Knudsen diffusion of various gases through a barium sulphate packed bed

The diffusion coefficients, D_k, of helium, krypton, carbon dioxide and air through a packed bed of barium sulphate calculated from the Knudsen diffusion flow equation were found to be a cumulative parameter obtained from the contribution of the diffusion coefficient through the voids of the packed bed, D_v, and the diffusion coefficient through the pores, D_p, within barium sulphate.The surface area of compacted and uncompacted material obtained from low temperature gas adsorption and the Brunauer, Emmett and Teller equation (BET), together with the void sizes and pore sizes in compacted material obtained by Barrett, Joyner and Halenda (B.J.H.) isotherm analysis, when compared with the surface area values obtained by Knudsen diffusion and permeametry, indicated that the coefficients D_v and D_p evaluate the void and pore areas in compacted barium sulphate, respectively.     

Effective diffusivity and optimum apparent density of vanadia catalysts for sulfur dioxide oxidation

The effective diffusivities of air and SO₂ in four industrial vanadium pentoxide catalysts were measured at steady-state using helium as the counter diffusing gas. An improved catalyst mounting technique and diffusion cell were employed. The nonsurface component of diffusion was successfully correlated using Bruggeman's model for tortuosity. and ¯a based on pore size distribution data or calculated from specific pore volume and surface. However, it was necessary to use flow porosity in place of open porosity. Since the same pore model can be used for the catalytic oxidation So₂, non-reacting flow measurements can be employed to predict effective diffusivities under reaction conditions in this case.With models for the effective diffusivity and the kinetics of the catalytic oxidation of SO₂, an optimum apparent density of the catalyst may be determined which gives the maximum rate of reaction per unit volume of catalyst. Calculations are given for the SVD catalyst.     

Surface diffusion of strongly adsorbing vapors in activated carbon by a differential permeation method

Conventional methods to determine surface diffusion of adsorbed molecules are proven to be inadequate for strongly adsorbing vapors on activated carbon. Knudsen diffusion permeability (B_k) for strongly adsorbing vapors cannot be directly estimated from that of inert gases such as helium. In this paper three models are considered to elucidate the mechanism of surface diffusion in activated carbon. The transport mechanism in all three models is a combination of Knudsen diffusion, viscous flow and surface diffusion. The collision reflection factor f (which is the fraction of molecules undergoing collision to the solid surface over reflection from the surface) of the Knudsen diffusivity is assumed to be a function of loading. It was found to be 1.79 in the limit of zero loading, and decreases as loading increases. The surface diffusion permeability increases sharply at very low pressures and then starts to decrease after it has reached a maximum (B_μm) at a threshold pressure. The initial rapid increase in the total permeability is mainly attributed to surface diffusion. Interestingly the B_μms for all adsorbates appear at the same volumetric adsorbed phase concentration, suggesting that the volume of adsorbed molecules may play an important role in the “surface” diffusion mechanism in activated carbon.     

Effective diffusion constant and adsorption constant of synthesized alumina,zirconia, and alumina–zirconia composite material

In this study, Al₂O₃, ZrO₂, and Al₂O₃–ZrO₂ composite materials were prepared with the sol–gel technique. X-ray diffraction analysis, differential scanning calorimetry–thermogravimetry, scanning electron microscopy–energy-dispersive X-ray spectrometry, nitrogen adsorption isotherm measurements, and helium pycnometry were used to characterize the resultant materials. Effective diffusion coefficients of helium and hydrogen and the adsorption equilibrium constant of hydrogen in the resultant materials were determined using single-pellet moment technique. The effective diffusivities of helium and hydrogen in both ZrO₂ and Al₂O₃–ZrO₂ composite pellets were found to be smaller than the value found for Al₂O_3, due to the lower tortuosity factor values of the Al₂O₃ pellet. It was found that hydrogen was weakly adsorbed on all resultant materials.     

Helium-driven element depletion and phase transformation in irradiated Ti3SiC2 at high temperature

Future nuclear reactors and advanced power generators require materials with good stability and damage tolerance under harsh conditions, including high temperatures and high-dose radiation. Ti₃SiC₂ MAX phase has good physical properties and mechanical strength. It can remain crystalline under serious microstructure damage due to the nanolaminate structure. In this study, the effects of helium in irradiated Ti₃SiC₂ at up to 1100 °C were investigated by microstructural and chemical composition analysis. The concentrated helium can grow into large bubbles without significant confinement or capture by the nano-laminated layers. A new hexagonal to fcc phase transformation mechanism, driven mainly by the evolution of the helium bubbles accompanied by Si diffusion and depletion, is found and investigated. Si interstitials are forced to move out from the peak helium region by the helium evolution and segregate at the outermost surface, forming a thin Si-O layer, at 1100 °C. The formation of the fcc phase is the result of chemical compositional changes and local compressive stress contributed by He bubbles.     

Preparation and oxygen permeation of U‐shaped perovskite hollow‐fiber membranes

The oxygen permeation of dense U‐shaped perovskite hollow‐fiber membranes based on Ba_0.5Sr_0.5Co_0.8Fe_0.2O_3?δ prepared by a phase inversion spinning process is reported. The perovskite hollow fibers with totally dense wall were obtained with the outer diameter of 1.147 mm and the inner diameter of 0.691 mm. The dependences of the oxygen permeation on the air flow rate on the shell side, the helium flow rate on the core side, the oxygen partial pressures, and the operating temperatures were experimentally investigated. According to the Wagner theory, it follows that the oxygen transport through the U‐shaped hollow‐fiber membrane is controlled by both surface reaction and bulk diffusion at the temperature ranges of 750–950°C. High oxygen permeation flux of 3.0 ml/(min cm²) was kept for about 250 h at 950°C under the conditions of the air feed flow rate of 150 ml/min and the helium flow rate of 50 ml/min. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

采用泰勒分散法测量蜡分子扩散系数

蜡分子扩散系数是蜡沉积预测模型中非常重要的物性参数。为测量蜡分子（高碳数正构烷烃）在液相体系中的分子扩散系数,建立了基于泰勒分散法的扩散系数测量装置,并对装置操作注意事项进行了详细探讨。采用该装置测量了丙酮水溶液、n-C₆+n-C₇溶液以及甲醇水溶液中溶质在溶剂中的分子扩散系数,以文献值对测量值进行校验,验证了装置的可靠性。分别以n-C₁₈、n-C₂₀、n-C₂₂、n-C₂₄、n-C₂₆为溶质,以n-C₇为溶剂,在不同温度、浓度下测量蜡分子在液相体系中的分子扩散系数,并将实验测量值与Hayduck-Minhas关系式计算值进行比较。结果表明：蜡分子扩散系数随温度升高而线性增大,随溶液中蜡分子摩尔分数的增大而以指数形式减小;在相同条件下,高碳数正构烷烃的分子扩散系数低于低碳数正构烷烃的分子扩散系数。采用Hayduck-Minhas关系式的计算结果比实验测量结果平均小50%,应用于蜡沉积预测时,将低估蜡分子扩散质量流。     

Effective Diffusivities and Convective Coefficients for CaO‐CaSO4 and CaO‐CaCl2 Pellets

Diffusion and convective flow in the pores of pellets formed by compressing mixtures of calcined limestone and CaSO₄/CaCl₂ powders have been studied experimentally by using the single pellet moment technique. The experiments were conducted in a diffusion cell by flowing nitrogen gas (carrier) through both faces of the pellet. Limestone powder was calcined in an atmosphere of N₂ at 800 °C and mixed with CaSO₄/CaCl₂ for diffusion experiments. Effective diffusivity of helium has been estimated by exposing the upper face of the pellet to a pulse of and matching the response peak on the lower face of the pellet with theoretical expressions. The values of the effective diffusivities increased with temperature, but decreased with increasing CaSO₄/CaCl₂ content in the pellet. The convective flow contribution to the diffusion flux was found to increase with increasing pressure drop across the pellet.     

Helium behaviour in stoichiometric and hyper-stoichiometric UO2

Understanding the long-term behaviour of the UO₂ spent fuel in terms of helium build-up and oxidation is a very important issue for safety aspects of storage and disposal. Although helium behaviour in stoichiometric UO₂ has been studied by many authors, it has not been well established and there is a lack of experimental studies in non-stoichiometric UO₂. In this study, an infusion technique was chosen to introduce helium in stoichiometric and hyperstoichiometric single and polycrystalline UO₂ and polycrystalline U₃O₈ samples. Characterization of the samples before and after infusion and after thermal desorption measurements were performed by thermogravimetry, X-ray diffraction, laser flash technique and scanning electron microscopy. It was observed that the increase of stoichiometry in UO₂ affects barely the dissolved helium quantity (under the same infusion conditions as in stoichiometric), while it has a more pronounced influence on the helium diffusion. These two effects are much more pronounced for U₃O₈.     

Isothermal and nonisothermal,laminar, inelastic,non-Newtonian tube-entrance flow following a contraction

The general equations of motion, including inertial and axial-diffusion terms, and the equation of energy, including axial-diffusion and radial-convection terms, were coupled with a temperature-dependent form of the Powell-Eyring flow equation and then solved simultaneously by numerical methods employing quasilinearization and the method of lines for flow from a larger tube of circular cross section through an abrupt contraction into a smaller tube. The small-tube walls were at a temperature equal to or higher or lower than that of the entering fluid. The Powell-Eyring equation has been demonstrated to represent inelastic flow better than do other simple equations for many simple non-Newtonian fluids, including suspensions of solids in fluids. Results are reported for the case in which the fluid does not adhere to the upstream-tube surface but does adhere to the smaller-tube surface, which approximates flow into the tubes of shell-and-tube heat exchangers and reactors. The computer results presented here included radial and axial velocity profiles; temperature profiles; and lengths of the small tube, L_eq, having a fully-developed-flow pressure loss equivalent to the excess pressure loss attributable to flow contraction and development in the tube. These are presented for a large-tube-small-tube-diameter ratio of 2 as functions of N_Pe of 5–100; N_Re of 0.01–100; z/D for the smaller tube; ψ(H), a temperature factor; and the Powell-Eyring-equation constants. In plots of L_eq against a normalized N_Re, the isothermal-flow non-Newtonian data appear to be close to computed Newtonian functions at higher N_Re. The effects of axial diffusion of momentum and energy and the conditions where they become important are quantatively shown. The results are in good agreement with previous reports in those circumstances where comparisons are appropriate.     

The use of the simplex method to characterize dry cellulose acetate membranes for gas separations

The normal and log-normal distributions are used to describe the pore size distribution of dry asymmetric cellulose acetate membranes for CO₂/CH₄ separations. Various optimization techniques are implemented to determine the distribution parameters R and σ as well as the constants A₁, and A₂, related to pore structure and surface transport. respectively. By using the Simplex method, a unique solution for the characterization parameters is easily obtained irrespective of the starting search point. The permeation data of helium was used to characterize the membranes and determine the flow parameters which can be used to predict the performance of those membranes in separating CO₂/CH₄ mixtures.     

Effect of penetrant size and shape on its transport through a thermoset adhesive: I. n-alkanes

The diffusion behaviors of a series of n-alkanes, ranging from C₆ to C₁₇, through a polyamide-type polymeric matrix have been investigated by means of mass uptake measurements. Since n-alkanes are known to display negligible interactions with the polymer matrix, this study serves to isolate the effects of penetrant size and shape on the transport process without undue interference from polymer-penetrant interactions. It is established that the diffusion of the n-alkanes through the polymer matrix studied is Fickian and proceeds via a Henry's law-type mechanism. The diffusion coefficients, D, are evaluated based on a thin-film approximation of the Fickian equation. The activation energies of diffusion, E_d, are determined from the temperature dependence of D, using the Arrhenius equation. Correlations between the Arrhenius terms, E_d and D₀, are also established which enable the prediction of diffusion coefficients for similar polymer-penetrant systems. It is also demonstrated by means of activation energy calculations and molecular simulations that the n-alkanes assume a linear geometry within the polymer matrix and diffuse along their long axes.     

The diffusion coefficient of copper sulphate in aqueous solution

The diffusion coefficient, D, of CuSO₄ in aqueous solution was determined at 298.1 K by chronopotentiometry and also with a rotating disc electrode using the mixed control Levich equation. For 0 < [CuSO₄] < 0.05 mol dm^?3, D = {7.35 ± 0.18 ? (5.3 ± 1.4) [CuSO₄]^{$\text{1}\text{2}$}} × 10^?10 m² s^?1, at a constant ionic strength of 1.58 mol dm^?3 maintained with either H₂SO₄ or Na₂SO₄ (pH = 2). It was shown that substantial variations in the concentration of the supporting electrolyte had negligible effect on the above values of D. It was found that literature values of D vary over a three-fold range, even when corrected to the same temperature and CuSO₄ concentration. Much of this variation probably arises from rotating disc determinations carried out at disc potentials where activation control is significant. This problem is overcome if the mixed control Levich equation is used to treat the data instead of the commonly used simple (diffusion only) Levich equation.     

Estimating the self-diffusion and mutual diffusion coefficients of binary mixtures on the basis of a modified van der Waals model

The previously proposed model is used to determine the values of the self-diffusion coefficient of He, Ne, Ar, Kr, Xe, H₂, D₂, N₂, O2, CO₂, NH₃, and CH₄ in the liquid and dense gaseous states, which were compared with the experimental data obtained at a pressure of ≈200 MPa and a temperature of ≈500 K. The calculations are carried out with the use of the equation of state of these substances in the form of a modified van der Waals model. The self-diffusion model was generalized for the case of mutual diffusion in binary mixtures, which is based on the modified model of the van der Waals state equation for mixtures. The modeled coefficient of mutual diffusion for a great number of binary mixtures of the above-mentioned individual substances is determined, and the results are compared with the known data. Without special calibration for the experiment, the model correctly predicts the relationship of the self-diffusion and mutual diffusion coefficients (with their variation by several orders of magnitude in the case where the density changes from gaseous to liquid) with both pressure and temperature. For most substances considered in the paper, the maximum deviations of calculations from the experiment do not exceed 30–50%.     

Column Dynamics for Adsorption of Bulk Binary Gas Mixtures on Activated Carbon

Abstract

Dynamics of adsorption from bulk N₂-He, CH₄-He, CO₂-He, CO₂-N₂, and CO₂-CH₄ binary mixtures were measured in a column packed with the BPL activated carbon. The data were analyzed using an adiabatic, isobaric, constant pattern model of column adsorption in conjunction with a linear driving force model for the adsorbate mass transfer. It was found that the mass transfer coefficients for adsorption of CO₂, CH₄, and N₂ were significantly lower during binary co-adsorption in the presence of each other than the corresponding pure component mass transfer coefficients in the presence of nonadsorbing helium. The reduction was more pronounced for the less strongly adsorbed species of the binary mixture. This kinetic interaction between the adsorbates could not be predicted a priori. Equilibrium isotherms for adsorption of pure N₂, CH₄, and CO₂ and for adsorption of CO₂-N₂ and CO₂-CH₄ binaries were also measured on the carbon. The isotherms obeyed the Langmuir equation.     

Surface Diffusion of Deuterium and Light Hydrocarbons in Microporous Vycor Glass

Abstract

The significance of the surface diffusion of helium through a microporous Vycor glass is emphasized, and the experimental evidence is presented. New permeability data of D₂, CH₄, C₂H₆, and C₃H₈ are reported over a wide temperature range, and the results are analyzed numerically. Interesting comparisons are made for D₂-H₂ and C₃H₈-CO₂ systems. Finally, the separation factors for CO₂-C₃H₈ and CH₄-C₃H₈ systems are discussed.

All the experimental work has been carried out with porous Vycor glass as the microporous medium. However, there is good reason to believe that the basic findings will hold for any other microporous barrier. Differences will only be a matter of magnitude and will be determined by the adsorption interaction of the respective gas-solid system.     

Adsorption of heavy metal cations from aqueous solutions by wool fibers

Adsorption of metal cations by kivircik wool from aqueous NiCl₂, CuCl₂, ZnCl₂, CdCl₂, HgCl₂ and Pb(NO₃)₂ solutions at 25°C and 50°C was investigated using atomic absorption spectroscopy. A fiber diffusion controlled adsorption rate model was used to predict the effective diffusion coefficients of metal ions in wool. It has been shown that wool is a potential adsorbent for removing toxic metal ions from contaminated water.     

Preparation of highly mesoporous carbon membranes via a sol-gel process using resorcinol and formaldehyde

This paper reports the preparation of highly mesoporous carbon membranes, which are obtained by the pyrolysis of sol-gel derived mesoporous polymer membranes using resorcinol and formaldehyde (RF). Two series of RF carbon membranes were prepared by changing the resorcinol to catalyst molar ratio. The nitrogen adsorption-desorption measurement shows that the RF carbon membranes possess a well-developed mesoporous structure with controlled pore diameters of 5.48 nm and 13.9 nm. The helium and nitrogen permeances of both RF carbon membranes were independent of the feed pressure, indicating that there was no contribution of viscous flow and the membranes are initially crack-free. The gas permeation result showed that the dominant mechanism of gas transport through both the RF carbon membranes is Knudsen diffusion. With regard to the permeation of condensable gases such as CH₄ and CO₂, it was observed that the surface flow also contributes to the total permeation.     

Sintering kinetics of ZrO2 nanopowders modified by group IV elements

The sintering behavior of tetragonal zirconia nanopowders modified by the group IV elements at the initial sintering stage was investigated. It was found that different additives SiO₂, SnO₂, and GeO₂ have a significant influence on the densification kinetics of 3Y-TZP nanopowders obtained by coprecipitation during sintering as it depends on the amount of additives (0-5 wt%). The shrinkage of zirconia-based specimens during the nonisothermal sintering was analyzed using the dilatometric data. The constant rate of heating technique was applied in order to determine the dominant mass transfer mechanism at the initial stage of sintering in modified zirconia nanopowders. It was found that there was a change in the mass transfer mechanism and diffusion activation energy in 3Y-TZP as a result of the additives. The dominant sintering mechanism in 3Y-TZP changed from the volume diffusion to the grain boundary diffusion due to the addition of SiO₂ and SnO₂ and the sintering activation energy increased in these cases. However, GeO₂ additive activated the viscous flow mechanism in sintering process of 3Y-TZP nanopowders which led to acceleration of the densification due to the decrease in the diffusion activation energy.