Critical review of coupled flux formulations for clay membranes based on nonequilibrium thermodynamics

Extensive research conducted over the past several decades has indicated that semipermeable membrane behavior (i.e., the ability of a porous medium to restrict the passage of solutes) may have a significant influence on solute migration through a wide variety of clay-rich soils, including both natural clay formations (aquitards, aquicludes) and engineered clay barriers (e.g., landfill liners and vertical cutoff walls). Restricted solute migration through clay membranes generally has been described using coupled flux formulations based on nonequilibrium (irreversible) thermodynamics. However, these formulations have differed depending on the assumptions inherent in the theoretical development, resulting in some confusion regarding the applicability of the formulations. Accordingly, a critical review of coupled flux formulations for liquid, current, and solutes through a semipermeable clay membrane under isothermal conditions is undertaken with the goals of explicitly resolving differences among the formulations and illustrating the significance of the differences from theoretical and practical perspectives. Formulations based on single-solute systems (i.e., uncharged solute), single-salt systems, and general systems containing multiple cations or anions are presented. Also, expressions relating the phenomenological coefficients in the coupled flux equations to relevant soil properties (e.g., hydraulic conductivity and effective diffusion coefficient) are summarized for each system. A major difference in the formulations is shown to exist depending on whether counter diffusion or salt diffusion is assumed. This difference between counter and salt diffusion is shown to affect the interpretation of values for the effective diffusion coefficient in a clay membrane based on previously published experimental data. Solute transport theories based on both counter and salt diffusion then are used to re-evaluate previously published column test data for the same clay membrane. The results indicate that, despite the theoretical inconsistency between the counter-diffusion assumption and the salt-diffusion conditions of the experiments, the predictive ability of solute transport theory based on the assumption of counter diffusion is not significantly different from that based on the assumption of salt diffusion, provided that the input parameters used in each theory are derived under the same assumption inherent in the theory. Nonetheless, salt-diffusion theory is fundamentally correct and, therefore, is more appropriate for problems involving salt diffusion in clay membranes. Finally, the fact that solute diffusion cannot occur in an ideal or perfect membrane is not explicitly captured in any of the theoretical expressions for total solute flux in clay membranes, but rather is generally accounted for via inclusion of an effective porosity, n(e), or a restrictive tortuosity factor, tau(r), in the formulation of Fick's first law for diffusion. Both n(e) and tau(r) have been correlated as a linear function of membrane efficiency. This linear correlation is supported theoretically by pore-scale modeling of solid-liquid interactions, but experimental support is limited. Additional data are needed to bolster the validity of the linear correlation for clay membranes. Copyright 2012 Elsevier B.V. All rights reserved.

Critical Review of Coupled Flux Formulations for Clay Membranes Based on Nonequilibrium Thermodynamics

Extensive research conducted over the past several decades has indicated that semipermeable membrane behavior (i.e., the ability of a porous medium to restrict the passage of solutes) may have a significant influence on solute migration through a wide variety of clay-rich soils, including both natural clay formations (aquitards, aquicludes) and engineered clay barriers (e.g., landfill liners and vertical cutoff walls). Restricted solute migration through clay membranes generally has been described using coupled flux formulations based on nonequilibrium (irreversible) thermodynamics. However, these formulations have differed depending on the assumptions inherent in the theoretical development, resulting in some confusion regarding the applicability of the formulations. Accordingly, a critical review of coupled flux formulations for liquid, current, and solutes through a semipermeable clay membrane under isothermal conditions is undertaken with the goals of explicitly resolving differences among the formulations and illustrating the significance of the differences from theoretical and practical perspectives. Formulations based on single-solute systems (i.e., uncharged solute), single-salt systems, and general systems containing multiple cations or anions are presented. Also, expressions relating the phenomenological coefficients in the coupled flux equations to relevant soil properties (e.g., hydraulic conductivity and effective diffusion coefficient) are summarized for each system. A major difference in the formulations is shown to exist depending on whether counter diffusion or salt diffusion is assumed. This difference between counter and salt diffusion is shown to affect the interpretation of values for the effective diffusion coefficient in a clay membrane based on previously published experimental data. Solute transport theories based on both counter and salt diffusion then are used to re-evaluate previously published column test data for the same clay membrane. The results indicate that, despite the theoretical inconsistency between the counter-diffusion assumption and the salt-diffusion conditions of the experiments, the predictive ability of solute transport theory based on the assumption of counter diffusion is not significantly different from that based on the assumption of salt diffusion, provided that the input parameters used in each theory are derived under the same assumption inherent in the theory. Nonetheless, salt-diffusion theory is fundamentally correct and, therefore, is more appropriate for problems involving salt diffusion in clay membranes. Finally, the fact that solute diffusion cannot occur in an ideal or perfect membrane is not explicitly captured in any of the theoretical expressions for total solute flux in clay membranes, but rather is generally accounted for via inclusion of an effective porosity, ne, or a restrictive tortuosity factor, tr, in the formulation of Fick's first law for diffusion. Both ne and tr have been correlated as a linear function of membrane efficiency. This linear correlation is supported theoretically by pore-scale modeling of solid-liquid interactions, but experimental support is limited. Additional data are needed to bolster the validity of the linear correlation for clay membranes.

A Coupled 2 × 2D Babcock–Leighton Solar Dynamo Model. I. Surface Magnetic Flux Evolution

The need for reliable predictions of the solar activity cycle motivates the development of dynamo models incorporating a representation of surface processes sufficiently detailed to allow assimilation of magnetographic data. In this series of papers we present one such dynamo model, and document its behavior and properties. This first paper focuses on one of the model's key components, namely surface magnetic flux evolution. Using a genetic algorithm, we obtain best-fit parameters of the transport model by least-squares minimization of the differences between the associated synthetic synoptic magnetogram and real magnetographic data for activity cycle 21. Our fitting procedure also returns Monte Carlo-like error estimates. We show that the range of acceptable surface meridional flow profiles is in good agreement with Doppler measurements, even though the latter are not used in the fitting process. Using a synthetic database of bipolar magnetic region (BMR) emergences reproducing the statistical properties of observed emergences, we also ascertain the sensitivity of global cycle properties, such as the strength of the dipole moment and timing of polarity reversal, to distinct realizations of BMR emergence, and on this basis argue that this stochasticity represents a primary source of uncertainty for predicting solar cycle characteristics.

The climate response to CO2 of the Hadley Centre coupled AOGCM with and without flux adjustment

Coupled atmosphere‐ocean general circulation models have a tendency to drift away from a realistic climatology. The modelled climate response to an increase of CO2 concentration may be incorrect if the simulation of the current climate has significant errors, so in many models, including ours, the drift is counteracted by applying prescribed fluxes of heat and fresh water at the ocean‐atmosphere interface in addition to the calculated surface exchanges. Since the additional fluxes do not have a physical basis, the use of this technique of “flux adjustment” itself introduces some uncertainty in the simulated response to increased CO2. We find that the global‐average temperature response of our model to CO2 increasing at 1% per year is about 30% less without flux adjustment than with flux adjustment. The geographical patterns of the response are similar, indicating that flux adjustment is not causing any gross distortion. The reduced size of the response is due to more effective vertical transport of heat into the ocean, and a somewhat smaller climate sensitivity. Although the response in both cases lies within the generally accepted range for the climate sensitivity, systematic uncertainties of this size are clearly undesirable, and the best strategy for future development is to improve the climate model in order to reduce the need for flux adjustment.

Physical controls on carbon dioxide transfer velocity and flux in low-gradient river systems and implications for regional carbon budgets

Outgassing of carbon dioxide (CO(2)) from rivers and streams to the atmosphere is a major loss term in the coupled terrestrial-aquatic carbon cycle of major low-gradient river systems (the term ""river system"" encompasses the rivers and streams of all sizes that compose the drainage network in a river basin). However, the magnitude and controls on this important carbon flux are not well quantified. We measured carbon dioxide flux rates (F(CO2)), gas transfer velocity (k), and partial pressures (p(CO2)) in rivers and streams of the Amazon and Mekong river systems in South America and Southeast Asia, respectively. F(CO2) and k values were significantly higher in small rivers and streams (channels <100 m wide) than in large rivers (channels >100 m wide). Small rivers and streams also had substantially higher variability in k values than large rivers. Observed F(CO2) and k values suggest that previous estimates of basinwide CO(2) evasion from tropical rivers and wetlands have been conservative and are likely to be revised upward substantially in the future. Data from the present study combined with data compiled from the literature collectively suggest that the physical control of gas exchange velocities and fluxes in low-gradient river systems makes a transition from the dominance of wind control at the largest spatial scales (in estuaries and river mainstems) toward increasing importance of water current velocity and depth at progressively smaller channel dimensions upstream. These results highlight the importance of incorporating scale-appropriate k values into basinwide models of whole ecosystem carbon balance.

Unsaturated Infinite Slope Stability Considering Surface Flux Conditions

A slope stability model is derived for an infinite slope subjected to unsaturated infiltration flow above a phreatic surface. Closed form steady state solutions are derived for the matric suction and degree of saturation profiles. Soil unit weight, consistent with the degree of saturation profile, is also directly calculated and introduced into the analyzes, resulting in closed-form solutions for typical soil parameters and an infinite series solution for arbitrary soil parameters. The solutions are coupled with the infinite slope stability equations to establish a fully realized safety factor function. In general, consideration of soil suction results in higher factor of safety. The increase in shear strength due to the inclusion of soil suction is analogous to making an addition to the cohesion, which, of course, increases the factor of safety against sliding. However, for cohesive soils, the results show lower safety factors for slip surfaces approaching the phreatic surface compared to those produced by common safety factor calculations. The lower factor of safety is due to the increased soil unit weight considered in the matric suction model but not usually accounted for in practice wherein the soil is treated as dry above the phreatic surface. The developed model is verified with a published case study, correctly predicting stability under dry conditions and correctly predicting failure for a particular storm.

On the analysis of travelling waves to a nonlinear flux limited reaction-diffusion equation

In this paper we study the existence and qualitative properties of travelling waves associated to a nonlinear flux limited partial differential equation coupled to a Fisher-Kolmogorov-Petrovskii-Piskunov type reaction term. We prove the existence and uniqueness of finite speed moving fronts of C2 classical regularity, but also the existence of discontinuous entropy travelling wave solutions.

Direct noninvasive estimation of myocardial tricarboxylic acid cycle flux in vivo using hyperpolarized (13)C magnetic resonance.

BACKGROUND: The heart relies on continuous energy production and imbalances herein impair cardiac function directly. The tricarboxylic acid (TCA) cycle is the primary means of energy generation in the healthy myocardium, but direct noninvasive quantification of metabolic fluxes is challenging due to the low concentration of most metabolites. Hyperpolarized (13)C magnetic resonance spectroscopy (MRS) provides the opportunity to measure cellular metabolism in real time in vivo. The aim of this work was to noninvasively measure myocardial TCA cycle flux (VTCA) in vivo within a single minute. METHODS AND RESULTS: Hyperpolarized [1-(13)C]acetate was administered at different concentrations in healthy rats. (13)C incorporation into [1-(13)C]acetylcarnitine and the TCA cycle intermediate [5-(13)C]citrate was dynamically detected in vivo with a time resolution of 3s. Different kinetic models were established and evaluated to determine the metabolic fluxes by simultaneously fitting the evolution of the (13)C labeling in acetate, acetylcarnitine, and citrate. VTCA was estimated to be 6.7±1.7μmol·g(-1)·min(-1) (dry weight), and was best estimated with a model using only the labeling in citrate and acetylcarnitine, independent of the precursor. The TCA cycle rate was not linear with the citrate-to-acetate metabolite ratio, and could thus not be quantified using a ratiometric approach. The (13)C signal evolution of citrate, i.e. citrate formation was independent of the amount of injected acetate, while the (13)C signal evolution of acetylcarnitine revealed a dose dependency with the injected acetate. The (13)C labeling of citrate did not correlate to that of acetylcarnitine, leading to the hypothesis that acetylcarnitine formation is not an indication of mitochondrial TCA cycle activity in the heart. CONCLUSIONS: Hyperpolarized [1-(13)C]acetate is a metabolic probe independent of pyruvate dehydrogenase (PDH) activity. It allows the direct estimation of VTCA in vivo, which was shown to be neither dependent on the administered acetate dose nor on the (13)C labeling of acetylcarnitine. Dynamic (13)C MRS coupled to the injection of hyperpolarized [1-(13)C]acetate can enable the measurement of metabolic changes during impaired heart function.

Spectro-imagerie optique à faible flux et comparaison de la cinématique Ha et HI d'un échantillon de galaxies proches

Un nouveau contrôleur de EMCCD (Electron multiplying Charge Coupled Device) est présenté. Il permet de diminuer significativement le bruit qui domine lorsque la puce EMCCD est utilisé pour du comptage de photons: le bruit d'injection de charge. À l'aide de ce contrôleur, une caméra EMCCD scientifique a été construite, caractérisée en laboratoire et testée à l'observatoire du mont Mégantic. Cette nouvelle caméra permet, entre autres, de réaliser des observations de la cinématique des galaxies par spectroscopie de champ intégral par interférométrie de Fabry-Perot en lumière Ha beaucoup plus rapidement, ou de galaxies de plus faible luminosité, que les caméras à comptage de photon basées sur des tubes amplificateurs. Le temps d'intégration nécessaire à l'obtention d'un rapport signal sur bruit donné est environ 4 fois moindre qu'avec les anciennes caméras. Les applications d'un tel appareil d'imagerie sont nombreuses: photométrie rapide et faible flux, spectroscopie à haute résolution spectrale et temporelle, imagerie limitée par la diffraction à partir de télescopes terrestres (lucky imaging), etc. D'un point de vue technique, la caméra est dominée par le bruit de Poisson pour les flux lumineux supérieurs à 0.002 photon/pixel/image. D'un autre côté, la raie d'hydrogène neutre (HI) à 21 cm a souvent été utilisée pour étudier la cinématique des galaxies. L'hydrogène neutre a l'avantage de se retrouver en quantité détectable au-delà du disque optique des galaxies. Cependant, la résolution spatiale de ces observations est moindre que leurs équivalents réalisés en lumière visible. Lors de la comparaison des données HI, avec des données à plus haute résolution, certaines différences étaient simplement attribuées à la faible résolution des observations HI. Le projet THINGS (The HI Nearby Galaxy Survey a observé plusieurs galaxies de l'échantillon SINGS (Spitzer Infrared Nearby Galaxies Survey). Les données cinématiques du projet THIGNS seront comparées aux données cinématiques obtenues en lumière Ha, afin de déterminer si la seule différence de résolution spatiale peut expliquer les différences observées. Les résultats montrent que des différences intrinsèques aux traceurs utilisées (hydrogène neutre ou ionisé), sont responsables de dissemblances importantes. La compréhension de ces particularités est importante: la distribution de la matière sombre, dérivée de la rotation des galaxies, est un test de certains modèles cosmologiques.

Atmosphere feedbacks during ENSO in a coupled GCM with a modified atmospheric convection scheme

The too diverse representation of ENSO in a coupled GCM limits one’s ability to describe future change of its properties. Several studies pointed to the key role of atmosphere feedbacks in contributing to this diversity. These feedbacks are analyzed here in two simulations of a coupled GCM that differ only by the parameterization of deep atmospheric convection and the associated clouds. Using the Kerry–Emanuel (KE) scheme in the L’Institut Pierre-Simon Laplace Coupled Model, version 4 (IPSL CM4; KE simulation), ENSO has about the right amplitude, whereas it is almost suppressed when using the Tiedke (TI) scheme. Quantifying both the dynamical Bjerknes feedback and the heat flux feedback in KE, TI, and the corresponding Atmospheric Model Intercomparison Project (AMIP) atmosphere-only simulations, it is shown that the suppression of ENSO in TI is due to a doubling of the damping via heat flux feedback. Because the Bjerknes positive feedback is weak in both simulations, the KE simulation exhibits the right ENSO amplitude owing to an error compensation between a too weak heat flux feedback and a too weak Bjerknes feedback. In TI, the heat flux feedback strength is closer to estimates from observations and reanalysis, leading to ENSO suppression. The shortwave heat flux and, to a lesser extent, the latent heat flux feedbacks are the dominant contributors to the change between TI and KE. The shortwave heat flux feedback differences are traced back to a modified distribution of the large-scale regimes of deep convection (negative feedback) and subsidence (positive feedback) in the east Pacific. These are further associated with the model systematic errors. It is argued that a systematic and detailed evaluation of atmosphere feedbacks during ENSO is a necessary step to fully understand its simulation in coupled GCMs.

Understanding projections of sea level rise in a Hadley Centre coupled climate model

Sea level changes resulting from CO2-induced climate changes in ocean density and circulation have been investigated in a series of idealised experiments with the Hadley Centre HadCM3 AOGCM. Changes in the mass of the ocean were not included. In the global mean, salinity changes have a negligible effect compared with the thermal expansion of the ocean. Regionally, sea level changes are projected to deviate greatly from the global mean (standard deviation is 40% of the mean). Changes in surface fluxes of heat, freshwater and wind stress are all found to produce significant and distinct regional sea level changes, wind stress changes being the most important and the cause of several pronounced local features, while heat and freshwater flux changes affect large parts of the North Atlantic and Southern Ocean. Regional change is related mainly to density changes, with a relatively small contribution in mid and high latitudes from change in the barotropic circulation. Regional density change has an important contribution from redistribution of ocean heat content. In general, unlike in the global mean, the regional pattern of sea level change due to density change appears to be influenced almost as much by salinity changes as by temperature changes, often in opposition. Such compensation is particularly marked in the North Atlantic, where it is consistent with recent observed changes. We suggest that density compensation is not a property of climate change specifically, but a general behavior of the ocean.