Calculated Dissolution Rate Research Articles

Mechanism of interaction between zirconium dioxide and fluoride melts

In this work, the mechanism of interaction between zirconium dioxide and fluoride melts was studied. Dissolution rates and maximum permissible oxide contents in the KF-AlF3 and NaF-AlF3 melts were determined under natural convection conditions at a temperature of 750 °C. The results of solubility measurement show that the limiting content of ZrO2 in the KF-AlF3 melt ([KF]/[AlF3] = 1.3) is 0.69 ± 0.10 mol. %, and in the NaF-AlF3 melt ([NaF]/[AlF3] = 1.3) at 800 °C it is 0.54 ± 0.04 mol. %. The calculated dissolution rate of zirconium oxide under these conditions in melts based on potassium fluoride and sodium fluoride is 0.022 mol/min and 0.017 mol/min, respectively. The influence of the cationic composition of the medium and the concentrations of additives on the liquidus temperatures of the melts was studied. It has been established that the increase in liquidus and solidus temperatures is facilitated by the addition of zirconium and aluminium oxides, as well as by the replacement of potassium fluoride with sodium fluoride while maintaining the molar ratio of the replaced cations. Analysis of thermal effects by differential scanning calorimetry (DSC) shows that, regardless of the molar ratio of the components, the onset of the thermal effect in melts based on potassium fluoride occurs at a temperature of 542 °C and in the systems with sodium fluoride additives at a temperature of 597 °C. Presumably, this dependence is associated with the melting of the KAlF4 and K2NaAl3F12 phases formed in the melts based on KF-AlF3 and KF-NaF-AlF3, respectively. It has been established that the melting of the KF-AlF3 mixture is accompanied with a mass loss of up to 1.3 wt. %, which is associated with partial evaporation of KAlF4.

Influence of etch pit development on the surface area and dissolution kinetics of the orthoclase (001) surface

The (001) orthoclase surface was dissolved at 180°C and at far from equilibrium conditions with an alkaline solution (pH180°C=9) in a titanium open flow reactor. Vertical scanning interferometer (VSI) and atomic force microscope (AFM) surface monitoring were periodically used during the reaction process in order to quantify the surface topography evolution. The dissolution of the (001) orthoclase face occurs with the formation of diamond shape etch pits. Diamond pit diagonals are parallel to the [100] and [010] axes, and the pit walls are parallel to (6 5 6), 65¯6, (6¯511) and 6¯5¯11 planes. The etch pit size and global surface retreat of the (001) surface were found to increase linearly with time. Based on statistical treatments of etch pit development monitoring by AFM, we designed a numerical model aimed at reproducing and quantifying the total surface evolution. Numerical results show that the stabilization of etch pits doubles the calculated dissolution rate, partly due to the intrinsically higher reactivity of pit walls, consistent with a dissolution process in line with the periodic bond chain (PBC) theory. In addition, normalizing the dissolution rate by the initial surface area of the (001) orthoclase surface induces a 20% overestimation of the calculated dissolution rate, while the total surface area of the dissolving face reaches a steady state after a few days of reaction. Additional simulations conducted to assess the impact of defect parameters revealed a weak dependence of the dissolution rate on dislocation density, consistent with previous experimental observations. Overall, the combined effect of the various defect parameters does not affect the dissolution rate by more than an order of magnitude, and probably contributes to a moderate extent to the dispersion of mineral dissolution rate data reported in the literature.

GILDES Model Simulations of the Atmospheric Corrosion of Zinc Induced by Low Concentrations of Carboxylic Acids

The GILDES computer based model was successfully applied to the atmospheric corrosion of zinc exposed to low concentrations of carboxylic acids in humidified air at room temperature. Under these exposure conditions the expected precipitated phases are zinc oxide (ZnO), zinc hydroxide (Zn(OH)2) and several forms of hydrated zinc carboxylate, Zn(CH3CH2COO)2·2H2O, Zn(CH3COO)2·2H2O and Zn(HCOO)2·2H2O. The results were compared to those from laboratory exposures obtained in the same conditions. The model correctly predicts the trend for ZnO and zinc carboxylate formation found in experimental exposures for the three acids tested. According to the simulations, surface protonation, surface acid base reactions, as well as ligand- and proton- induced dissolution reactions play a major role in the initial atmospheric corrosion of zinc. Henry's law constant (KH) is found to be an important parameter but uncertain due to different reported literature values. When KH is increased the formation rate of zinc carboxylate also increases. KH increases in the sequence propionic acid < acetic acid < formic acid, the same order as found for the calculated dissolution rate.

In vitro biodurability of the product of thermal transformation of cement–asbestos

To safely recycle the product of the thermal transformation of cement–asbestos as secondary raw material, its toxicity potential should be assessed by in vitro biodurability tests. In this work, the acellular in vitro biodurability of the products of transformation of cement–asbestos at 1200°C (named KRY·AS) was tested using both inorganic and organic simulated lung fluids at pH 4.5. The dissolution kinetics were followed using chemical, mineralogical and microstructural analyses. The total dissolution time estimated from the experiments with inorganic HCl diluted solution is one order of magnitude higher than that determined from the experiments with buffered Gamble solution (253 days vs. 20 days). The key parameter determining the difference in dissolution rate turns out to be the solidus/liquidus ratio which prompts a fast saturation of the solution with monosilicic acid. The calculated dissolution rate constants showed that the biodurability in vitro of KRY·AS is much lower with respect to that of standard chrysotile asbestos (total estimated dissolution time of 20 days vs. 298 days, respectively). This proves a low potential toxicity of this secondary raw material.

Dissolution of uranium metal without hydride formation or hydrogen gas generation

This study shows that metallic uranium will cleanly dissolve in carbonate-peroxide solution without generation of hydrogen gas or uranium hydride. Metallic uranium shot, 0.5–1 mm diameter, was reacted with ammonium carbonate–hydrogen peroxide solutions ranging in concentration from 0.13 M to 1.0 M carbonate and 0.50 M to 2.0 M peroxide. The dissolution rate was calculated from the reduction in bead mass, and independently by uranium analysis of the solution. The calculated dissolution rate ranged from about 4 × 10 −3 to 8 × 10 −3 mm/h, dependent primarily on the peroxide concentration. Hydrogen analysis of the etched beads showed that no detectable hydrogen was introduced into the uranium metal by the etching process.

The mineral dissolution rate conundrum: Insights from reactive transport modeling of U isotopes and pore fluid chemistry in marine sediments

Pore water chemistry and 234U/ 238U activity ratios from fine-grained sediment cored by the Ocean Drilling Project at Site 984 in the North Atlantic were used as constraints in modeling in situ rates of plagioclase dissolution with the multicomponent reactive transport code Crunch. The reactive transport model includes a solid-solution formulation to enable the use of the 234U/ 238U activity ratios in the solid and fluid as a tracer of mineral dissolution. The isotopic profiles are combined with profiles of the major element chemistry (especially alkalinity and calcium) to determine whether the apparent discrepancy between laboratory and field dissolution rates still exists when a mechanistic reactive transport model is used to interpret rates in a natural system. A suite of reactions, including sulfate reduction and methane production, anaerobic methane oxidation, CaCO 3 precipitation, dissolution of plagioclase, and precipitation of secondary clay minerals, along with diffusive transport and fluid and solid burial, control the pore fluid chemistry in Site 984 sediments. The surface area of plagioclase in intimate contact with the pore fluid is estimated to be 6.9 m 2/g based on both grain geometry and on the depletion of 234U/ 238U in the sediment via α-recoil loss. Various rate laws for plagioclase dissolution are considered in the modeling, including those based on (1) a linear transition state theory (TST) model, (2) a nonlinear dependence on the undersaturation of the pore water with respect to plagioclase, and (3) the effect of inhibition by dissolved aluminum. The major element and isotopic methods predict similar dissolution rate constants if additional lowering of the pore water 234U/ 238U activity ratio is attributed to isotopic exchange via recrystallization of marine calcite, which makes up about 10–20% of the Site 984 sediment. The calculated dissolution rate for plagioclase corresponds to a rate constant that is about 10 2 to 10 5 times smaller than the laboratory-measured value, with the value depending primarily on the deviation from equilibrium. The reactive transport simulations demonstrate that the degree of undersaturation of the pore fluid with respect to plagioclase depends strongly on the rate of authigenic clay precipitation and the solubility of the clay minerals. The observed discrepancy is greatest for the linear TST model (10 5), less substantial with the Al-inhibition formulation (10 3), and decreases further if the clay minerals precipitate more slowly or as highly soluble precursor minerals (10 2). However, even several orders of magnitude variation in either the clay solubility or clay precipitation rates cannot completely account for the entire discrepancy while still matching pore water aluminum and silica data, indicating that the mineral dissolution rate conundrum must be attributed in large part to the gradual loss of reactive sites on silicate surfaces with time. The results imply that methods of mineral surface characterization that provide direct measurements of the bulk surface reactivity are necessary to accurately predict natural dissolution rates.

Fate of Rising CO2 Droplets in Seawater

The sequestration of fossil fuel CO2 in the deep ocean has been discussed by a number of workers, and direct ocean experiments have been carried out to investigate the fate of rising CO2 droplets in seawater. However, no applicable theoretical models have been developed to calculate the dissolution rate of rising CO2 droplets with or without hydrate shells. Such models are important for the evaluation of the fate of CO2 injected into oceans. Here, I adapt a convective dissolution model to investigate the dynamics and kinetics of a single rising CO2 droplet (or noninteracting CO2 droplets) in seawater. The model has no free parameters; all of the required parameters are independently available from literature. The input parameters include: the initial depth, the initial size of the droplet, the temperature as a function of depth, density of CO2 liquid, the solubility of CO2 liquid or hydrate, the diffusivity of CO2, and viscosity of seawater. The effect of convection in enhancing mass transfer is treated using relations among dimensionless numbers. The calculated dissolution rate for CO2 droplets with a hydrate shell agrees with data in the literature. The theory can be used to explore the fate of CO2 injected into oceans under various temperature and pressure conditions.

Reaction of hydroquinone with hematite: II. Calculated electron-transfer rates and comparison to the reductive dissolution rate

The rate of reaction of hematite with quinones and the quinone moieties of larger molecules may be an important factor in limiting the rate of reductive dissolution of hematite, especially by iron-reducing bacteria. It is possible that the rate of reductive dissolution of hematite in the presence of excess hydroquinone at pH 2.5 may be limited by the electron-transfer rate. Here, a reductive dissolution rate was measured and compared to electron-transfer rates calculated using Marcus theory. An experimental rate constant was measured at 9.5×10 −6 s −1 and the reaction order with respect to the hematite concentration was found to be 1.1. Both the dissolution rate and the reaction order of hematite concentration compare well with previous measurements. Of the Marcus theory calculations, the inner-sphere part of the reorganization energy and the electronic coupling matrix element for hydroquinone self-exchange electron transfer are calculated using ab initio methods. The second order self-exchange rate constant was calculated to be 1.3×10 7 M −1 s −1, which compares well with experimental measurements. Using previously published data calculated for hexaquairon(III)/(II), the calculated electron-transfer rate for the cross reaction with hydroquinone also compares well to experimental measurements. A hypothetical reductive dissolution rate is calculated using the first-order electron-transfer rate constant and the concentration of total adsorbed quinone. Three different models of the hematite surface are used as well as multiple estimates for the reduction potential, the surface charge, and the adsorption density of hydroquinone. No calculated dissolution rate is less than five orders of magnitude faster than the experimentally measured one.

Dedolomitization in different alkaline media: Application to Portland cement paste

The dedolomitization reaction kinetics is studied through several long-term experiments consisting of an aqueous dispersion of fine powders of dolomite and portlandite with alkalinity between 0.1 and 1 M KOH, at 25 and 75 °C. The experimental results are numerically simulated to calculate the apparent dissolution constant rates for dolomite, k dol. At low temperature, two dissolution stages were observed. In an early stage, part of dolomite powder dissolves quickly until an apparent steady is reached. After several days, the reaction continues at a lower rate. The calculated dissolution rate for dolomite in the first stage is one order of magnitude higher than that of the second stage. At 75 °C, the k dol is two orders of magnitude higher than at 25 °C. The addition of alkali increases the k dol at high temperature, but reduces it at room temperature.

Interferometric study of the dolomite dissolution: a new conceptual model for mineral dissolution

The dissolution rate and mechanism of three different cleavage faces of a dolomite crystal from Navarra (near Pamplona), Spain, were studied in detail by vertical scanning interferometry techniques. A total of 37 different regions (each about 124 × 156 μm in size) on the three sample surfaces were monitored as a function of time during dissolution at 25°C and pH 3. Dissolution produced shallow etch pits with widths reaching 20 μm during 8 h of dissolution. Depth development as a function of time was remarkably similar for all etch pits on a given dolomite surface. On the basis of etch pit distribution and volume as a function of time, the calculated dissolution rate increases from near zero to 4 × 10 −11 mol cm −2 s −1 over 5 h. The time variation is different for each of the three cleavage surfaces studied. In addition, the absolute dissolution rates of different parts of the dolomite crystal surface can be computed by using a reference surface. The different surfaces yield an “average” rate of 1.08 × 10 −11 mol cm −2 s −1 with a standard deviation of 0.3 × 10 −11 mol cm −2 s −1 based on about 60 analyses. The mean absolute rate of the dolomite surface is about 10 times slower than the rate calculated from etch pit dissolution alone. On the other hand, earlier batch rate data that used BET surface areas yield rates that are at least 30 to 60 times faster than our directly measured mean dissolution rate for the same pH and temperature. A conceptual model for mineral dissolution has been inferred from the surface topography obtained by the interferometry investigations. In this model, mineral dissolution is not dominated by etch pit formation itself but rather by extensive dissolution stepwaves that originate at the outskirts of the etch pits. These stepwaves control the overall dissolution as well as the dependence on temperature and saturation state.

The Development of a Modified Dissolution Method Suitable for Investigating Powder Mixtures

ABSTRACTA novel dissolution method was developed, suitable for powder mixtures, based on the USP basket apparatus. The baskets were modified such that the powder mixtures were retained within the baskets and not dispersed, a potential difficulty that may arise when using conventional USP basket and paddle apparatus. The advantages of this method were that the components of the mixtures were maintained in close proximity, maximizing any drug:excipient interaction and leading to more linear dissolution profiles. Two weakly acidic model drugs, ibuprofen and acetaminophen, and a selection of pharmaceutical excipients, including potential dissolution-enhancing alkalizing agents, were chosen for investigation. Dissolution profiles were obtained for simple physical mixtures. The f1 fit factor values, calculated using pure drug as the reference material, demonstrated a trend in line with expectations, with several dissolution enhancers apparent for both drugs. Also, the dissolution rates were linear over substantial parts of the profiles.For both drugs, a rank order comparison between the f1 fit factor and calculated dissolution rate, obtained from the linear section of the dissolution profile, demonstrated a correlation using a significance level of P = 0.05. The method was proven to be suitable for discriminating between the effects of excipients on the dissolution of the model drugs. The method design produced dissolution profiles where the dissolution rate was linear for a substantial time, allowing determination of the dissolution rate without mathematical transformation of the data. This method may be suitable as a preliminary excipient-screening tool in the drug formulation development process.

ESTIMATING IN VITRO GLASS FIBER DISSOLUTION RATE FROM COMPOSITION

A method is presented for calculating the dissolution rate constant of a borosilicate glass fiber in the lung, as measured in vitro, from the oxide composition in weight percent. It is based upon expressing the logarithm of the dissolution rate as a linear function of the composition. It was found that the calculated dissolution rate constant agreed with the measured value within the variation of the measured data in a set of compositions in which the dissolution rate constant ranged over a factor of 100. The method was shown to provide a reasonable estimate of dissolution over a considerably wider range of composition than what was used to determine the parameters, such as a set of data in which the dissolution rate constant varied over a factor of 100,000. The dissolution rate constant may be used to estimate whether disease would ensue following animal inhalation or intraperitoneal studies.

Dissolution Rates of Calcite (10 [formula omitted]4) Obtained by Scanning Force Microscopy: Microtopography-Based Dissolution Kinetics on Surfaces with Anisotropic Step Velocities

This paper reports on our use of scanning force microscopy (SFM) to study calcite dissolution rates. Until now, calculation of rates has been limited to surfaces on which steps retreat at an isotropic velocity. More commonly, on surfaces where steps in different directions retreat at different velocities, the rate depends on the velocities and the densities of the differently oriented steps. Here, we show that calculating rates from SFM image sequences is possible for anisotropic surfaces if the ratio of step lengths in different directions is constant in the analyzed images (e.g., by considering steps at nonintersecting pits exclusively). In contrast to nonintersecting pits, high velocity steps are formed at intersecting pits on the calcite (10 1 ̄ 4) surface. At these steps, material can be removed without the slow nucleation of kink sites. The morphology of these steps is not straight and they become easily pinned by particles or impurities. Therefore, measuring the velocity of step retreat directly in the images fails, but calculating the dissolution rate of surface regions with high velocity steps is still possible. Dissolution rate is roughly similar in both the deep etch pits and the areas with high velocity steps at intersecting pits. Consequently, we suggest that the formation of high velocity steps contributes considerably to the weak enhancement of the rate with increasing dislocation density because additional etch pits within the intersectional regions do not significantly increase the rate. The calculated dissolution rate of ∼1.5 × 10 −6 mol m −2 s −1 on the calcite (10 1 ̄ 4) surface in water at 24°C and pCO 2 = 10 −3.5 atm corresponds well to the rates obtained from batch experiments. Thus, SFM can be regarded as an instrument capable of acquiring rates even on surfaces with anisotropic step velocities.

Correlations between in vivo and in vitro dissolution rates of (alpha-bromoisovaleryl)urea polymorphs.

Correlations between the in vivo and in vitro dissolution rates of (α-bromoisovaleryl) urea polymorphs were investigated. The calculated dissolution rate constants obtained in the in vitro dissolution experiments were 0.135 and 0.133 (cm/min) for form I and form II, respectively. On the other hand, the crystals were administered intraduodenally into rats and the time course data of the plasma concentration were analyzed by the least-squares method on the basis of the Hixson-Crowell dissolution model for the intestinal dissolution process. The in vivo dissolution rate constants were obtained as 0.0629 and 0.0758 (cm/min) for form I and form II, respectively. These in vivo and in vitro dissolution rate constants are based on the Noyes-Nernst dissolution theory and should be comparable in nature. Nevertheless, the in vivo rate constants were about a half of those in vitro. This result suggests that the stirring efficiency in the intestine is about a half of that of the in vitro dissolution experiment in this study.

Dissolution of an ellipsoidal bubble in a slightly viscous liquid

The steady-state velocity, the degree of deformation, and the convective-diffusion-limited rate of quasisteady-state growth (or dissolution) are considered for gas bubbles having shapes close to those of spheres or disks. It is assumed that there are no surface-active substances in the liquid. A qualitative agreement is found between the calculated dissolution rate and the experimental data.