Interfacial Solute Concentration Research Articles

Modelling particle dissolution in stirred vessels

Particle dissolution in stirred vessels is a unit operation commonly encountered in several production sectors, such as the mineral, pharma and chemical industries. It is commonly conducted batch-wise under time-dependent conditions, a circumstance that complicates model set-up. This paper presents a set of models for simulating batch dissolution of polydisperse particles in stirred vessels. These models cover all scenarios of particle batch dissolution, regardless of whether the initial particle quantity exceeds or falls short of achieving solution saturation. Consequently, they address cases where particles are either completely dissolved or remain partially undissolved. The models also account for both single-sized and multi-sized particles. Convenient model simplifications are also provided for the cases of final solute concentration much smaller than saturation (low final concentration models). All models are successfully experimentally validated. The single-size large final concentration model is employed to set up experimental runs that, apart from their use in predictive simulations, may be employed for simultaneously measuring mass transfer coefficient and interfacial solute concentration using suitable experimental runs. The ability to measure interfacial solute concentration is also exploited for assessing whether it coincides, or not, with the solute saturation concentration, a common assumption when dealing with solid-liquid mass transfer, which in the present case is found to hold true. The simpler single-size low-final-concentration model is very convenient for measuring the mass transfer coefficient alone. Finally, the multi-size model is utilised to evaluate the sensitivity of the estimated mass transfer coefficient in the single-size model to the particle size range employed during experimental measurements of mass transfer coefficients.

Process simulation of modelled reverse osmosis for desalination of seawater

Abstract Model equations for prediction of process parameters of reverse osmosis for desalination of seawater were developed via mathematical derivation from basic equations for the reverse osmosis process. A model equation relating the interfacial solute concentration () with the process pressure difference () was developed. Taking the of reverse osmosis as the basic independent variable, further model equations relating other process parameters such as the solute concentration polarity , water flux , osmotic pressure , water output rate (q), power density (Pd) and specific energy consumption (SEC) were developed. Simulation of hypothetical reverse osmosis data using Microsoft Excel Worksheet and Microsoft Windows 10 on a 64-bit operating system was carried out. Simulation results showed that the optimum fluid bulk concentration was = 0.0004 mole/cm3. The optimum rate of increase in the solute rejection factor per unit rise in ΔP was 0.45%. The optimum solute rejection factor was 97.6%. The optimum water output rate, specific energy consumption and power density were 103.2 L/h, 3.65 kWh/m3 and 6.09 W/m2, respectively.

Application of a simple subregular solution model to the computation of phase boundaries and free dendritic growth in the Ag-Cu system

Adopting of a simple, but dependable analytic thermodynamic solution model in the simulation of phase transformation kinetics reduces the complexity of computation and the need for extensive thermodynamic data and hence is desired in the practical application of kinetic theories in materials processing. A simple subregular solution model with linear temperature dependency, which can calculate G curves with limited information extracted from an equilibrium phase diagram, is presented and applied to the calculation of (1) the binary Ag-Cu phase diagram with metastable phase boundaries and (2) the kinetics of free dendritic growth in supercooled Ag-Cu melts. The simple T-dependent subregular solution model can duplicate the published Ag-Cu phase diagram with the predicted metastable extensions to the same accuracy as that of calculations with highly structured models that require more computation and wider range of thermodynamic data. Its integration with a free dendritic growth model permits the calculation of correct values of the driving force at non-Henrian interfacial solute concentrations that occur in rapid solidification. The use of the simple T-dependent subregular solution model to calculate the interfacial driving force greatly improves the mathematical stability in the transition stage from mass transfer-limited growth to heat transfer-limited crystal growth.

Cellular automaton-based study of factors that affect dynamic solid phase transformation kinetics

In this study, we simulated the β to α solid phase transformation in the preferred crystallographic orientation of TA15 alloy using a virtual front tracking modified cellular automaton model. The transformation kinetics were resolved by coupling the interface moving velocity and solute diffusion equations. The simulated phase transformation kinetics and microstructure agreed well with the results predicted by the Zener–Hillert equation and experimental data. We quantified the effects of temperature, interface curvature, preferred growth angle, and kinetic parameters, including solute diffusion and the interface mobility coefficient, on new phase morphologies and micro-segregation. Furthermore, diffusion/mixed/interface controlled transformations were distinguished by differences in the interfacial solute concentration from the initial solute concentration and the equilibrium solubility of the parent phase. Three transformation modes were simulated by varying the diffusion coefficient, interface mobility coefficient, and transformation driving force factor.

A Fokker–Planck equation for a piecewise entropy functional defined in different space domains. An application to solute partitioning at the membrane–water interface

A nonlinear Fokker–Planck equation is proposed for a system subject to different statistics (in the present study, the Gibbs–Boltzmann and Fermi–Dirac statistics) defined in different contiguous regions of space. We solved the time-dependent mono-dimensional equation numerically, and solved the time-independent mono-dimensional equation analytically under the effect of a generic external potential equation. These zones are connected by a sharp but continuous transition region. Accurate numerical procedures ensure the convergence of the Fokker–Planck equation in the transition layer. We applied our general procedure to investigate both the stationary and the time-dependent kinetics of solute partitioning between aqueous and membrane phases. Because of the relative volumes of solute, water, and lipid (Vsolute≈Vwater<<Vlipid), the mixing entropy functional in water contains both solute and solvent contributions, while within the membrane only the solute entropy plays a significant role. Also, the potential term differs in space due to the solute interactions with different environments. Lastly, we added the effect of an electrostatic potential (occurring in all membrane systems) localized at the water interface which may deplete or increase the interfacial solute concentration. Rather surprisingly we found a strong coupling between the surface potential and the imposed asymmetric statistics. The effects are relevant when entropic and potential contributions are comparable; otherwise, the standard Boltzmannian behavior is recovered.

Solute Effects on β-Sn Grain Boundary Energy and Shear Stress

The excess enthalpy and shear strain behavior of the β-Sn (101) grain boundary containing various amounts of Ag and Cu solute atoms was investigated using molecular simulation. An increase in either type of solute at the interface lowers the excess enthalpy of the grain boundary. The enthalpies of segregation for both solute types are computed as the slope of excess enthalpy of the grain boundary per area versus interfacial solute concentration per area. For Ag, ΔHSEG=0.64(9) eV/atom , and for Cu, ΔHSEG=0.45(8) eV/atom , indicating a preference for grain boundary segregation. These results agree with other simulation work that attributes a larger decrease in grain boundary energy to a solute with a larger atomic radius. A (301) special boundary of β-Sn was also investigated and found ΔHSEG=0.12(9) eV/atom for Ag and ΔHSEG=0.06(9) eV/atom for Cu. Statistically, this shows the possibility for excess enthalpy increase when Cu is present at the (301) boundary. Under constant shear strain, addition of solu...

Optimized design of multilayer barrier films incorporating a reactive layer. II. Solute dynamics in two‐layer films

AbstractExtending the model of transient permeation through the reactive barrier film presented in part I of this series to two‐layer reactive–passive barrier structures, we devote part II to the analysis of the evolution of interfacial solute concentrations between the layers. The concepts developed earlier are applied to the transient ingress analysis of two‐layer films where one of the layers contains a noncatalytic solute scavenger. In particular, we show that for reactive–passive films, the averaging approximation of the transient interfacial solute concentration provides good agreement with numerical results for the transient effective flux. The applicability range of this averaging and the error introduced by it are quantified. For the passive–reactive films, the same averaging fails to predict the effective flux dynamics. A new method of ingress analysis is presented for such structures to correct the situation. The method is based on the effective flux dynamics in the homogeneous reactive membrane and the dynamic reactive to the passive–reactive flux scaling between the initial and final solute concentration profiles corresponding to the scavenger activation and scavenger exhaustion times. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 1952–1965, 2006

Measuring dipolar width across liquid-liquid interfaces with 'molecular rulers'.

Molecular dynamics simulations have previously described how the physical properties across immiscible liquid-liquid interfaces should converge from aqueous to organic limits, but these predictions have largely gone untested, owing to difficulties associated with probing buried interfaces. X-ray and neutron scattering experiments have created detailed pictures of molecular structure at these boundaries, but such scattering studies cannot probe how surface-altered solvent structures affect interfacial solvating properties. Given that surface-mediated solvent properties control interfacial solute concentrations and reactivities, identifying the characteristic dimensions of interfacial solvation is essential for formulating predictive models of solution phase surface chemistry. Here we use specially synthesized solvatochromic surfactants that act as 'molecular rulers' and resonance-enhanced second-harmonic generation to measure the dipolar width of weakly and strongly associating liquid-liquid interfaces. Dipolar width describes the distance required for a dielectric environment to change from one phase to another. Our results show that polarity converges to a nonpolar limit on subnanometre length scales across a water-cyclohexane interface. However, polarity across the strongly associating, water-1-octanol interface is dominated by a nonpolar, alkane-like region. These data call into question the use of continuum descriptions of liquids to characterize interfacial solvation, and demonstrate that interfacial environments can vary in a non-additive manner from bulk solution limits.

Protein crystal growth under forced solution flow: experimental setup and general response of lysozyme

We have experimentally studied the effects of solution flow on the growth kinetics of the protein lysozyme. To this end, we have expanded our interferometry setup [Vekilov et al., J. Crystal Growth 146 (1995) 289] by a novel crystallization cell and solution recirculation system. This combination permits monitoring of interface morphology and kinetics with a depth resolution of 200 Å at bulk flow rates of up to 2000 μm/s. Particular attention was paid to the prevention of protein denaturation that is often associated with the pumping of protein solutions. We found that at bulk flow rates u<250 μm/s the average growth rate and step velocity, R avg and v avg, increase with increasing u. This can be quantitatively understood in terms of the enhanced, convective solute supply to the interface. With high-purity solutions, u>250 μm/s lead to growth deceleration, and, at low supersaturations σ, to growth cessation. When solutions containing ∼1% of other protein impurities were used, growth deceleration occurred at any u>0 and cessation in the low σ experiments was reached at about half the u causing cessation with pure solution. The flow-induced changes in R avg and v avg, including growth cessation, were reversible and reproducible, independent of the direction of the u-changes and solution purity. Hence, we attribute the deceleration to the convection-enhanced supply of impurities to the interface, which at higher flow rates overpowers the effects of enhanced interfacial solute concentration. Most importantly, we found that convective transport leads to a significant reduction in kinetics fluctuations, in agreement with our earlier expectations for the lysozyme system [Vekilov et al., Phys. Rev. E 54 (1996) 6650]. This supports our hypothesis that these long-term fluctuations represent an intrinsic response feature of the coupled bulk transport-interfacial kinetics system in the mixed growth control regime.

Influence of interfacial curvature on the growth and dissolution kinetics of a spherical precipitate

The Green's function method was used to simulate the growth and dissolution of precipitates taking into account the influence of the curvature on the interfacial solute concentration. The dissolution time does not appear to be altered significantly unless the initial radius of a particle is very small, i.e. less than a few tens of nanometer. In the growth of a critical nucleus the curvature effect can be significant at an early stage. The increase in the growth time does not appear to be significant when the particle has grown to a size of optical microscopy.

The influence of surface tension on the diffusion-controlled growth or dissolution of spherical gas bubbles

Surface tension can markedly affect the growth or dissolution of small gas bubbles but, even when spherical symmetry is maintained and the interfacial concentration assumed constant, generally valid analytical solutions for the change of size with time cannot be obtained; approximations of limited validity are therefore often used. However, accurate and efficient methods for computing the diffusion-controlled growth or dissolution of spheres in such conditions have recently been developed; the results obtained when interfacial solute concentration is assumed constant have been published and validated by comparing them, where possible, with the equivalent analytical solutions. This paper extends that work to include the effects of a constant surface tension, for both Henry’s and Sievert’s laws. The numerical results are valid for as wide a range of parameters as is likely to be needed and are compared with the few analytical solutions available for particular cases. It is shown that, when surface tension is introduced, a complete description of the problem requires an additional saturation parameter as well as the dimensionless surface tension. It is also shown that Henry’s and Sievert’s laws can have very different effects on dissolving bubbles: when Sievert’s law applies a higher surface tension can increase time for a bubble to dissolve but this paradox can be resolved by examining the competing effects involved.

On the theory of steady state lamellar eutectic solidification at high solidification rates

AbstractThe famous theory of JACKSON and HUNT for the unidirectional eutectic solidification is extended considering the effect of the solidification rate on the interfacial solute concentration. Contributions attributed to nonsymmetric phase diagrams lead to corrections of the constant K in the λ2V = K relation between the lamellar half‐spacing λ and the solidification rate V. For high solidification rates deviations from this relation are derived.

A self-consistent theory of steady-state lamellar solidification in binary eutectic systems

The potential theoretic methods developed recently at NRL for solving the diffusion equation are applied to the free-boundary problem which describes lamellar solidification in binary eutectic systems. By using these techniques, the original free-boundary problem is reduced to a set of coupled nonlinear integro-differential equations which when solved yield the shape of the solid/liquid interface and the solute concentration on the interface. A simplified version of the general integro-differential equations is derived by assuming that (1) the solute diffusion length is large compared with the lamellar spacing, and (2) the solid/liquid interface is approximately isothermal. Numerical solutions to the approximate equations are obtained and are utilized to assess the effect of interface curvature on the interfacial solute concentrations, and to check the new theory for consistency with experiment.

Droplet Circulation and Interfacial Disturbances in Gas-Liquid Systems

DURING recent years the process of liquid-liquid extraction has become progressively more important and the mechanism of solute transfer between liquid droplets and a second substantially immiscible liquid environment has received considerable attention. In the course of their work in this field, Lewis and Pratt1 observed that when solute transfer, for example, acetone, occurred between hydrocarbon droplets and water, then in many cases, the droplets exhibited rapid and violent oscillations which they termed ‘kicking’. Systems which exhibited this effect were found to have higher mass transfer rates than those predicted from theoretical considerations2. More recently the phenomenon of droplet oscillation in liquid-liquid systems has been the subject of extensive study, notably by Haydon3 and Davies and Haydon4. These workers concluded that droplet oscillation was the result of the interfacial solute concentration becoming non-uniform, thereby giving rise to local interfacial tension variations which resulted in temporary droplet instability.