Dissolution Kinetic Model Research Articles

On-line monitoring of in-vitro oral bioaccessibility tests as front-end to liquid chromatography for determination of chlorogenic acid isomers in dietary supplements

A novel fully automated in-vitro oral dissolution test assay as a front-end to liquid chromatography has been developed and validated for on-line chemical profiling and monitoring of temporal release profiles of three caffeoylquinic acid (CQA) isomers, namely, 3-CQA,4-CQA and 5-CQA, known as chlorogenic acids, in dietary supplements. Tangential-flow filtration is harnessed as a sample processing approach for on-line handling of CQA containing extracts of hard gelatin capsules and introduction of protein-free samples into the liquid chromatograph. Oral bioaccessibility/dissolution test assays were performed at 37.0±0.5°C as per US Pharmacopeia recommendations using pepsin with activity of ca. 749,000 USP units/L in 0.1mol/L HCl as the extraction medium and a paddle apparatus stirred at 50rpm. CQA release rates and steady-state dissolution conditions were determined accurately by fitting the chromatographic datasets, namely, the average cumulative concentrations of bioaccessible pools of every individual isomer monitored during 200min, with temporal resolutions of ≥10min, to a first-order dissolution kinetic model. Distinct solid-to-liquid phase ratios in the mimicry of physiological extraction conditions were assessed. Relative standard deviations for intra-day repeatability and inter-day intermediate precision of 5-CQA within the 5–40µg/mL concentration range were <3.4% and <5.5%, respectively. Trueness of the automatic flow method for determination of 5-CQA released from dietary supplements in gastric fluid surrogate was demonstrated by spike recoveries, spanning from 91.5–104.0%, upon completion of the dissolution process. The proposed hyphenated setup was resorted for evaluating potential differences in dissolution profiles and content of the three most abundant chlorogenic acid isomers in dietary supplements from varied manufacturers.

Coarsening and dissolution of γ′ precipitates during solution treatment of AD730™ Ni-based superalloy: Mechanisms and kinetics models

The kinetics of γ′ size and volume fraction changes during solution treatment of the advanced Ni-based superalloy, AD730™ are determined and the underlying mechanisms are investigated. High resolution Differential Thermal Analysis (DTA) and thermodynamic modeling were used to design and perform solution heat treatment experiments. Semi-analytical models are developed to describe the dissolution and coarsening processes. The results from the proposed models, supported by electron microscopy observations, indicate that coarsening occurs before complete dissolution takes place. Agglomeration is shown to be the governing coarsening mechanism for this alloy after calculation of the coefficients for both the Ostwald ripening and agglomeration mechanisms. Electron microscopy observations revealed that the early stages of agglomeration occur by neck formation between two neighboring particles. The splitting of γ′ particles was identified as one of the main dissolution mechanisms. Based on the obtained results, a dissolution kinetics model is proposed to quantify the volume fraction of dissolved γ′ particles and estimate the activation energy of this process for AD730™. A coarsening model based on the time-temperature dependence of the γ′ coarsening rate coefficient is also proposed taking the concentration of elements, γ′ volume fraction and the temperature into consideration. Based on this model, a method is developed to predict γ′ size evolution during aging heat treatment process and an optimum heat treatment to reach the desired γ′ distribution is proposed. The validity and accuracy of the proposed models were verified by carrying out different heat treatment experiments.

Ultrasonic-Assisted Dissolution of Polystyrene in Decahydronaphthalene for the Preparation of Poly(Cyclohexylethylene)

Dissolution process of polystyrene in decahydronaphthalene solution was conducted and compared under different conditions. The effects of dissolution time and temperature on the dissolution ratio of polystyrene were performed with the assistance of ultrasonic and mechanical agitation, respectively. The dissolution ratio of polystyrene increased with the increment of dissolution time and dissolution temperature, polystyrene dissolved faster under ultrasonic-assisted process. The polystyrene dissolution kinetic model was developed and used to calculate the dissolution rate constant. The kinetic model showed good agreement with the experimental data, and the dissolution rate constant indicated that ultrasonic can obviously enhance the dissolution process of polystyrene in decahydronaphthalene solution.

An analytical model for secondary phase dissolution kinetics

An analytical model for dissolution kinetics of secondary phase particles upon isothermal annealing has been proposed. Considering the interactions of solute diffusion fields in front of the secondary phase/matrix interface upon dissolution, a Johnson–Mehl–Avrami type equation, subjected to necessary modification, was derived, in combination with a classic dissolution model for single-particle system. Compared with the semiempirical dissolution models, which are used to fit the experimental results and phase-field method simulation, the current model follows an analogous form, but with the time-dependent kinetic parameters. Distinct from the model fitting work published recently, the current model is derived from the diffusion-controlled transformation theory, while the modeling quality is guaranteed by the physically realistic model parameters. On this basis, the current model calculation leads to a clear relationship between the secondary phase volume fraction and the time. Accordingly, model predictions for isothermal θ′ dissolution in Al–3.0wt%–Cu alloy and silicon dissolution in Al–0.8wt%–Si alloy were performed; good agreement with the published experimental data has been achieved.

A comprehensive stochastic model of phyllosilicate dissolution: Structure and kinematics of etch pits formed on muscovite basal face

Accurate modeling of phyllosilicate dissolution kinetics is a complex problem involving recognition of the influence of structure, chemical composition, lattice defects, and surface topography on local and global dissolution mechanisms. Previous research has provided a wealth of experimental observations that illustrate the dominant role of etch pits in formation of the steps on the basal face of mica during the dissolution reaction. The shape of the etch pits bears important information on surface reactivity and dissolution rate anisotropy at given environmental conditions. In order to understand the influence of various kinetic factors on etch pit and step morphology, as well as the overall dissolution mechanisms, we have developed a new Kinetic Monte Carlo model simulating dissolution of these minerals. The model considers the effects of chemical composition, structural position, the number of first and second-order nearest neighbors and the steric hindrance of surface atoms on the etch pit morphology and step reactivity. We describe several complexity levels of the model which are characterized by the different ranges of the effects considered. These levels were developed in order to find the most optimal model capable of predicting experimentally observed etch pit morphologies. Our simulation results show that the models based on the sole consideration of the first coordination sphere in general can predict etch pit shape and orientation, while recognition of the site reactivity difference imposed by the steric factors helps us to explain the geometry of monolayer pit superposition. However, the distinction of the ledge and kink sites at all the experimentally observed surface steps is possible only with the use of the second-order neighbors. Based on these findings, we propose a mechanistic scheme explaining the role of the first and second-order coordination numbers in step stabilization and correct prediction of the etch pit structure.

A dissolution kinetics model and its application to duplex stainless steels

This work proposes a semi-empirical model for isothermal particle dissolution. An impingement factor in the form yc+1 is introduced to generalize the exponential law found in the recent literature and numerically obtained by means of the phase field method. A procedure is described for calibration of the model parameters that uses information from isothermal experiments. The model was applied to isothermal dissolution of σ phase in duplex stainless steels. A very good agreement was obtained between experimental and analytical results.

Unifying Batch-Dissolution Kinetics for Salts: Probing the Back Reaction for Gypsum and Calcite by Means of the Common-Ion Effect

Recent success in fitting the shrinking object model for dissolution kinetics to biogenic silica, silica gel, simple salts, sucrose and gypsum prompted this study of the effects of common ions upon gypsum dissolution kinetics. Middle-ground dissolutions were mainly studied, in which shrinkage of the surface area, S, is significant, and the system approaches, but does not reach, saturation, c sat. Dissolution was monitored by conductimetry. At a constant ionic strength of 0.060 M, the net rate for gypsum dissolution is given by $$ {\text{Net}}\,{\text{Rate}} = k_{\text{b}} \cdot S \cdot (c_{\text{sat}} - c ) $$ , where k b is a rate constant, and c can be expressed alternatively in terms of either [Ca2+], [SO4 2−] and [e±], that part of the electrolyte concentration contributed by gypsum dissolution, or as the equivalent total concentrations of these species, for example, [SO4 2−]T. The presence of either calcium or sulphate as a common ion slows dissolution, and the effect of this upon c sat, k b and k f, the forward rate constant, is discussed. Contrary to previous experience, it is emphasised that each fitting of the shrinking object model demands its own value of the Solubility of gypsum, c sat, which can be derived from the Solubility Product. This experience with gypsum is aligned with previous work on calcite, to develop a unified approach to the batch dissolution of salts. It highlights serious deficiencies in the way earlier common-ion experiments were conceived and enacted, and in particular with the rate equation of Sjoberg (Geochim Cosmochim Acta 40:441–447, 1976) for calcite above a pH of 7. Common-ion experiments are shown to be crucially important for probing the back reaction to dissolutions and might be applied to the far bigger problem of silicate-mineral dissolution, where ‘non-linear kinetics’ are often observed.

Conditions Optimization and Kinetics for the Cleaning of Ceramic Membranes Fouled by BaSO4 Crystals in Brine Purification Using a DTPA Complex Solution

We investigated the cleaning efficiency and kinetics of multichannel ceramic membranes fouled during brine purification. The foulants were first characterized by means of SEM, EDX, and XRD analyses, and we found that mainly BaSO4 crystals were deposited on the membrane surface. A cleaning solution composed of diethylenetrinitrilopentaacetic acid (DTPA), oxalic acid, and NaOH was developed to regenerate the fouled ceramic membranes. The membranes could be completely recovered with the cleaning solution. The cleaning rate increased with the concentration of DTPA (CDTPA) and temperature (T) but was not sensitive to the crossflow velocity (CFV) or transmembrane pressure (TMP). The optimized cleaning condition was CDTPA = 1.0 × 10–3 mol/L, T = 50 °C, CFV = 3.0 m/s, and TMP = 0.10 MPa. A dissolution kinetics model associated with both the concentration factor and temperature factor was developed, which fitted well the experimental results. This model was used to determine the reaction rate constants during the ...

Kinetic modeling of glucose and fructose dissolution in 2-methyl 2-butanol

With the objective of developing simulation models for sugar bioconversion processes in non-aqueous media, the present study investigated the dissolution kinetics of glucose and fructose in 2-methyl 2-butanol at temperatures between 20 °C and 80 °C. For both sugars a two-phase dissolution process was observed, characterized by an initially fast dissolution lasting a few minutes, followed by a much slower dissolution phase extending up to 24 h. The experimental results are described by a combined sugar dissolution and mutarotation kinetic model that considers the dissolution of the sugar anomeric form present in the solid particles, namely α- d-glucopyranose and ß- d-fructopyranose, and its subsequent mutarotation in solution. The initial dissolution step is assumed limited by the solute transport from the surface to the bulk solution, and the corresponding sugar transport coefficient evaluated from established mass transport correlations. The second slower dissolution phase is solely controlled by the sugar mutarotation rate, and modeled as a first-order reversible reaction. The determined values of the mutarotation rate and equilibrium constants can be related to the solution temperature by an Arrhenius and Van’t Hoff relationship, respectively.

Dissolved plume attenuation with DNAPL source remediation, aqueous decay and volatilization — Analytical solution, model calibration and prediction uncertainty

A vertically-integrated analytical model for dissolved phase transport is described that considers a time-dependent DNAPL source based on the upscaled dissolution kinetics model of Parker and Park with extensions to consider time-dependent source zone biodecay, partial source mass reduction, and remediation-enhanced source dissolution kinetics. The model also considers spatial variability in aqueous plume decay, which is treated as the sum of aqueous biodecay and volatilization due to diffusive transport and barometric pumping through the unsaturated zone. The model is implemented in Excel/VBA coupled with (1) an inverse solution that utilizes prior information on model parameters and their uncertainty to condition the solution, and (2) an error analysis module that computes parameter covariances and total prediction uncertainty due to regression error and parameter uncertainty. A hypothetical case study is presented to evaluate the feasibility of calibrating the model from limited noisy field data. The results indicate that prediction uncertainty increases significantly over time following calibration, primarily due to propagation of parameter uncertainty. However, differences between the predicted performance of source zone partial mass reduction and the known true performance were reasonably small. Furthermore, a clear difference is observed between the predicted performance for the remedial action scenario versus that for a no-action scenario, which is consistent with the true system behavior. The results suggest that the model formulation can be effectively utilized to assess monitored natural attenuation and source remediation options if careful attention is given to model calibration and prediction uncertainty issues.

A simple model for complex dissolution kinetics: A case study of norfloxacin

A new semi-empirical model, particularly useful for studying complex dissolution kinetics, is presented here. It uses only two ‘fit parameters’, each possessing physically relevant units (in the time domain). The model is based on the idea that dispersion (variation) in the activation energy barrier may arise in certain cases, as a result of (quantized) molecular kinetic energies affecting the speed of the rate-determining step (r.d.s.) of the dissolution event. For such ‘dispersive dissolutions’, the r.d.s. is assumed to involve 2D denucleation. The author's dispersive kinetic model is shown to be applicable to the dissolution of various formulations of norfloxacin which produce very asymmetric, sigmoidal concentration versus time ( C– t) profiles. It is derived by assuming an activation energy distribution having the functional form of the Maxwell–Boltzmann (M–B) distribution, coupled with a first-order rate expression. However, this model can also be reduced to give the same functional form as the classical Noyes–Whitney equation, in order to accurately fit/describe dissolution profiles which appear logarithmic (such profiles are due to dissolution phenomena that are not dispersive; i.e. for cases where the activation energy is essentially single-valued). Thus, the kinetic model presented in this work may potentially find broad applicability to the modeling of various dissolution trends observed in the literature.

Dissolution kinetic model for metal powders — a case of varying surface area

A kinetic model for leaching particulate metals in a batch system was developed. The leaching mechanism was analyzed by solving a series of ordinary differential equations relating heterogeneous reaction kinetics at the solid/liquid interface to mass transfer of reactant and products. Special emphasis was given to the effects of substrate surface area changes and initial particle distribution on the overall leaching rate. The dissolution of gold powders in acidic solution with bromine as an oxidant was used as a model system. The effects of particle size. particle distribution, chemical reaction order, rate constant and mass transfer coefficient on the overall metal powder dissolution rate are analyzed and discussed.

Experimental and Theoretical Study of the Surface-Controlled Dissolution of Cylindrical Particles. Application to Solubilization of Potassium Hydrogen Carbonate in Hot Dimethylformamide

In this paper we present a mathematical model for the surface-controlled dissolution of cylindrical solid particles. This is employed to interpret experimental data published previously for the dissolution of potassium bicarbonate in dimethylformamide at elevated temperatures. Significant kinetic differences in assuming cylindrical rather than spherical shapes are reported with the former representing a closer approximation to the true shape of the particles as revealed by scanning electron microscopy. From the fits of experimental data to the cylindrical model for the surface-controlled dissolution, the dissolution rate constant, k, for the dissolution of KHCO(3) in DMF was found to be (9.6 +/- 1.6) x 10(-9) mol cm(-2) s(-1) at 100 degrees C, and the activation energy for the dissolution was 34.5 kJ mol(-1) over the temperature range of 60-100 degrees C. Comparison between cylindrical and spherical dissolution theory highlights the importance of considering the particle shapes for realistic modeling of surface-controlled dissolution kinetics.

Evaluation of an upscaled model for DNAPL dissolution kinetics in heterogeneous aquifers

Estimates of contaminant fluxes from DNAPL sources as a function of time and DNAPL mass reduction are important to assess the long-term sustainability and costs of monitored natural attenuation and to determine the benefits of partial source removal. We investigate the accuracy of the upscaled mass transfer function (MTF) proposed by Parker and Park [Parker JC, Park E. Modeling field-scale dense nonaqueous phase liquid dissolution kinetics in heterogeneous aquifers. WRR 2004;40:W05109] to describe field-scale dissolved phase fluxes from DNAPL sources for a range of scenarios generated using high-resolution 3-D numerical simulations of DNAPL infiltration and long-term dissolved phase transport. The results indicate the upscaled MTF is capable of accurately describing field-scale DNAPL dissolution rates as a function of time. For finger-dominated source regions, an empirical mass depletion exponent in the MTF takes on values greater than one which results in predicted mass flux rates that decrease continuously with diminishing DNAPL mass over time. Lens-dominated regions exhibit depletion exponents less than one, which results in more step-function like mass flux versus time behavior. Mass fluxes from DNAPL sources exhibiting both lens- and finger-dominated subregions were less accurately described by the simple MTF, but were well described by a dual-continuum model of the same form for each subregion. The practicality of calibrating a dual-continuum model will likely depend on the feasibility of obtaining spatially resolved field measurements of contaminant fluxes or concentrations associated with the subregions using multilevel sampling or some other means.

Kinetics of the SiO 2 aerogel dissolution in aqueous NaOH solutions: experiment and model

The paper is devoted to the study of the kinetics of silica aerogel dissolution in 0.05–0.79 M NaOH aqueous solutions at temperatures 15–56°C. The aerogel samples are prepared via common one- and two-step procedures, and differ considerably in the primary particle size. Kinetic peculiarities of the process are studied under both reaction and diffusion controlled modes and kinetic parameters are established by experimental curve fitting. The dissolution activation energy is found to be equal to 82±6 kJ/mol for all the aerogels. The dissolution kinetic curves appear to be S-shaped, so that the process rate passes through a maximum. The coincidence of SAXS and BET specific surface areas indicates that the aerogels have no closed porosity so the initial rate increase cannot be explained by the opening of closed pores. A new modification of the Iler dissolution kinetic model has been developed to describe the experimentally observed kinetic curves.

Rheological behavior of drug suspensions in Gelucire ® mixtures and proxyphylline release from matrix hard gelatin capsules

Mixtures of Gelucires ® 50/02 and 50/13 showing different hydrophilic-lipophilic balances (HLB) and of proxyphylline were used to prepare suspensions at a concentration of 25% and to manufacture extended release hard gelatin capsules by cooling. The rheological behaviors of Gelucire ® mixtures with and without drug were determined by adjustment of the rheograms to the Ostwald power-law and by statistical assessment of the flow index. Pure Gelucire ® mixtures were very slightly shear thickening whereas proxyphylline suspensions had a thixotropic shear thinning behavior. These rheological behaviors can be explained by the chemical composition and by the ratio of the two Gelucires ® used. Extended release of proxyphylline was obtained with all these mixtures. Drug release increased with Gelucire ® mixture HLB owing to higher erosion. A viscosity-release relationship was found and allowed, with these two Gelucires ® of extreme HLB and viscosities, to define the formulations which will give an optimal drug release, by the determination of their suspension viscosity. Modeling of dissolution kinetics has generally shown the predominance of surface erosion of the plugs relative to drug diffusion inside the matrix. This was confirmed by the better linearization of percentage released, according to Hixson–Crowell as compared with Higuchi.

Modelling of ammoniacal oxygen leaching of metallic iron in a stirred slurry reactor

A new model for iron dissolution kinetics by oxidative ammoniacal leaching similar to that encountered in the Becher process for synthetic rutile manufacture is proposed. The model takes into account solid-liquid and gas-liquid oxygen mass transfer as well as oxidation of Fe 2+ to Fe 3+ ions as the controlling steps in the initial linear phase of the overall process. The model has been validated for the system containing metallic iron particles in a multiphase, sparged, agitated reactor under isothermal conditions. Along with kinetic measurements, the variation in pH and oxidation reduction potential were also monitored continuously. Both disc type turbines and axial flow turbines were used as the agitators. The model was found to be applicable over a modest range of process parameters (8 ≤ specific energy dissipation rate ≤ 15 kW/m 3, 8 × 10 −5 ≤ air flow rate ≤ 2 × 10 −4 m 3/s, iron particle size 230 μm, partial pressure of oxygen ≤2.03 × 10 4 Pa and 5 ≤ weight percentage of iron particles ≤ 40). The results indicate that Sano's correlation for solid-liquid mass transfer and Linek's correlation for gas-liquid mass transfer are adequate for describing the data. The rate of iron dissolution was insensitive to the loading of iron particles, which is explained as being due to the solid particles acting as oxygen sinks inside an encapsulated shell around the bubble. Variations in pH, oxidation reduction potential and Fe 2+ ion concentration with solid loading and oxygen partial pressure are consistent with the overall reaction mechanism proposed in this work.

A dissolution kinetic model for metals in solutions

A kinetic model for the batch leaching of various metals using different lixiviants was developed. The overall material balances for the reactants and products at the solid/liquid interface were formulated for various types of heterogeneous reactions at the interface. The solutions to these mass balances are identified analytically, as well as numerically. Applications of these numerical solutions to various leaching systems using rotating discs or powders are discussed. The metal-dissolution systems addressed include cobalt, nickel and copper in acid, cyanide and ammoniacal solutions.

Calorimetric study of the dissolution of Guinier-Preston zones and η′ phase in Al-4.5at.%Zn-1.75at.%Mg

Differential scanning calorimetry was used to study the energetics and the dissolution kinetics of Guinier-Preston zones and η′ phases in Al-4.5at.%Zn-1.75at.%Mg alloys aged for various times at 298 or 393 K. The results show that for samples aged at 298 K the dissolution enthalpies, which are proportional to the pre-existing particle volume fractions, increase with the aging time, whereas for samples aged at 393 K the ΔH r values exhibit a maximum after aging for 16 days. However, the peak and reversion temperatures always increase with the aging time regardless of the aging temperature. Using an integrated kinetic function, developed on the basis of a difusion-limited dissolution kinetic model under non-isothermal conditions, the calculated curves were fitted to the experimental data, allowing precipitate sizes to be computed. Furthermore, good correlation was observed between the strength of these alloys and the measured particle size.

Powder Suspension Method for Critically Re-Examining the Two-Site Model for Hydroxyapatite Dissolution Kinetics

A powder dissolution method has been developed, and experiments with the hydroxyapatite suspensions confirm earlier conclusions based on dissolution from hydroxyapatite disks. Although a quantitative assessment of the properties of site 1 was not possible from the data obtained in the present study, a rather accurate and independent evaluation of the properties and the behavior of site 2 of the two-site model for hydroxyapatite dissolution was possible, and the results clearly validate the original two-site model. The present work together with the earlier disk studies show that dissolution from site 2 is well described by a first-order expression, rate = kc2 (Cs2 - C), where kc2 is a first-order rate constant, Cs2 is the apparent solubility for site 2 (defined by an ion activity product, KHAP, of the form a10Ca2+ a6PO43−a2OH−, and the solution conditions), and C is the microenvironmental solution concentration of hydroxyapatite. For four different precipitated hydroxyapatite preparations, a single KHAP value of 1 × 10−128 ± 1 was found to be consistent with experiments using solutions covering wide ranges of partial saturation and calcium-phosphate ratios. The hydroxyapatite powder and pellet methods (including the data evaluation procedures) now offer a powerful combination for investigating the complex kinetics associated with dental enamel dissolution in particular and enamel chemistry in general.