Well-stirred Solutions Research Articles

Uphill transport in improved reverse electrodialysis by removal of divalent cations in the dilute solution: A Nernst-Planck based study

Reverse electrodialysis is a relatively new technology for non-carbon based and renewable energy harvesting from river and sea water. Because of the existing salinity gradients between those two types of water, selective transport of counter-ions from the sea to the river water through an ion-exchange membrane generates a voltage drop across it, which can drive electricity through an external electric device. The decrease in power density caused by the presence of divalent ions in the solutions because of the uphill transport of these ions against their concentration gradient can be mitigated by treating the river water in order to remove such type of ions. In this work, the effects of the fraction of salt with divalent cation in the dilute solution on the energy harvesting process in a permeable cation-exchange membrane system with well-stirred bathing solutions under reverse electrodialysis conditions, are theoretically investigate on the basis of the Nernst-Planck transport equations. Interesting results, which are related to the uphill transport of the cations against their concentration gradient, emerge from the asymmetric distribution of the cationic concentrations in the inner boundaries of the membrane because of the ionic partitioning in permeable membranes.

Effect of Film Diffusion on the Ion-Exchange Kinetics of a Tracer Ion in Nafion-117 Membrane from a Mixture of Salt Solution.

The ion-exchange kinetics of a tracer ion (Cs+ and Ba2+) in presence of a bulk ion (Na+/H+) has been measured in Nafion-117 membrane for a range of concentrations of NaCl/HNO3 using the nonstationary radiotracer method. A systematic increase in the ion-exchange rate and decrease in the partition coefficients of the tracer ions between membrane and solution have been observed with the increase in bulk ion concentration. The sigmoidal nature of experimental profiles indicates film-diffusion-controlled kinetics even for well-stirred solutions. In the absence of an existing analytical or numerical solution, a simple empirical approach has been proposed to find the variable membrane surface concentration and has been used to solve the membrane diffusion equation by the finite difference method. The fitting of the experimental curves with a single diffusion coefficient for Cs+/Ba2+ has been achieved. The exchange rate has been found to be independent of the stirring speed beyond a limiting speed.

A diffusional bimolecular propensity function

We derive an explicit formula for the propensity function (stochastic reaction rate) of a generic bimolecular chemical reaction in which the reactant molecules move about by diffusion, as solute molecules in a bath of much smaller and more numerous solvent molecules. Our derivation assumes that the solution is macroscopically well stirred and dilute in the solute molecules. It effectively extends the physical rationale for the chemical master equation and the stochastic simulation algorithm from well-stirred dilute gases to well-stirred dilute solutions, with the former becoming a limiting case of the latter. This extension is important for cellular systems, where the solvent molecules are typically water and the solute (reactant) molecules are much larger organic structures, whose relatively low populations often require a discrete-stochastic formalism. In the course of our derivation, we illuminate some limitations on the ability of the classical diffusion equation to accurately describe how a diffusing molecule moves on spatial and temporal scales that are relevant to collision-induced chemical reactions.

Unstirred layers in measurements of CO2 permeability of the red cell membrane

We have used the mass spectrometric 18O technique to measure at 37°C CO2 permeability, PCO2, of human red blood cells (RBC) in saline, to which dextran of mol.wt. 60 kDa at concentrations between 0 and10 g% had been added. Apparent PCO2 was found to fall with increasing [dextran] down to 1/3, which was interpreted as an effect of unstirred layers around the RBC, USLe, that increase in thickness d with rising [dextran]. The viscosity of the dextran solutions was determined in an Ubbelohde viscometer. Plotting 1/PCO2 vs. solution viscosity gave a straight line. As theoretical hydrodynamics predict that USLe disappear at 0 viscosity, we extrapolated the straight line to a viscosity of 0, giving a "true" PCO2 of 0.16 cm/s, ~ 30% higher than the 0.12 cm/s measured in saline. We interpret the difference of these figures using the relation of diffusion resistances 1/PCO2,apparent ‐ 1/PCO2,true = d / DCO2, solution, where DCO2, solution is the CO2 diffusion coefficient in the saline of the unstirred layer. We obtain from this a d in saline of 0.5 µm. This figure is compatible with previous estimates of δfor RBCs in well‐stirred solutions. We conclude that USLe cause a moderate underestimation of PCO2. We also present a theoretical model showing that the intracellular unstirred layer (USLi) in RBC causes an additional underestimation of PCO2 by 30%, leading to a PCO2 in the absence of both USLe and USLi of ~ 0.2 cm/s.

Total Loss of Femoral Head and Acetabulum in Rapidly Destructive Hip Disease

The antibiotic nitrofurantoin is transported against an electrochemical gradient into milk.A monolayer of CIT₃ cells, a subline of the Comma 1D normal mouse mammary epithelial cell line, transports [¹⁴C]-nitrofurantoin against a concentration gradient from the basal to the apical solution when grown on membrane filters. In a side-by-side diffusion chamber with well-stirred solutions on both sides, the transfer rate is 50% higher in the basal-to-apical than in the apical-to-basal direction. Nonlabeled nitrofurantoin (500 μM) in the basal chamber equalized the transport in both directions, suggesting that a specific transporter is responsible for the basal-to-apical increment in flux. From inhibition studies, the apparent affinity of this transporter for nitrofurantoin is 50 μM. Changes in pH between 6.4 and 7.8 had no effect on the active transport component of the flux but did affect the passive flux component. Passive flux of the nonionized molecule was 2.6 times faster than that of the ionized molecule, but the ionized molecule did appear to cross the membrane passively. Our findings show that nitrofurantoin is actively transported across a mammary epithelial cell monolayer by a transporter whose affinity for nitrofurantoin does not depend on the anionic charge on nitrofurantoin. The pH dependence of a parallel passive pathway suggests that both nonionized and ionized forms of nitrofurantoin cross the membranes of the mammary epithelial cell by passive diffusion.

Electrochemical deposition of ternary and binary systems from an alkaline electrolyte—a demanding way for manufacturing p-doped bismuth and antimony tellurides for the use in thermoelectric elements

Alkaline solution, especially diphosphate solutions, can be used as electrolytes for the galvanic deposition of p-type semiconductors. A ternary Bi–Sb–Te alloy semiconductor was deposited at a Ni-covered cathode surface at potentials lower than −0.6 V (Ag/AgCl), under potentiostatic condition in well-stirred solutions. Additionally, it was possible to deposit antimony telluride, a binary p-semiconductor, from the ternary electrolyte. The kinetics of the process was investigated by cyclic voltammetric measurements. The influence of the electrolyte convection on the electrocrystallization was analysed with the help of rotating disc electrode. The semiconductor layers were characterized by electrochemical impedance spectroscopy.

Microdialysis Sampling Membrane Performance during in Vitro Macromolecule Collection

Microdialysis sampling is well-established for sampling small molecules. Recently, there has been an increased interest toward collecting macromolecules using microdialysis sampling. In this work, fluorescein isothiocyanate-labeled dextrans (FITC-dextrans) with molecular weight between 10 and 70 kDa were chosen as representative molecules to study analyte mass transport properties during microdialysis sampling using different lengths (2 and 10 mm) of 100-kDa MWCO polyethersulfone membranes. Experiments were performed in both well-stirred and quiescent phosphate-buffered saline solutions as well as in a 0.3% agar solution. Different fundamental parameters affecting microdialysis sampling of macromolecules, including effective membrane diffusion coefficients, were evaluated. The applicability of the most-often-cited Bungay et al. mass transfer model was compared to experimental data for the FITC-dextrans. For the larger macromolecules, the membrane provides a significant mass transport resistance most likely caused by hindered diffusion. These experimental aspects that are critical to microdialysis sampling of macromolecules are presented.

Accuracy of the Diffusive Gradients in Thin-Films Technique: Diffusive Boundary Layer and Effective Sampling Area Considerations

When using the diffusive gradients in thin-films (DGT) technique in well-stirred solutions, the diffusive boundary layer has generally been ignored on the assumption that it is negligibly thin compared to the total thickness of delta g, i.e., the sum of the thickness of the prefilter and diffusive gel. Deployment of devices with different diffusive layer thicknesses showed that the thickness of the DBL was approximately 0.23 mm in moderate to well-stirred solutions, but substantially thicker in poorly or unstirred solutions. Measurement of the distribution of Cd in the DGT resin gel at high spatial resolution (100 microm) using laser ablation inductively coupled plasma mass spectrometry showed that the effective sampling window had a larger diameter (2.20 cm) than the geometric diameter of the exposure window (2.00 cm). Lateral diffusion in the gel, which had previously been neglected, therefore increased the effective surface area of the device by approximately 20%. The concentrations measured by DGT agreed well with the known concentrations in standard solutions for all diffusion layer thicknesses, when the effective area and the appropriate diffusive boundary layer (DBL) were used. The extent of the error associated with neglecting the DBL and using the geometric window area depends on the gel layer thickness and the true thickness of the DBL, as determined by the deployment geometry and flow regime. When DGT measurements were made in well-stirred solutions using a 0.80-mm diffusive gel, the effect of neglecting the DBL and using the inappropriate geometric area offset each other, with the error being <+/-10%. For precise measurements, and especially work involving speciation or kinetic measurements, where DGT devices with different diffusive gel layer thicknesses are deployed, it is necessary to use the effective area and the appropriate DBL thickness in the full DGT equation, which allows for the use of layer-specific diffusion coefficients.

Influence of the concentration boundary layers on membrane potential in a single-membrane system

The influence of the concentration boundary layers on membrane potential in a single-membrane system on basis of the Kedem-Katchalsky equations was described in cases of horizontally mounted neutral membrane separates mechanically stirred and unstirred binary electrolytic solutions at different concentrations. The measure of this influence is following expression Δ Ψ CBL = Δ Ψ m − Δ Ψ s , in which Δ Ψ m is a membrane potential in conditions of well-stirred solutions and Δ Ψ m – potential in conditions of unstirred solutions. Results of five sets of calculations were presented. In first the Δ Ψ CBL as a function of ratio solution concentrations ( C h / C l ) at constant value of concentration Rayleigh number ( R C ) was calculated, in second – the Δ Ψ CBL as a function of R C at constant of C h / C l , in third – the Δ Ψ CBL as a function of R C at constant concentration polarization coefficient ( ζ s ), in fourth – the critical values of Rayleigh number ( R C ) crit as a function of ζ s at constant of C h / C l and in fifth – the (Δ Ψ CBL ) max as a function of ζ s at constant of C h / C l . Calculations were made for the case where on a one side of the membrane aqueous solution of NaCl at steady concentration 10 −3 mol 1 −1 ( C l ) was placed and on the other aqueous solutions of NaCl at concentrations from 10 −3 mol 1 −1−10 −2mol 1 −1 ( C h ). Their densities were greater than NaCl solution's at 10 −3 mol 1 −1. It was shown that voltage concentration boundary layers effect depends on hydrodynamic state of a complex concentration boundary layer–membrane–concentration boundary layer, what is controlled by R C and ζ s .

Intracranial delivery of recombinant nerve growth factor: release kinetics and protein distribution for three delivery systems.

Three different polymeric delivery systems, composed of either poly(ethylene-co-vinyl acetate) (EVAc) or poly(lactide-co-glycolide) (PLGA), were used to administer recombinant human nerve growth factor (rhNGF) intracranially in rats. The delivery systems were characterized with respect to release kinetics, both in the brain and in well-stirred buffer solutions. During incubation in buffered saline, the delivery systems released rhNGF in distinct patterns: sustained (EVAc), immediate (PLGA1) and delayed (PLGA2). One 10-mg delivery system was implanted in each rat and an ELISA technique was used to determine the amount of rhNGF in 1-mm coronal brain slices produced immediately after removal of the delivery system. High levels of rhNGF (as high as 60,000 ng in a brain slice of approximately 50 microliters) were recovered from the brain tissue at 1, 2, and 4 weeks after implantation. With all three delivery systems, the amount of rhNGF in each brain slice decreased exponentially with distance from the implant site: the distance over which concentration decreased by 10-fold was 2-3 mm for all delivery systems. When rhNGF release was moderate (10 to 200 ng rhNGF/day), the total amount of rhNGF in the brain increased linearly with release rate, suggesting an overall rate of rhNGF elimination of 0.4 hr-1 or a half-life of 1.7 hr. With higher release rates (500 to 50,000 ng rhNGF/day), total amounts of rhNGF in the brain were considerably higher than anticipated based on this rate of elimination. Polymeric controlled release can provide high, localized doses of rhNGF in the brain. All of the experimental data were consistent with penetration of rhNGF through the brain tissue with a diffusion coefficient approximately 8 x 10(-7) cm2/s, which is approximately 50% of the diffusion coefficient in water.

The effective diffusion coefficient and the distribution constant for small molecules in calcium‐alginate gel beads

The effective diffusion coefficient, D(e), and the distribution constant, K(i), for selected mono- and disaccharides and organic acids were determined in homogeneous calcium-alginate gel with and without entrapped bacteria. Results were obtained from transient concentration changes in well-stirred solutions of limited volume, in which the gel beads were suspended. The effective diffusioncoefficients and the distribution constants were estimated by fitting mathematical model predictions to the experimental data using a nonlinear model fitting program (MODFIT). Both single solute diffusion and multiple solute diffusion were performed. A small positive effect was obtained onthe values of D(e) for the system of multiple solute diffusion; however, the values of K(i) were not significantly influenced. For the nine solutes tested, D(e) for 2% Ca-alginate gel beads was found to be approximately 85% of the diffusivity measured in water. The effects on D(e) and K(i), for lactose and lactic acid were determined for variations of alginate concentration, pH, temperature, and biomass content in the beads. D(e) decreased linearly for both lactose and lactic acid with increasing cell concentration in the Ca-alginate gel. K(i), was constant for both lactose and lactic acid with increasing cell concentration. D(e) was significantly lower at pH 4.5 than at pH 5.5 and 6.5 for both lactose and lactic acid. Furthermore, D(e) seemed to decrease with increased alginate concentration in the range of 1% to 4%. The diffusion rate increased with increasing temperature, and the activation energy for the diffusion process for both lactose and lactic acid was constant in the temperature range tested. (c) 1995 John Wiley & Sons Inc.

Counterdiffusion of lactose and lactic acid in κ-carrageenan/locust bean gum gel beads with or without entrapped lactic acid bacteria

The effective diffusion coefficient ( D e) and equilibrium partition factor ( K p) for lactose and lactic acid in κ-carrageenan (2.75% w/w)/locust bean gum (0.25% w/w) (LBG) gel beads (1.5−2.0 mm diameter), with or without entrapped Lactobacillus casei subsp. casei (L. casei), were determined at 40°C. Results were obtained from transient concentration changes in well-stirred solutions of finite volume in which the beads were suspended. Mathematical models of unsteady-state diffusion into and/or from a sphere and appropriate boundary conditions were used to calculate effective diffusion coefficients of lactose and lactic acid from the best fit of the experimental solute concentration changes. The effective diffusivities of lactose and lactic acid were 5.73 × 10 −10 and 9.96 × 10 −10 m 2 s −1, respectively. Furthermore, lactic acid was found to modify gel structure since lactose diffusion characteristics ( D e and K p) differed significantly from an earlier study and in the literature. In gel beads heavily colonized with L. casei, the effective diffusion coefficients of lactose and lactic acid were respectively 17% and 24% lower than for cell-free beads. Partition coefficients also confirmed the obstruction effect due to the cells, and decreased from 0.89 to 0.79, and from 0.98 to 0.87, for lactose and lactic acid, respectively. External mass transfer was estimated by an unsteady-state model in infinite volume using the Biot number. The effect of external mass transfer resistance on D e results and the data reported in the literature are discussed.

Diffusion of lactose in k‐carrageenan/locust bean gum gel beads with or without entrapped growing lactic acid bacteria

Effective diffusion coefficients (De) of lactose in kappa-carrageenan (2.75% wt/wt)/locust bean gum (0.25% wt/wt) (LBG) gel beads (1.5-2.0-mm diameter)with or without entrapped lactic acid bacteria (LAB) were determined at 40 degrees C. The effects of lactose concentration, bacteria strain (Streptococcus salivarius subsp. thermophilus and Lactobacillus casei subsp. casei) and cell content at various steps of the fermentation process (after immobilization, pre-incubation of the beads and successive fermentations) were measured on De as a first step for process modelling. Results were obtained from transiend concentration changes n well-stirred lactose solutions in which the beads were suspended. A mathematical model of unsteady-state diffusion in a sphere was used, and De was obtained from the best fit of the experimental data. Diffusivity of lactose in cell-tree beads was significantly lower than in pure water mainly because of the obstruction effect of the polymer chains and the hydration region. Furthermore, effective diffusivity and equilibrium partition factor were independent of lactose concentration in the range from 12.5 to 50 g/L. No significant difference was found for De (effective diffusivity) and Kp (partition) coefficients between beads entrapping S. thermophilus (approximately 5 x 10(9) CFU/mL) and cell-free beads. On the other hand higher cell counts obtained with L. casei (close to 1.8 x 10(11) CFU/mL) increased mass transfer resistance resulting in lower effective diffusivities and Kp. Finally, the effects of the type of bacteria and their distribution in the beads on the diffusivity were also discussed.

A theoretical analysis of donnan dialysis across charged porous membranes

A previously developed model [1] for the transport of ions in charged capillary tubes is used to determine the effect of membrane properties (average pore radius and surface charge density) and solution concentration on steady-state ion and solution fluxes in two types of Donnan dialysis separations. Specifically, the concentration of a dilute metal ion solution into an acid stripping solution by ion exchange across a cation exchange membrane and the removal of an acid contaminant from a metal ion solution using an anion exchange membrane are studied. The model is able to predict the changes in metal ion flux caused by changes in acid and metal ion concentrations in the strip and feed solutions in the Donnan dialysis experiments performed by Lake and Melsheimer [2]. These effects could not be explained by the mass-transfer resistance model used by Lake and Melsheimer [2] and by others [3,4] to describe ion transport across a charged membrane in Donnan dialysis separations. The time-dependent ion concentrations in well-stirred solutions undergoing Donnan dialysis are also modeled. The results are shown to match the experimental data of Ng and Snyder [4] when the boundary layer resistance are negligible and reasonable values for the membrane pore parameters are assumed.

Diffusion of sucrose and yohimbine in calcium alginate gel beads with or without entrapped plant cells

The diffusion characteristics of sucrose, a nutrient, and yohimbine, a secondary metabolite, in alginate gel beads, with or without entrapped periwinkle (Catharanthus roseus) or apple (Malus domestica) cells, were investigated. Effective diffusivities of both solutes in the gel beads were determined by two different methods from transient concentration changes in well-stirred solutions where the beads were suspended. The linear plot method developed in this work is easy to use and requires no data from the initial periods of diffusion experiments. It was found that while the cell-free beads provided only minor diffusional resistance to both solutes, the effective diffusivities of both solutes decreased significantly with the presence of cells in the beads and the amount of reduction was proportional to the amount of cell loading. Further, the effective diffusivity of sucrose appeared to be slightly larger than that of yohimbine under identical conditions. It was also observed that permeabilization of apple cells with dimethyl sulfoxide (DMSO) led to an increase in effective diffusivity with the effect being more significant for yohimbine.

Mathematical models on diffusion of oxygen to and within plant roots, with special emphasis on effects of soil-root contact

In relation to explanations of anaerobiosis in the field, mathematical models presented in part I are evaluated in the light of the disparity between the low oxygen pressure required by plant roots in well-stirred nutrient solutions and the rather high values apparently required in the field. Water film and rhizosphere respiration do not fully explain this disparity. Soil-root contact as described in part I is shown to considerably affect the partial pressure of oxygen required for unrestricted aerobic respiration.

Diffusion characteristics of substrates in Ca‐alginate gel beads

The diffusion characteristics of several substrates of varying molecular sizes into and from Ca-alginate gel beads in well-stirred solutions were investigated. The values of the diffusion coefficient (D) of substrates such as glucose, L-tryptophan, and alpha-lactoalbumin [with molecular weight (MW) less than 2 x 10(4)] into and from the gel beads agreed with those in the water system. Their substrates could diffuse freely into and from the gel beads without disturbance by the pores in the gel beads. The diffusion of their substrates into and from the gel beads was also not disturbed by increasing the Ca-alginate concentration in the beads and the CaCl(2) concentration used in the gel preparation. In the case of higher molecular weight substances such as albumin (MW = 6.9 x 10(4)), gamma-globulin (MW = 1.54 x 10(5)) and fibrinogen (MW = 3.41 x 10(5)), the diffusion behaviors of the substrates into and from the gel beads were very different. No diffusion of their substrates into the gel beads from solutions was observed, and only albumin was partly absorbed on the surface of the gel beads. The values of D of their substrates from the gel beads into their solutions were smaller than their values in the water system, but all their substrates could diffuse from the gel beads. The diffusion of high molecular weight substrates was limited more strongly by the increase of Ca-alginate concentration in the gel beads than by the increase of the CaCl(2) concentration used in the gel preparation. Using these results, the capacity of Ca-alginate gel as a matrix of immobilization was discussed.

Nonstationary diffusion through membranes. 1. Transient diffusion through a membrane separating two unequal volumes of well-stirred solutions

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTNonstationary diffusion through membranes. 1. Transient diffusion through a membrane separating two unequal volumes of well-stirred solutionsC. J. P. Hoogervorst, J. A. P. P. Van Dijk, and J. A. M. SmitCite this: J. Phys. Chem. 1978, 82, 11, 1311–1318Publication Date (Print):June 1, 1978Publication History Published online1 May 2002Published inissue 1 June 1978https://doi.org/10.1021/j100500a023RIGHTS & PERMISSIONSArticle Views101Altmetric-Citations17LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (997 KB) Supporting Info (1)»Supporting Information Supporting Information Get e-Alerts

Studies on recrystallised aluminium mono-hydroxide precipitates. Kinetics of dissolution by sodium hydroxide solutions

Boehmite powders were prepared by controlled hydrolysis of aluminium isopropoxide solution and recrystallisation in hot water; these were cylinders (fibres) of lengths (I 0) = 0.06 to 0.10μm. The dissolution of dilute suspensions of these powders in well-stirred sodium hydroxide solutions was studied at 35 ° to 65 °C. Reaction solid and solution were analysed after different times by chemical and physical methods. Reaction occurred by three-directional dissolution of the cylinders: the reactions of the first (non-aggregated) thirty percent material were four-third order w. r. t. powder weight (and second order w. r. t. powder surface area). The initial rate constantsk wi (g−″ hr−1) for reactions with sodium hydroxide of unit mean ionic activity at 20 °C varied from 0.012 to 0.040. Rate constants increased linearly with the mean ionic activity of the hydroxide solution and exponentially with reciprocal temperature, five-six times for 15 °C temperature rise. Energies of activation varied from 115–125 kJ mole−1.

Studies on recrystallised aluminium hydroxide precipitates

Aluminium hydroxide gels were recrystallised in high pH solution for 2–1000 h to give a series of Gibbsite powdersP11/2,P11/8,P1/48,P11/360 andP11/X, consisting of hexagonal platelet crystals; their average platelet lengths (l 0) were 0.03, 0.06, 0.13, 0.26 and 0.45 microns. The dissolution of dilute suspensions of these powders in well-stirred sodium hydroxide solutions were studied at 20–65°C Reaction solid and solution were analysed after different times by chemical and physical methods. Reaction occurred by two-directional dissolution of the platelet crystals. The reactions of GibbsiteP11/X (prepared by prolonged 1000 h crystallisation) were first order w.r.t. powder weight (and second order w.r.t. powder effective surface area); the reactions of the other Gibbsites were first order for the first twenty percent rapid dissolution and then slower. The initial rate constantsk w1 (h−1) and half-lifest 0.5 (h) for reactions ofP11/2,P11/8,P11/48.P11/360 andP11/X with sodium hydroxide solution of unit mean ionic activity at 20°C were 1.70, 0.9; 0.60, 2.2; 0.22, 5.5; 0.07, 14 and 0.02, 38 respectively. Rate constants increased linearly with the mean ionic activity of the hydroxide solution and increased exponentially with reciprocal absolute temperature, four to five times for 15°C temperature rise. Half-lifes decreased in a similar manner. Energies of activation varied from 76–83 kJ/mol. The rates of dissolution are determined by the rate of the chemical reaction between adsorbed hydroxyl ions and adjacent reactive aluminium hydroxide sites on the powder crystal surface.