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1.
The cubic equation recently derived for the increase in concentration of a solute with time, as the solid dissolves in batch according to the shrinking sphere model at high under-saturation, is extended to dissolutions of mixtures of differently sized particles. This problem needs to be solved if batch dissolutions are to play their part in the proposed amelioration of global warming and associated climate change by accelerated ‘re-burial’ of excess CO2 in ocean sediment. The upgraded model was tested using sodium chloride dissolved in 50% aqueous propanone, whence the model fitted two separate runs with 500 and 212 μm, and 212 and 38 μm, diameter crystals, respectively. The key to simulating dissolution in this way lies in the dissolutions being independent of each other. It is further shown that although this condition was implicit in the recent derivation of the cubic equation, it was not recognised at the time. The work should be applicable to any batch dissolution of mixed particles at high under-saturation, and hence, may find use in many industrial and laboratory dissolutions. Simulations show how agglomerated mixtures can yield a straight line on the plot of ln(1 − C/C T) versus time, as was reported to occur recently with sodium chloride taken ‘straight from the bottle’. It is shown that this probably explains why exponential dissolutions may have seemed appropriate to the dissolution of biogenic silica in earlier literature. This study suggests that a new round of biogenic silica dissolutions, but with sieved samples, would be worthwhile, with the likelihood that shrinking sphere behaviour might well be found to characterise the kinetics. The opportunity is taken to investigate a number of aspects of the shrinking sphere model not generally discussed before, e.g. the graph for the change in surface area with time. The limitations of using cubic salt crystals with the shrinking sphere model are discussed.  相似文献   

2.
Dissolution Kinetics of Dolomite in Water at Elevated Temperatures   总被引：1，自引：0，他引：1  
Kinetic experiments of dolomite dissolution in water over a temperature range from 25 to 250°C were performed using a flow through packed bed reactor. Authors chose three different size fractions of dolomite samples: 18–35 mesh, 35–60 mesh, and 60–80 mesh. The dissolution rates of the three particle size samples of dolomite were measured. The dissolution rate values are changed with the variation of grain size of the sample. For the sample through 20–40 mesh, both the release rate of Ca and the release rate of Mg increase with increasing temperature until 200°C, then decrease with continued increasing temperature. Its maximum dissolution rate occurs at 200°C. The maximum dissolution rates for the sample through 40–60 mesh and 60–80 mesh happen at 100°C. Experimental results indicate that the dissolution of dolomite is incongruent in most cases. Dissolution of fresh dolomite was non-stoichiometric, the Ca/Mg ratio released to solution was greater than in the bulk solid, and the ratio increases with rising temperatures from 25 to 250°C. Observations on dolomite dissolution in water are presented as three parallel reactions, and each reaction occurs in consecutive steps as
where the second part is a slow reaction, and also the reaction could occur as follows:
The following rate equation was used to describe dolomite dissolution kinetics
where refers to one of each reaction among the above reactions; k ij is the rate constant for ith species in the jth reaction, a i stands for activity of ith aqueous species, n is the stoichimetric coefficience of ith species in the jth reaction, and define . The experiments prove that dissolved Ca is a strong inhibitor for dolomite dissolution (release of Ca) in most cases. Dissolved Mg was found to be an inhibitor for dolomite dissolution at low temperatures. But dissolution rates of dolomite increase with increasing the concentration of dissolved Mg in the temperature range of 200–250°C for 20–40 mesh sample, and in the temperature range of 100–250°C for 40–80 mesh sample, whereas the Mg2+ ion adsorption on dolomite surface becomes progressively the step controlling reaction. The following rate equation is suitable to dolomite dissolutions at high temperatures from 200 to 250°C.
where refers to dissolution rate (release of Ca), and are molar concentrations of dissolved Ca and Mg, k ad stands for adsorption reaction rate constant, K Mg refers to adsorption equilibrium constant. At 200°C for 40–60 mesh sample, the release rate of Ca can be described as:
  相似文献   

3.
The full potential of batch dissolution experiments in geochemical and industrial applications has been hampered by the lack of an equation to describe the increase in dissolved solid concentration with time. This study provides new experimental results on the dissolution of salts and new equations, which describe dissolution according to the shrinking sphere model. Sieved salts were found to dissolve according to the shrinking sphere model while the dissolution of the parent material, raw (agglomerated) salt, fitted an exponential dissolution curve. The implications of this to the development of a systematic approach to batch dissolution, irrespective of the solid, is explored. Mathematical equations are derived for the dissolution of solids in under-saturated systems, which are much simpler than ones available, so far. In turn these provide easier comprehension of the workings of the shrinking sphere model. Finally, existing results for biogenic silica dissolution are reviewed in the light of the above-mentioned experimental and modelling advances. An earlier claim that shrinking sphere dissolution had been observed is refuted.  相似文献   

4.
Recently, the increase in dissolved concentration in the batch dissolution of various salts or sucrose has been successfully modelled with three equations, one a cubic in time. However, from three separate earlier investigations with ocean sediments and phytoplankton frustules, there is residual suspicion that biogenic silica does not follow this behaviour. This paper shows that the Shrinking Object Model applies to the dissolution of sieved silica gel particles, as well as to a sample of unsieved, freeze-dried frustules of Odentella sp. Silica gel, being readily available in quantities that can be sieved, is a useful surrogate for biogenic silica in allowing problems of experimental design to be overcome. The dissolutions covered three possible analytic integrations that arise from the model: an exponential for approach to saturation with excess solid silica; the approach to near saturation with either a slight excess or deficiency of silica; dissolution at high under-saturation. Good agreement was found between experimental results and mathematical modelling. The paper provides template calculations by which future raw results can be parameterized. Nevertheless, the reasons for non-linear kinetics reported in earlier work have not been identified, and so controversy over non-linear dissolution kinetics is enhanced. Stirring regime was found to be important with silica gel dissolution, and so biogenic silica dissolution is therefore likely to be ‘transport limited’ at low stirring rate. Accordingly, all archived and future data should be scrutinized for stirring effects before being applied to the oceanic environment. A rigorous test for determining whether a substance’s dissolution deviates from the model is recommended as a preliminary to any future dissolutions, whether in batch or with the chemo-stat. A fixed amount of frustule sample is added to a series of buffered mixtures containing increasing background silicic acid concentrations. Absence of any problem is marked by a linear plot between the increase in silicic concentration accruing over a fixed reaction period and that of the background silicic acid. A novel mathematical proof is provided to justify the test’s use. The reasons for the earlier deviations from expected behaviour of, for example, oceanic sediments, are discussed. Lastly, the paper provides a novel approach to the dissolution of a population of particles of mixed sizes which will probably find ready future application in oceanography.  相似文献   

5.
Interaction of freshly precipitated silica gel with aqueous solutions was studied at laboratory batch experiments under ambient and near neutral pH-conditions. The overall process showed excellent reversibility: gel growth could be considered as an opposite process to dissolution and a linear rate law could be applied to experimental data. Depending on the used rate law form, the resulting rate constants were sensitive to errors in parameters/variables such as gel surface area, equilibrium constants, Si-fluxes, and reaction quotients. The application of an Integrated Exponential Model appeared to be the best approach for dissolution data evaluation. It yielded the rate constants k dissol ∼ (4.50 ± 0.68) × 10−12 and k growth ∼ (2.58 ± 0.39) × 10−9 mol m−2 s−1 for zero ionic strength. In contrast, a Differential Model gave best results for growth data modeling. It yielded the rate constants k dissol ∼ (1.14 ± 0.44) × 10−11 and k growth ∼ (6.08 ± 2.37) × 10−9 mol m−2 s−1 for higher ionic strength (I ∼ 0.04 to 0.11 mol L−1). The found silica gel solubility at zero ionic strength was somewhat lower than the generally accepted value. Based on the and standard Gibbs free energy of silica gel formation was calculated as and −850,318 ± 20 J mol−1, respectively. Activation energies for silica gel dissolution and growth were determined as and respectively. An universal value for growth of any silica polymorph, is not consistent with the value for silica gel growth, which questions the hypothesis about one unique activated complex controlling the silica polymorph growth.  相似文献   

6.
Recent improvements to experiments and modelling of batch dissolution in a turbulent reactor, based upon the shrinking object model, are extended to middle loadings of gypsum, that is, in the region between low and high loadings, which lead, respectively, to high under-saturation or saturation with a great excess of solid left undissolved. Dissolved calcium sulphate concentration was monitored by change in electrical conductivity. This investigation uses an improved, ion-pair model for CaSO 4 0 to allow for the presence of calcium or sulphate added as common ions. The study demonstrates that the full dissolution curve for 5.82 mM loadings of 106-μm particles of gypsum (~1.00 g L?1) in de-ionised water barely changed in the presence of either 4.64 or 8.09 mM calcium chloride, or 4.39 mM sodium sulphate. However, this masked a doubling of dissolution rate imposed by comparable increases in ionic strength from sodium chloride. The results are consistent with the ion pair, CaSO 4 0 , being the key species in the rate-determining step of the back-reaction, and perhaps all salt dissolutions, including calcium carbonate. In this case, the rate equation is as follows: \( {\frac{{{\text{d}}c}}{{{\text{d}}t}}} = \frac{S}{V} \cdot (k_{1} - k_{2}^{\prime } \cdot [{\text{CaSO}}_{ 4}^{0} ]) \), where k 1 and k 2′ are rate constants. The reported observations are interpreted as effects of ionic strength and common ion concentrations upon the formation equilibrium for the ion pair. This rate equation readily transforms mathematically to one involving the product of [Ca2+] and [SO4 2?] in the back-reaction. The parallel of this with the well-known PWP equation used in calcium carbonate dissolution is discussed, with the CaHCO3 + ion pair of the equation being replaced by that of CaCO 3 0 . Meanwhile, the earlier use of the product, [Ca2+]½ × [CO3 2?]½, in the back-reaction term of another dissolution rate equation for calcite is shown to be incorrect. Finally, it is argued that the shrinking object model should be repositioned as a logical derivative of the hydrodynamical approach to dissolution.  相似文献   

7.
The deformation behavior of calcite has been of longstanding interest. Through experiments on single crystals, deformation mechanisms were established such as mechanical twinning on in the positive sense and slip on and both in the negative sense. More recently it was observed that at higher temperatures slip in both senses becomes active and, based on slip line analysis, it was suggested that slip may occur. So far there had been no direct evidence for basal slip, which is the dominant system in dolomite. With new torsion experiments on calcite single crystals at 900 K and transmission electron microscopy, this study identifies slip unambiguously by direct imaging of dislocations and diffraction contrast analysis. Including this slip system in polycrystal plasticity simulations, enigmatic texture patterns observed in compression and torsion of calcite rocks at high temperature can now be explained, resolving a long-standing puzzle.  相似文献   

8.
The objective of this study was to describe the proton promoted disproportion of synthetic manganite (γ-MnOOH) and to characterise the resulting phase transformations. The solution and remaining solid phase after disproportionation was analysed by techniques including atomic absorbance spectroscopy, X-ray diffraction (XRD), atomic force microscopy (AFM) and scanning electron microscopy (SEM). In suspensions with pH between 5 and 7, −log[H+] was monitored for 17 months and equilibrium constants were determined at 9, 12 and 17 months of reaction time for the following reaction (25 °C, 0.1 M (Na)NO3):
The formed MnO2 ages with time and the equilibrium constant for a metastable phase (ramsdellite or nsutite) as well as the most stable phase, pyrolusite (β-MnO2), was determined. Furthermore, combined pH and pe (Eh) measurements were performed to study the equilibrium;
Real-time AFM measurements of the dissolution showed shrinkage of the length of the manganite needles with time (2 hours). After 1 week SEM images showed that this decreased length also was followed by a reduced thickness of the manganite needles. From the SEM images the morphology of the formed Mn(IV) oxides was studied. At pH 2.6, pyrolusite (β-MnO2) and MnCl2 were found in the XRD patterns. Throughout the pH range there were indications of ramsdellite (MnO1.97) in the XRD patterns, which coincided with the existence of a fraction of needle shaped crystals with smaller dimensions (compared to manganite) in the SEM images. These observations together with the long term dissolution experiments suggest that the dissolution of manganite initially forms a ramsdellite or nsutite phase that over time rearranges to form pyrolusite.  相似文献   

9.
The deformation-related microstructure of an Indian Ocean zircon hosted in a gabbro deformed at amphibolite grade has been quantified by electron backscatter diffraction. Orientation mapping reveals progressive variations in intragrain crystallographic orientations that accommodate 20° of misorientation in the zircon crystal. These variations are manifested by discrete low-angle (<4°) boundaries that separate domains recording no resolvable orientation variation. The progressive nature of orientation change is documented by crystallographic pole figures which show systematic small circle distributions, and disorientation axes associated with 0.5–4° disorientation angles, which lie parallel to rational low index crystallographic axes. In the most distorted part of the grain (area A), this is the [100] crystal direction. A quaternion analysis of orientation correlations confirms the [100] rotation axis inferred by stereographic inspection, and reveals subtle orientation variations related to the local boundary structure. Microstructural characteristics and orientation data are consistent with the low-angle boundaries having a tilt boundary geometry with dislocation line [100]. This tilt boundary is most likely to have formed by accumulation of edge dislocations associated with a 〈001〉{100} slip system. Analysis of the energy associated with these dislocations suggest they are energetically more favorable than TEM verified 〈010〉{100} slip. Analysis of minor boundaries in area A indicates deformation by either (001) edge, or [100](100) and [001](100) screw dislocations. In other parts of the grain, cross slip on (111), and (112) planes seems likely. These data provide the first detailed microstructural analysis of naturally deformed zircon and indicate ductile crystal-plastic deformation of zircon by the formation and migration of dislocations into low-angle boundaries. Minimum estimates of dislocation density in the low-angle boundaries are of the order of ∼3.1010 cm−2. This value is sufficiently high to have a marked effect on the geochemical behavior of zircon, via enhanced bulk diffusion and increased dissolution rates. Therefore, crystal plasticity in zircon may have significant implications for the interpretation of radiometric ages, isotopic discordance and trace element mobility during high-grade metamorphism and melting of the crust.  相似文献   

10.
The impact of land-use change on the quality of groundwater in the Xiaotjiang watershed, China was assessed for the period 1982–2004. Groundwater samples were collected from 30 monitoring points across the watershed, and were representative of the various changes, determined by remote sensing and geographical information systems. The results indicate that 610 km2 (60% of the total watershed area) were subject to land-use change during the period. The most important changes were the conversion of 135 km2 of forested land to cultivated land, and 211 km2 of unused land to cultivated land. The main impact was ascribed to diffuse pollution from fertilizers applied to newly cultivated land, and from building development. Overall the groundwater pH value was significantly increased, as were the concentrations of ions , , , , and Cl− in groundwater whilst the concentrations of Ca2+ and declined. More precisely, in the regions where forested land and unused land were converted into cultivated land, the pH value and the concentrations of Mg2+, , , , , Cl− increased whilst the concentrations of Ca2+ and declined. However in the region where cultivated land was converted into construction land, the pH value and the concentrations of Ca2+, Mg2+, , , , , , Cl− increased.
Résumé  L’impact des changements de l’utilisation du territoire sur la qualité de l’eau souterraine dans le bassin versant de Xiaojiang, en Chine, a été évalué de 1982 à 2004. Des échantillons d’eau souterraine ont été récoltés à partir de 30 points d’observation éparpillés sur le bassin, représentant les divers changements déterminés par télédétection et système d’information géographique. Les résultats indiquent que 610 km2 (soit 60% de la surface du bassin) ont été sujets à des modifications de l’utilisation du territoire sur cette période. Les changements les plus importants furent la conversion de 135 km2 de forêt et 211 km2 de terres inutilisées en terres cultivées. Le principal impact est attribué à la pollution diffuse des engrais utilisés en agriculture et pour les batiments. De manière générale le pH de l’eau souterraine a augmenté significativement, ainsi que les concentrations des ions , , , , et Cl−, tandis que les concentration en Ca2+ et ont diminué. Plus précisément dans les régions transformées en terres cultivées, la valeur du pH et les concentrations en Mg2+, , , , , Cl− ont augmenté tandis que les concentrations en Ca2+ et ont diminué. Toutefois dans les régions cultivées converties en zones de construction, le pH et les concentrations en Ca2+, Mg2+, , , , , , Cl− ont augmenté.
Resumen  El impacto del cambio en uso de la tierra en la calidad del agua en la cuenca Xiaojiang, China fue evaluado para el periodo 1982–2004. Muestras de agua subterránea fueron tomadas de 30 puntos de monitoreo a través de la cuenca, y fueron representativas de los múltiples cambios, determinados por sensores remotos y sistemas de información geográfica. Los resultados indican que 610 km2 (60% del área total de la cuenca) estaban sujetos a cambios de uso de la tierra durante el periodo estudiado. Los cambios más importantes fueron la conversión de 135 km2 de bosques a tierra cultivada, y 211 km2 de tierra sin uso (ociosa) a tierra cultivada. El impacto principal fue causado por contaminación difusa de fertilizantes aplicados a la tierra recientemente cultivada, y a desarrollo de construcciones. En general el pH en agua subterránea creció significantemente, al igual que las concentraciones de los iones , , , , y Cl− en agua subterránea mientras que las concentraciones de Ca2+ y decrecieron. Mas precisamente, en las regiones donde bosque y tierra ociosa fueron convertidas en tierra cultivada, el valor de pH y las concentraciones de Mg2+, , , , , Cl− crecieron mientras las concentraciones de Ca2+ y decrecieron. Sin embargo en la región donde tierra cultivada fue convertida en construcciones, el valor de pH y las concentraciones de Ca2+, Mg2+, , , , , , Cl− crecieron.
  相似文献   

11.
The rate of non-oxidative galena dissolution in seawater compositions over the pH range of 2–4.5 was determined from batch reactor experiments. The derivative at zero time of a polynomial fit of the Pb concentration versus time data for the first 30 min was used to determine the rate. A plot of RGn (rate of galena dissolution) versus pH for data from six experiments is linear (R2?=?0.96), with a slope of 0.5. The rate equation describing the rate of galena dissolution as a function of hydrogen ion activity is
$$R_{\text{Gn}} = - \,10^{ - 10.72} \left( {a_{{{\text{H}}^{ + } }} } \right)^{0.50}$$
Varying the concentration of dissolved oxygen produced no significant effect on the measured rates. The activation energy, based on four experiments carried out over the temperature range of 7–30 °C, is 61.1 kJ/mol.
  相似文献   

12.
Solubility of hydrogen in olivine: dependence on temperature and iron content   总被引：11，自引：0，他引：11  
  相似文献   

13.
We present here a numerical modelling study of dislocations in perovskite CaTiO3. The dislocation core structures and properties are calculated through the Peierls–Nabarro model using the generalized stacking fault (GSF) results as a starting model. The GSF are determined from first-principles calculations using the VASP code. The dislocation properties such as collinear, planar core spreading and Peierls stresses are determined for the following slip systems: [100](010), [100](001), [010](100), [010](001), [001](100), [001](010), and All dislocations exhibit lattice friction, but glide appears to be easier for [100](010) and [010](100). [001](010) and [001](100) exhibit collinear dissociation. Comparing Peierls stresses among tausonite (SrTiO3), perovskite (CaTiO3) and MgSiO3 perovskite demonstrates the strong influence of orthorhombic distortions on lattice friction. However, and despite some quantitative differences, CaTiO3 appears to be a satisfactory analogue material for MgSiO3 perovskite as far as dislocation glide is concerned.  相似文献   

14.
The activity of silica in kimberlites,revisited   总被引：1，自引：1，他引：0  
The activity of silica in a silicate liquid in equilibrium with olivine and orthopyroxene decreases with increasing pressure. In contrast, the activity of silica in an unbuffered silicate liquid changes little with pressure. Although the implications of these pressure dependencies have been considered by previous authors in terms of inferring pressures of origin of magmas, less consideration has been given to the implications of these dependencies on the evolution of the magma en route to the surface, or to the mantle through which the magma passes. In this paper, a combination of Schreinemakers’ analysis in isothermal section and calculated reactions in space is used to (a) rationalize the absence of orthopyroxene xenocrysts in kimberlites and the relative abundance of olivine “megacrysts” therein, (b) propose another reason for the paucity of xenocrystic mantle-derived carbonates in kimberlites, (c) explain why clinopyroxene is much less reactive in the kimberlite melt than is orthopyroxene, and (d) explore the implications of the relative stabilities of olivine, orthopyroxene, and clinopyroxene in kimberlitic magma for the mantle through which the magma transits.
Robert W. LuthEmail:
  相似文献   

15.
The models recognize that ZrSiO4, ZrTiO4, and TiSiO4, but not ZrO2 or TiO2, are independently variable phase components in zircon. Accordingly, the equilibrium controlling the Zr content of rutile coexisting with zircon is ZrSiO4 = ZrO2 (in rutile) + SiO2. The equilibrium controlling the Ti content of zircon is either ZrSiO4 + TiO2 = ZrTiO4 + SiO2 or TiO2 + SiO2 = TiSiO4, depending whether Ti substitutes for Si or Zr. The Zr content of rutile thus depends on the activity of SiO2 as well as T, and the Ti content of zircon depends on and as well as T. New and published experimental data confirm the predicted increase in the Zr content of rutile with decreasing and unequivocally demonstrate that the Ti content of zircon increases with decreasing . The substitution of Ti in zircon therefore is primarily for Si. Assuming a constant effect of P, unit and that and are proportional to ppm Zr in rutile and ppm Ti in zircon, [log(ppm Zr-in-rutile) + log] = A1 + B1/T(K) and [log(ppm Ti-in-zircon) + log − log] = A2 + B2/T, where the A and B are constants. The constants were derived from published and new data from experiments with buffered by either quartz or zircon + zirconia, from experiments with defined by the Zr content of rutile, and from well-characterized natural samples. Results are A1 = 7.420 ± 0.105; B1 = −4,530 ± 111; A2 = 5.711 ± 0.072; B2 = −4,800 ± 86 with activity referenced to α-quartz and rutile at P and T of interest. The zircon thermometer may now be applied to rocks without quartz and/or rutile, and the rutile thermometer applied to rocks without quartz, provided that and are estimated. Maximum uncertainties introduced to zircon and rutile thermometry by unconstrained and can be quantitatively assessed and are ≈60 to 70°C at 750°C. A preliminary assessment of the dependence of the two thermometers on P predicts that an uncertainty of ±1 GPa introduces an additional uncertainty at 750°C of ≈50°C for the Ti-in-zircon thermometer and of ≈70 to 80°C for the Zr-in-rutile thermometer.  相似文献   

16.
Solubility experiments were conducted for the dissolution reaction of brucite, Mg(OH)2 (cr): Experiments were conducted from undersaturation in deionized (DI) water and 0.010–4.4 m NaCl solutions at 22.5°C. In addition, brucite solubility was measured from supersaturation in an experiment in which brucite was precipitated via dropwise addition of 0.10 m NaOH into a 0.10 m MgCl2 solution also at 22.5°C. The attainment of the reversal in equilibrium was demonstrated in this study. The solubility constant at 22.5°C at infinite dilution calculated from the experimental results from the direction of supersaturation by using the specific interaction theory (SIT) is: with a corresponding value of 17.0 ± 0.2 (2σ) when extrapolated to 25°C. The dimensionless standard chemical potential (μ°/RT) of brucite derived from the solubility data in 0.010 m to 4.4 m NaCl solutions from undersaturation extrapolated to 25°C is −335.76 ± 0.45 (2σ), with the corresponding Gibbs free energy of formation of brucite, , being −832.3 ± 1.1 (2σ) kJ mol−1. In combination with the auxiliary thermodynamic data, the is calculated to be 17.1 ± 0.2 (2σ), based on the above Gibbs free energy of formation for brucite. This study recommends an average value of 17.05 ± 0.2 in logarithmic unit as solubility constant of brucite at 25°C, according to the values from both supersaturation and undersaturation. Sandia National Laboratories is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under Contract DE-AC04-94AL85000.  相似文献   

17.
Recent work has emphasized that the empirical rate equation for batch dissolution of a solid consists of a forward term involving the surface area minus a back reaction term involving surface area and concentration of dissolved solid. Integrated forms exist for use at extremes of high under-saturation and of very heavy solid loadings which lead to saturation. A middle condition allows for significant decrease in solid supply and simultaneous arrival at saturation. This study tests the three approaches simultaneously to the batch dissolution of gypsum, thereby demonstrating a consistent applicability of the afore-mentioned rate equation. Previously, some mineral dissolutions have displayed so-called nonlinear kinetics and hence have not appeared to conform to this rate equation. This paper provides a template for future investigation of those situations; dissolution experiments are not easy to perform, and instances of the so-called nonlinear kinetics may represent experimental artefact. The relationship between this empirical approach and that of Transition State Theory used in mineral dissolution is discussed, and a new, linear proof for the applicability of the ‘middle ground’ equations is demonstrated. Stirring experiments highlight the difference between the conditions in fluidized bed and laminar flow reactors. Gypsum dissolution is found to be transport limited at all but very vigorous laboratory stirring conditions, although the relationship between the rate of shrinkage of gypsum particles and stirring seems to be relatively simple. A stirring factor is applied to the rate equation overall to allow for differences in reactor design, and it is suggested that this should also be applicable to laminar flow reactors. The link between batch and chemo-stat dissolutions is stressed, together with a need to contour dissolution data on a new graph of particle size versus stirring rate.  相似文献   

18.
The diffusion of water in a peralkaline and a peraluminous rhyolitic melt was investigated at temperatures of 714–1,493 K and pressures of 100 and 500 MPa. At temperatures below 923 K dehydration experiments were performed on glasses containing about 2 wt% H2O t in cold seal pressure vessels. At high temperatures diffusion couples of water-poor (<0.5 wt% H2O t ) and water-rich (~2 wt% H2O t ) melts were run in an internally heated gas pressure vessel. Argon was the pressure medium in both cases. Concentration profiles of hydrous species (OH groups and H2O molecules) were measured along the diffusion direction using near-infrared (NIR) microspectroscopy. The bulk water diffusivity () was derived from profiles of total water () using a modified Boltzmann-Matano method as well as using fittings assuming a functional relationship between and Both methods consistently indicate that is proportional to in this range of water contents for both bulk compositions, in agreement with previous work on metaluminous rhyolite. The water diffusivity in the peraluminous melts agrees very well with data for metaluminous rhyolites implying that an excess of Al2O3 with respect to alkalis does not affect water diffusion. On the other hand, water diffusion is faster by roughly a factor of two in the peralkaline melt compared to the metaluminous melt. The following expression for the water diffusivity in the peralkaline rhyolite as a function of temperature and pressure was obtained by least-squares fitting:
where is the water diffusivity at 1 wt% H2O t in m2/s, T is the temperature in K and P is the pressure in MPa. The above equation reproduces the experimental data (14 runs in total) with a standard fit error of 0.15 log units. It can be employed to model degassing of peralkaline melts at water contents up to 2 wt%.  相似文献   

19.
Mechanisms of hydrogen incorporation and diffusion in iron-bearing olivine   总被引：1，自引：1，他引：0  
The incorporation and diffusion of hydrogen in San Carlos olivine (Fo90) single crystals were studied by performing experiments under hydrothermal conditions. The experiments were carried out either at 1.5 GPa, 1,000°C for 1.5 h in a piston cylinder apparatus or at 0.2 GPa, 900°C for 1 or 20 h in a cold-seal vessel. The oxygen fugacity was buffered using Ni–NiO, and the silica activity was buffered by adding San Carlos orthopyroxene powders. Polarized Fourier transform infrared (FTIR) spectroscopy was utilized to quantify the hydroxyl distributions in the samples after the experiments. The resulting infrared spectra reproduce the features of FTIR spectra that are observed in olivine from common mantle peridotite xenoliths. The hydrogen concentration at the edges of the hydrogenated olivine crystals corresponds to concentration levels calculated from published water solubility laws. Hydrogen diffusivities were determined for the three crystallographic axes from profiles of water content as a function of position. The chemical diffusion coefficients are comparable to those previously reported for natural iron-bearing olivine. At high temperature, hydrogenation is dominated by coupled diffusion of protons and octahedrally coordinated metal vacancies where the vacancy diffusion rate limits the process. From the experimental data, we determined the following diffusion laws (diffusivity in m2 s−1, activation energies in kJ mol−1): for diffusion along [100] and [010]; for diffusion along [001]. These diffusion rates are fast enough to modify significantly water contents within olivine grains in xenoliths ascending from the mantle.  相似文献   

20.
Opening and resetting temperatures in heating geochronological systems   总被引：2，自引：0，他引：2  
We present a theoretical model for diffusive daughter isotope loss in radiochronological systems with increasing temperature. It complements previous thermochronological models, which focused on cooling, and allows for testing opening and resetting of radiochronometers during heating. The opening and resetting temperatures are, respectively,
where R is the gas constant, E and D 0 are the activation energy and the pre-exponential factor of the Arrhenius law for diffusion of the daughter isotope, a the half-size of the system (radius for sphere and cylinder and half-thickness for plane sheet) and τ the heating time constant, related to the heating rate by
For opening and resetting thresholds corresponding to 1 and 99% loss of daughter isotope, respectively, the retention parameters for sphere, cylinder and plane sheet geometries are A op = 1.14 × 105, 5.07 × 104 and 1.27 × 104 and A rs = 2.40, 1.37 and 0.561. According to this model, the opening and resetting temperatures are significantly different for most radiochronometers and are, respectively, lower and higher than the closure temperature. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.  相似文献   

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