diffusion Coefficient in Dairy Powder Calculated by Digital Image Processing and through Machine Learning Algorithms of CLSM Micrographs.

Rehydration of dairy powders is a complex and essential process. A relatively new quantitative mechanism for monitoring powders' rehydration process uses the effective diffusion coefficient. This research focused on modifying a previously used labor-intensive method that will be able to automatically measure the real-time water diffusion coefficient in dairy powders based on confocal microscopy techniques. Furthermore, morphological characteristics and local hydration of individual particles were identified using an imaging analysis procedure written in Matlab©-R2023b and image analysis through machine learning algorithms written in Python™-3.11. The first model includes segmentation into binary images and labeling particles during water diffusion. The second model includes the expansion of data set selection, neural network training and particle markup. For both models, the effective diffusion follows Fick's second law for spherical geometry. The effective diffusion coefficient on each particle was computed from the dye intensity during the rehydration process. The results showed that effective diffusion coefficients for water increased linearly with increasing powder particle size and are in agreement with previously used methods. In summary, the models provide two independent machine measurements of effective diffusion coefficient based on the same set of micrographs and may be useful in a wide variety of high-protein powders.

Measurement of Effective Hydrogen-Methane Gas Diffusion Coefficients in Reservoir Rocks

Summary If hydrogen is stored in depleted gas fields, the remaining hydrocarbon gas can be used as cushion gas. The composition of the backproduced gas depends on the magnitude of mixing between the hydrocarbon gas and the hydrogen injected. One important parameter that contributes to this process of mixing is molecular diffusion. Although diffusion models are incorporated in the latest commercial reservoir simulators, effective diffusion coefficients for specific rock types, pressures, temperatures, and gas compositions are not available in the literature. Thus, laboratory measurements were performed to improve storage performance predictions for an underground hydrogen storage (UHS) project in Austria. An experimental setup was developed that enables measurements of effective multicomponent gas diffusion coefficients. Gas concentrations are detected using infrared light spectroscopy, which eliminates the necessity of gas sampling. To test the accuracy of the apparatus, binary diffusion coefficients were determined using different gases and at multiple pressures and temperatures. Effective diffusion coefficients were then determined for different rock types. Experiments were performed multiple times for quality control and to test reproducibility. The measured binary diffusion coefficients without porous media show a very good agreement with the published literature data and available correlations based on the kinetic gas theory (Chapman-Enskog, Fuller-Schettler-Giddings). Measurements of effective diffusion coefficients were performed for three different rock types that represent various facies in a UHS project in Austria. A correlation between static rock properties and effective diffusion coefficients was established and used as input to improve the numerical model of the UHS. This input is crucial for the simulation of backproduced gas composition and properties which are essential parameters for storage economics. In addition, the results show the impact of pressure on effective diffusion coefficients, which impacts UHS performance.

Theoretical and experimental study of foam stability mechanism by nanoparticles: Interfacial, bulk, and porous media behavior

Abstract Foam flooding has been applied as a promising method in enhanced oil recovery to obviate the challenges of gas flooding such as fingering, channeling and overriding. However, long-term foam stability is crucial for mobility control. In this work, the effective mechanisms on foam stability in the presence of CaCO3 nanoparticles were assessed both theoretically and experimentally. The static and dynamic behaviors of cationic surfactant (HTAB) foam in the presence of CaCO3 nanoparticles with different hydrophobicity were evaluated. The CaCO3 nanoparticles were treated with a series of long-chain fatty acids to generate a range of wettability. Afterward, the underlying mechanisms were revealed by conducting the supplementary experiments, including measurements of effective diffusion coefficient (Deff), Henry's constant (KH), interfacial tension (IFT), and zeta potential of nanoparticles. Further, efforts were made to analyze the interfacial interactions using xDLVO theory. By increasing of nanoparticles hydrophobicity, the continuous reduction of effective diffusion coefficient, solubility, and IFT was observed, which means higher foam stability. However, the adsorption of modified nanoparticles on the air-solution interface could reduce the total disjoining pressure between two parallel plates, supported by xDLVO prediction. This phenomenon has an adverse effect on the thin film stability. Therefore, there would be an optimum extent of nanoparticles surface modification to obtain the most stable foam stability, which was in agreement with the both bulk and porous media observations. The optimum condition was shifted to the nanoparticles modified with the lower chain fatty acids by increasing the concentration of fatty acid solutions. In this case, the negative effect of reduced disjoining pressure was more pronounced.

Measurement of effective diffusion coefficients in dairy powders by confocal microscopy and sorption kinetic profiles

Abstract A new method for the visualisation and determination of local diffusion coefficients in dairy powders is described based on real-time visualisation of penetration of fluorescent dyes into individual particles of spray-dried dairy powders including skim milk powder, milk protein concentrate and whey protein isolate. The rehydration process was controlled by adding polyethylene glycol (PEG) as a viscosity modifier to the aqueous phase in ratios of 1:0, 1:1, 1:3 and 1:4 aqueous rhodamine to PEG, respectively. Real-time effective diffusivity values were obtained from analysis of confocal laser scanning microscope images. Particle size was measured optically. Results indicated that for all dairy powders, rehydration rates were highly dependent on particle size. Effective diffusivity increased linearly with increasing particle size and average effective diffusivity of the liquid phase was calculated for all particle size distributions using this dependence. The Guggenheim-Anderson-de Boer (GAB) water sorption relationship was used to model water sorption isotherms over a broad range of water activities. Vapour phase systems had significantly higher effective diffusivity than liquid phase systems. The results obtained by this new method is broadly in agreement with previously published works, suggesting this new method may be used to measure the hydration of individual powder particles.

The diffusion of SO42− in Opalinus Clay: Measurements of effective diffusion coefficients and evaluation of their importance in view of microbial mediated reactions in the near field of radioactive waste repositories

Through-diffusion experiments with 36Cl−, 35SO42− and HTO in Opalinus Clay (OPA) samples from a deep borehole in North-East Switzerland (Benken; BE) have been performed. The effect of burial depth on the experimental results has been investigated.It could be shown that the effective diffusion coefficients decrease with sample depth for all three tracers. Moreover, there was a good correlation with the texture of the samples. The diffusion coefficients for HTO are the largest (De = 5.4–8.8 × 10−12 m2 s−1), followed by those for 36Cl− (De = 0.7–1.9 × 10−12 m2 s−1), and finally 35SO42− (De = 0.2–0.6 × 10−12 m2 s−1). 36Cl− was partially excluded from the total porosity resulting in an accessible porosity smaller than the total porosity (εCl = 0.041–0.064). 35SO42−, on the other hand, showed interaction with OPA resulting in a capacity factor (α) larger than the total porosity (εtot = 0.13–0.16). Using extended Archie's law the accessible porosity for 35SO42− was estimated between 0.013 and 0.030. This enabled to evaluate the sorption coefficient of 35SO42− from the measured capacity factor, resulting in values of Kd between 6 × 10−5 and 9 × 10−5 m3 kg−1.

Atomic Transport in Nano-Crystalline Silicides Studied by <i>In Situ</i> Auger Electron Spectroscopy: Interfacial Reaction Effect

Silicide growth via reaction between a metallic film and a Si substrate has been well documented. In general, atomic transport kinetic during the growth of silicides is considered to be the same as during equilibrium diffusion, despite the reaction and its possible injection of point-defects in the two phases on each side of the interface. To date, the main studies aiming to investigate atomic transport during silicide growth used immobile markers in order to determine which element diffuses the fastest during growth and in which proportion. The quantitative measurements of effective diffusion coefficients during growth was also performed using Deal-and-Groove-type of models, however, these effective coefficients are in general not in agreement with the interdiffusion coefficients calculated using the equilibrium diffusion coefficients measured during diffusion experiments. In general, atomic transport kinetic measurements during growth and without growth are performed using different types of samples for experimental reasons. In this paper, we discuss the possible use of ultrahigh vacuum in situ Auger electron spectroscopy in order to measure the effective diffusion coefficient during growth, as well as the equilibrium self-diffusion coefficients, in the same samples, in the same experimental conditions. The first results on the Pd-Si system show that atomic transport during Pd2Si growth is several orders of magnitude faster than at equilibrium without interfacial reaction.

Measurements of effective diffusion coefficients of helium and hydrogen through gypsum

An experimental apparatus, which was based on the ¼-scale garage previously used for studying helium release and dispersion in our laboratory, was used to obtain effective diffusion coefficients of helium and hydrogen (released as forming gas for safety reasons) through gypsum panel. Two types of gypsum panel were used in the experiments. Helium or forming gas was released into the enclosure from a Fischer burner11Certain commercial entities, equipment, or materials may be identified in this document in order to describe an experimental procedure or concept adequately. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the entities, materials, or equipment are necessarily the best available for the purpose. located near the enclosure floor for a fixed duration and then terminated. Eight thermal-conductivity sensors mounted at different vertical locations above the enclosure floor were used to monitor the temporal and spatial gas concentrations. An electric fan was used inside the enclosure to mix the released gas to ensure a spatially uniform gas concentration to minimize stratification. The temporal variations of the pressure difference between the enclosure interior and the ambience were also measured. An analytical model was developed to extract the effective diffusion coefficients from the experimental data.

Experimental measurements of effective diffusion coefficient of oxygen–nitrogen mixture in PEM fuel cell diffusion media

PEM fuel cells are increasingly designed to operate at high current densities. At these densities, mass transport limitations become very significant, but they are not well understood, with many modeling studies but few experimental observations. The use of accurate transport coefficients to simulate the mass transport at high current densities is crucial. In this study, experimental measurements have been carried out to determine the effective diffusion coefficient in the carbon paper gas diffusion layer that is commonly used in PEM fuel cells. It was found that almost all the existing theoretical models significantly overpredict the effective diffusion coefficient by as much as 4–5 times; thus, underestimating the transport limitations considerably. Further, the effects of temperature, Teflon treatment for hydrophobicity and porosity on the effective diffusion coefficient were investigated. It was found that temperature does not affect the overall diffusibility of the gas. The diffusibility is decreased with the increase of Teflon treatment and decrease in porosity. Further work on better understanding the diffusion process in the gas diffusion layer is under way.

Tracer Diffusion in Sintered Stainless Steel Filters: Measurement of Effective Diffusion Coefficients and Implications for Diffusion Studies with Compacted Clays

AbstractThe use of porous filters is indispensable in laboratory- and field-scale diffusion studies, where sample confinement is needed for mechanical reasons. Examples are diffusion studies with compacted swelling clays or brittle clay stones. Knowledge of the diffusion properties of these filters is important in cases where they contribute significantly to the overall diffusive resistance in the experimental setup. In the present study, measurements of effective diffusion coefficients (Db) in porous, stainless steel filter discs are reported for tritiated H2O (HTO), 22Na+, Cs+, and Sr2+ before and after use of the filters in diffusion experiments with different clay minerals. The Db values for used filters were found to be less than those of the as-received filters by ∼30–50%. The Db values measured for the diffusion of HTO, 22Na+, Cs+, and Sr2+ in unused and used stainless steel filter discs correlated fairly well with the respective molecular diffusion coefficients in bulk water. Although such correlations are inherently associated with some uncertainties, they allow reasonable estimates to be made for diffusants for which no Db values are available. For the first time, a procedure is outlined that allows an integrative assessment to be made for the impact of the uncertainties in the filter diffusion properties on the combined standard uncertainties of the diffusion parameters obtained from through-diffusion experiments. This procedure can be used in the design and optimization of through-diffusion experiments in which the diffusive resistance of the porous filters must not be ignored. Shown here, as a general rule of thumb, is that, if the effective diffusion coefficient in the porous filter is at least three times larger than that in the clay, the choice of geometrical boundary conditions is rather uncritical, as long as the thickness of the clay sample is greater than that of the porous filters.

Direct measurement of effective diffusion coefficients in nanochannels using steady-state dispersion effects

We present a method to measure effective diffusion coefficients of fluorescently labeled molecules inside a nanofluidic system. Molecules with small diffusion coefficients show a larger lateral dispersion than highly diffusive species, which is counterintuitive. We performed measurements with wheat germ agglutinin proteins and obtained an effective diffusion coefficient which is four orders of magnitude lower than its free diffusion coefficient. Our technique which is a direct and relatively simple measurement of the effective diffusion coefficients inside nanochannels of well controlled dimensions could help fundamental studies in membranes and separation sciences.

Detection of open or closed porosity in low- κ dielectrics by solvent diffusion

The presence of open porosity in a porous interlayer dielectric (ILD) can seriously degrade the ultimate performance and reliability of a device. A simple method for detecting the open porosity in ILDs would facilitate the design of materials with pore morphologies compatible with the required specifications of a particular device. The measurement of effective diffusion coefficients in a low- κ ILD over a range of porosities is shown to permit the detection of open porosity. An example illustrating the simplicity of this method is presented using toluene solvent in a well-characterized porous organosilicate material. The result using this method is consistent with available data in the literature.

Model for the determination of diffusion coefficients of heterovalent ions in macroporous ion exchange resins by the zero-length column method

A generalized theoretical model for the measurement of effective diffusion coefficients of heterovalent ions in macroporous ion-exchange resins by the zero-length column method was developed. The model includes the resistance to mass transfer both in the particle and in the film and described ion fluxes with Nernst–Planck equations. Equilibrium was described using the Langmuir type empirical equation. The values of intraparticle diffusivity of Cu 2 + , Cd 2 + , Zn 2 + , and H + on commercial Lewatit TP-207 were obtained by non-linear regression, these values agree fairly well with data reported previously in literature. The following trend was observed: D Cu > D Zn > D Cd .

A generalized model for the measurement of effective diffusion coefficients of heterovalent ions in ion exchangers by the zero-length column method

A generalized theoretical model for the measurement of effective diffusion coefficients of heterovalent ions in ion exchange resins by the zero-length column method was developed. The model included the resistance to mass transfer both in the particle and in the film and described ion fluxes with Nernst–Planck equations. Equilibria were described using a model based on the mass action law. The values of intraparticle diffusivity of Cu 2+, Cd 2+, Zn 2+, and H + on commercial Amberlite IR-120 were obtained by non-linear regression, these values agree fairly well with data reported previously in literature. The following trend was observed: D Cu> D Zn> D Cd.

Effect of Hemoglobin Polymerization on Oxygen Transport in Hemoglobin Solutions

The effect of hemoglobin (Hb) polymerization on facilitated transport of oxygen in a bovine hemoglobin-based oxygen carrier was studied using a diffusion cell. In high oxygen tension gradient experiments (HOTG) at 37°C the diffusion of dissolved oxygen in polymerized Hb samples was similar to that in unpolymerized Hb solutions during oxygen uptake. However, in the oxygen release experiments, the transport by diffusion of dissolved oxygen was augmented by diffusion of oxyhemoglobin over a range of oxygen saturations. The augmentation was up to 30% in the case of polymerized Hb and up to 100% in the case of unpolymerized Hb solution. In experiments performed at constant, low oxygen tension gradients in the range of physiological significance, the augmentation effect was less than that in the HOTG experiments. Oxygen transport in polymerized Hb samples was approximately the same as that in unpolymerized samples over a wide range of oxygen tensions. However, at oxygen tensions lower than 30 mm Hg, there were more significant augmentation effects in unpolymerized bovine Hb samples than in polymerized Hb. The results presented here are the first accurate, quantitative measurements of effective diffusion coefficients for oxygen transport in hemoglobin-based oxygen carriers of the type being evaluated to replace red cells in transfusions. In all cases the oxygen carrier was found to have higher effective oxygen diffusion coefficients than blood.

Reactions of unconverted isocyanate in molded RIM parts and their implications to outgassing

AbstractA convenient, cheap, and reliable method was developed and evaluated to measure the extent of conversion and subsequent water/diisocyanate reaction kinetics for injection molded (RIM) parts using cryogenic grinding and conventional Fourier Transform Infra‐Red (FTIR) spectroscopy. The reliability of the method was independently confirmed by using in‐mold fiber‐optic FTIR and attenuated total reflectance spectroscopy (Priester, private communication, The Dow Chemical Company 1994). The reaction of isocyanate with water produces carbamic acid, which is believed to immediately decompose to carbon dioxide (CO2) and amine, leading to outgassing during the paint cure. Given previous measurements of effective diffusion coefficients of water and CO2, if the molded RIM parts are stored under typical humid conditions for hours, most of the CO2 should form as a product of isocyanate/water reaction and diffuse out of the part. However, our results indicate that relatively little CO2 evolution occurs during ambient storage for up to 6 h, and significant evolution occurs for long times during subsequent high temperature post cure. Therefore, in contrast to the earlier expectations, the outgassing phenomenon seems to be due to carbamic acids that decompose slowly at ambient conditions and become unstable at higher temperatures. Therefore, to assure minimum outgassing in this RIM system one must (1) operate the post cure oven at higher temperatures than the paint baking oven, or (2) keep parts in ambient storage at least for 24 h to allow slow decomposition of carbamic acids, or (3) transfer them to the post cure oven immediately after removal from the mold, thereby preventing possible water/diisocyanate reactions.

A new method for experimental measurement of diffusion coefficients in reservoir fluids

A simple method is presented for determining diffusion coefficients of dense gases in liquids using a PVT cell. When a non-equilibrium gas is brought into contact with a liquid in a sealed container at a constant temperature, the final state is determined by thermodynamic equilibrium. However, the time which is required to reach the final state is determined from the diffusion process in each phase. At the gas-liquid interface, thermodynamic equilibrium exists between the two phases at all times, but the position of the interface as well as the pressure may change with time. The rate of change of pressure and the interface position as a function of time depends on the rate of diffusion in each phase and therefore on the diffusion coefficients. No compositional measurements are necessary for this method of measuring diffusion coefficients; hence, it is less expensive than conventional methods. Results obtained by this method for the binary system of methane and n-pentane at 311 K and 70 bar yielded diffusion coefficients within ± 5% of literature values. The technique can be easily applied to multicomponent systems for measurement of effective diffusion coefficients in reservoir fluids.

Measurement of effective diffusion coefficient of radon in porous media with etched track radon monitors

We have developed two methods to measure the effective diffusion coefficient of radon in porous media. We used etch track type radon monitors to measure the radon exposure on both the exposure and the measuring sides. We have used a computer code to model the transport of radon through porous media. We found the effective diffusion coefficient by changing its value in the code to find the best fit of model calculation to experimental data.

液相が共存する高温用セメントの使用による，高温における多孔質体中ガス有効拡散係数の“その場”測定

液相が共存する高温用セメントの使用による，高温における多孔質体中ガス有効拡散係数の“その場”測定

数種の多孔性材料中における３重水素水の有効拡散係数

Diffusion coefficients of radionuclides in some porous structural materials and porous components of earth stratum are important as the basis for the safety evaluation of the storage and disposal of radioactive wastes.In our previous works, the method of analysis and experiment using a permeative type diffusion cell for measurement of effective diffusion coefficient was established, and experimental results were reported.In this paper, effective diffusion coefficients of 3H2O in mortar, concrete, brick, clay layer, and sand layer were measured, and characteristics of these pore structure were discussed on the basis of tourtusity factor.