The generation of multi-group cross section data for LWR analysis usually starts by identifying some characteristic “lattice” — be it a pin-cell, a fuel assembly, or a collection of fuel assemblies. For each such lattice, a very-fine-group transport calculation (e.g., 50 – 10,000 groups) is performed to obtain the neutron flux and reaction rate distributions within the lattice. Unless this transport calculation explicitly models anisotropic scattering, an approximation for transport-corrected-P 0 cross sections for each nuclide must be introduced before the multi-group lattice transport calculation can be performed. In addition, lattice reaction rates and fluxes are used to compute energy-condensed and/or spatially- homogenized transport cross sections (or diffusioncoefficients) for use in downstream multi-group (e.g., 2 – 100 groups) core calculations. Here, additional approximations are required to compute the appropriate transport cross section that preserves some selected characteristic of the lattice calculation. All production lattice physics codes [ 3 – 6 ] make such approximations, often without substantial justifi- cation. Moreover, the most useful of these approximations are often considered to be proprietary, and the literature remains largely silent on useful methods. One example might be that of the transport- corrected-P 0 methods that have been employed in CASMO for more than 40 years. Only recently has Herman [ 7 ] published details of the method used in CASMO to generate transport-corrected-P 0 cross sections for 1 H in LWR lattices. Herman was able to compute CASMO’s “exact” transport cross section that matched continuous-energy Monte Carlo (MC) neutron leakages (integrated into 70 fine energy groups) from a slab of pure hydrogen. This transport correction is markedly different from that computed using the “micro-balance” argument [ 8 ] which produces the classic “out-scatter” approxi- mation — with its transport-to-total ratio of 1/3 for purely isotropic center-of-mass neutron scattering with free gas 1 H model. CASMO developers recognized long ago that this definition of transport cross section produced excellent eigenvalues for small LWR critical assemblies with large neutron leakages, while the classic out-scatter approximation produced errors in eigenvalue as large as 1000 pcm. In addition, SIMULATE-3 nodal code developers observed (more than 30 years ago) that the CASMO transport cross section also produced two-group diffusioncoefficients that eliminated radial power tilts observed in large 4-loop PWR cores when using the out-scatter approximation.
Most of the models proposed in literature for binary diffusioncoefficients of solids in supercritical fluids are restricted to infinite dilution; this can be explained by the fact that most of experimental data are performed in the dilute range. However some industrial processes, such as supercritical fluid separation, operate at finite concentration for complex mixtures. In this case, the concentration dependence of diffusioncoefficients must be considered, especially near the upper critical endpoint (UCEP) where a strong decrease of diffusioncoefficients was experimentally observed. In order to represent this slowing down, a modified version of the Darken equation was proposed in literature for naphthalene in supercritical carbon dioxide. In this paper, the conditions of application of such a modelling are investigated. In particular, we focus on the order of magnitude of the solubility of the solid and on the vicinity of the critical endpoint. Various equations proposed in literature for the modelling of the infinite dilution diffusioncoefficients of the solutes are also compared. Ten binary mixtures of solids with supercritical carbon dioxide were considered for this purpose.
Figure 5: Comparison between formation factor of lithium, and HTO obtained experimentally
Differences obtained between these factors must normally tend to zero since it is the same formula- tions which were tested by the two tracers. Because of some disturbances that can take place during tests, such an error exists. Among these disturbing factors, may be mentioned two possible reasons. From one perspective, it was noticed during the tests, a slight drop of temperature in the room where were placed the cells, this fall of temperature can cause a decrease in effective diffusioncoefficients and thus increase the formation factor F. From another perspective, the increase in the formation factor may be due to the presence of chlorides ions in the upstream solution (solution of LiCl). These ions diffusing into mortars can involve some possible modifications in the mi- crostructure of materials, in particular in the porosity of the hydrates. Otherwise, since hydrates porosity in CEM I based materials represents a smaller fraction of total porosity (compared to a CEM V material for example), the effect produced by chloride ions on the
共Received 29 December 2009; accepted 17 March 2010; published online 20 April 2010兲
In this work, an in-house made Loschmidt diffusion cell is used to measure the effective O 2 – N 2
diffusioncoefficients through four porous samples of different simple pore structures. One-dimensional through-plane mass diffusion theory is applied to process the experimental data. It is found that both bulk diffusion coefficient and the effective gas diffusioncoefficients of the samples can then be precisely determined, and the measured bulk one is in good agreement with the literature value. Numerical computation of three-dimensional mass diffusion through the samples is performed to calculate the effective gas diffusioncoefficients. The comparison between the measured and calculated coefficient values shows that if the gas diffusion through a sample is dominated by one-dimensional diffusion, which is determined by the pore structure of the sample, these two values are consistent, and the sample can be used as a standard sample to test a gas diffusion measurement system. 关doi: 10.1063/1.3385673 兴
and improve the errors caused by spatial homogenization and energy condensation with MGXS generated using Monte Carlo codes [1,23–27], but the accuracy improvement for angular approximations remains a challenging task and open question.
Most Monte Carlo-based MGXS generation applications aim to improve the accuracy of full core diffusion calculations and are focused on generating few-group cross sections and diffusioncoefficients. The recent study by Boyd  has investigated the accuracy by directly using full core continuous energy Monte Carlo simulations to compute MGXS for full core deterministic multi-group transport calculations. But due to the difficulty caused by the anisotropy in scattering reactions, the study in  adopted the isotropic- in-LAB (isotropic in the laboratory system) approximation in both the Monte Carlo and deterministic simulations.
For sugar solutions, the reduction of oxygen diffusion coef- ficients reaches 30% for the highest concentrations (100 g L −1 ),
leading to a minimal value of 1.39 × 10 −9 m 2 s −1 . This latter value
is fully relevant when compared to the results of Van Stroe-Biezen et al.  who measured, using an electrochemical method, the diffusion coefficient of oxygen in glucose solutions; indeed, these authors found a reduction in diffusivity of 26% when the glucose concentration varied from 0 to 100 g L −1 in their fermentation media. The decrease in viscosity with increasing concentrations of glucose ( Table 1 ) is mainly responsible for such change in diffusioncoefficients. This is illustrated in Fig. 4 b where the usual depen- dence of D with the inverse of viscosity is verified, as predicted by the Stokes–Einstein equation and the correlation of Wilke and Chang (1954)  . The rate of change of D/D water with concentra-
Experimental measurement techniques, e.g., gas chromatogra- phy, nuclear magnetic resonance (e.g., PFG NMR), and diffusion cell methods, have been developed to determine the EGDCs of porous materials [9–13] . Kramer and co-workers measured the EGDC in carbon paper using electrochemical impedance spectroscopy [14,15] . Zhang et al.  used a Wicke–Kallenbach diffusion cell to measure the EGDC of a catalyst monolith washcoat. A closed- tube method with a Loschmidt diffusion cell is considered as one of the most reliable methods to determine binary diffusion coeffi- cients of gases [16–19] . Using a Loschmidt cell, bulk binary diffusioncoefficients of O 2 –N 2 were precisely measured under the experi-
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Chloride, bromide and sulphate concentration profiles have been analysed through the Opalinus Clay of Mont Terri in the framework of the Deep Borehole Experiment. Aqueous leaching and out diffusion experiments were carried out to acquire anion concentrations and estimate pore diffusioncoefficients. Out diffusion technique gave consistent values of chloride and bromide compared to the concentration profiles acquired so far at the tunnel level of the Mont Terri rock laboratory. Concentrations acquired by leaching experiments show a maximum chloride concentration of 16.1 ± 1.7 g/l at the basal part of Opalinus Clay which is higher than the value of 14.4 ± 1.4 g/l obtained by out diffusion at the same level. This excess of chloride is likely due to dissolution of Cl - bearing minerals or release of Cl initially contained in unaccessible porosity. Bromide to chloride ratios are virtually the same as that of seawater, whereas sulphate to chloride ratios are significantly higher. Those latter are probably due to pyrite oxidation and dissolution of sulphate-bearing minerals occurring during sample collection and preparation. An anisotropy ratio of 2.4 was estimated for pore diffusion coefficient in the Opalinus Clay sandy facies.
In the present work, we use the time-dependent wavepacket diffusion (TDWPD) method [ 41 ] to investigate the diffusion coef ﬁcient of the one-dimensional molecular-crystal model when both the static and dynamic disorders are present. Formally, TDWPD can be understood as an approximation to the exact stochastic Schrödinger equation (SSE) [ 42 – 46 ] or stochastic wavefunction methods [ 47 ]. The TDWPD has a similar structure to the HSR; except we start from the coherent-state representation of the phonon, and the dynamic disorders are then incorporated by stochastic complex-valued forces, which are quantitatively generated from their quantum correlation functions. The TDWPD method essentially overcomes the de ﬁciency of HSR, i.e. it incorporates the quantum tunneling effect and approximately satis ﬁes the detailed balance principle. Moreover, its demand on computational time is similar to that of HSR, and it can thus be applied to nanoscale systems. To compare with existing theories, we also present the results from Red ﬁeld theory [ 38 , 48 – 50 ], which is a standard approach to describe the coherent motions of carriers. The diffusion coef ﬁcients from the (FGR) and Marcus formula are further illustrated to investigate the validity of the TDWPD in the strong dynamic disorder limit.
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1.4.2 The Thermogravitational Column
Another method for measuring thermal diffusioncoefficients is the thermogravitational column which consists of two vertical plates separated by a narrow space under a horizontal  or vertical  thermal gradient. The principle is to use a thermal gradient to simultaneously produce a mass flux by thermal diffusion and a convection flux. Starting from a mixture of homogeneous composition, the coupling of the two transport mechanisms leads to a separation of the components. In most experimental devices, the applied thermal gradient is horizontal and the final composition gradient is globally vertical. The separation rate in this system defined as the concentration difference between the top and the bottom cell. Thermogravitational column was devised by Clusius and Dickel (1938). The phenomenology of thermogravitational transport was exposed by Furry et al. (1939), and was validated by many experiments. The optimal coupling between thermal diffusion and convection ratio (maximum separation) correspond to an optimal thickness of the cell in free fluid (less than one millimetre for usual liquids) and an optimal permeability in porous medium [56, 57]. The so called packed thermal diffusion cell (PTC) was described and intensively used to perform experiments on varieties of ionic and organic mixtures [54, 21, 66]. The separation in a thermogravitational column can be substantially increased by inclining the column . Recently, Mojtabi et al., 2003, showed that the vibrations can lead whether to increase or to decrease heat and mass transfers or delay or accelerate the onset of convection .
Our discussion regarding model selection using contraction coefficients can be naturally extended to include proba- bility density functions (pdfs). For instance, the local approximations introduced in Subsection I-A were used to study AWGN channels in a network information theory context in [ 18 ]. We now consider the relationship between the local and global contraction coefficients in the Gaussian regime. To this end, we introduce the classical AWGN channel [ 7 ]. Definition 4 (AWGN Channel). The single letter AWGN channel has jointly distributed input random variable X and output random variable Y , where X and Y are related by the equation:
F X = ρV 2 SC X (α)
F Y = ρV 2 SC Y (α)
où ρ est la masse volumique du fluide en mouvement autour de l’aile, C X (α) et C Y (α) les coefficients
d’influence de l’angle d’incidence α, pour la force de traînée et pour la force de portance. De cette façon, les coefficients C X (α) et C Y (α) devenaient indépendants du fluide considéré. Des mesures
d’une cellule réflectrice afin d’approcher une matrice de diffusion voulue. Cette étude est motivée par le besoin grandissant de contrôler le coefficient de réflexion en co- polarisation des méta-surfaces ainsi que le couplage entre polarisations incidente et croisée, en amplitude et en phase. L’utilité de la synthèse est montrée avec une application de conversion de polarisation linéaire en polarisation circulaire, la bande sous 3dB du rapport elliptique obtenue est de 17% autour de 16GHz. Toutes les simulations sont effectuées sous CST.