Bulk Supersaturation Research Articles

Steps behaving badly: Nonlinear dynamics and a terrace-loading instability during solution growth of lysozyme crystals

A detailed finite-element model for step motion during solution crystal growth is applied to analyze the nonlinear growth dynamics of lysozyme. Insights from this model are applied to develop a much simpler, lumped-parameter model to describe step motion for this growth system. Bifurcation analysis applied to the lumped-parameter model demonstrates a critical bulk supersaturation at which an equidistant step train loses stability, via a supercritical Hopf bifurcation, to a stable, time-periodic system that exhibits a single step bunch. As supersaturation is further increased, additional bifurcations lead to more complicated behaviors, such as quasi-periodic patterns, multiple step bunches, and period doubling. The initial instability of the step train arises from the dynamics of terrace loading due to slow adsorption and step incorporation kinetics under high bulk supersaturation. These effects cause a time lag in the surface supersaturation level with respect to changes in terrace width, producing a phase shift of the surface supersaturation field in the direction of step motion and driving the formation of step bunches.

Assessing the Kinetics and Pore‐Scale Characteristics of Biological Calcium Carbonate Precipitation in Porous Media using a Microfluidic Chip Experiment

AbstractBiomineralization through microbially or enzymatically induced calcium carbonate precipitation (MICP/EICP) by urea hydrolysis has been widely investigated for various engineering applications. Empirical correlations relating the amount of mineral precipitation to engineering properties like strength, stiffness, or permeability show large variations, which can be partly attributed to the pore‐scale characteristics of the precipitated minerals. This study aimed to gain insight into the precipitation kinetics and pore‐scale characteristics of calcium carbonate minerals through time lapse imaging of a transparent microfluidic chip, which was flushed 10 times with a reactive solution to stimulate EICP. An image processing algorithm was developed to detect the individual precipitated minerals and separate them from the grains and trapped air. Statistical analysis was performed to quantify the number and size distribution of precipitated minerals during each treatment cycle and the cumulative volume, surface area, bulk precipitation rate, nucleation rate, and supersaturation were calculated and compared with a simple numerical model and more complex theory on precipitation kinetics. The analysis showed that results were significantly affected by the assumed particle shape. The supersaturation, which controls the crystal nucleation and growth rates, was shown to be a function of the hydrolysis rate, the kinetic order and growth rate constant, and available surface area for mineral growth. Possible explanations for observed discrepancies between observations and theory, including diffusion limitations, the presence of inhibiting compounds, local pore clogging or observation bias, and limitations of the methodology, are discussed.

Numerical simulation of the hydrodynamics and mass transfer in the capping of large size Z-cut plates

Numerical simulation of the hydrodynamics and mass transfer involved in the capping of large size Z-cut KDP plates has been performed. The variations of surface supersaturation with thin layer height, bulk supersaturation and rotation rate are analyzed. The results show that keeping still is very unfavorable for the growth of thin layer, a certain rotation rate should be applied to the Z-cut plate to increase the concentration gradient across the (0 0 1) face, thus making sure that thin layers can grow from the edges while small pyramids barely grow from the face center. Given the result that end faces of thin layers nearly bear a bulk supersaturation, a relative low bulk supersaturation will be better to ensure both the growth of thin layers and the good surface uniformity brought by low supersaturation. Moreover, as thin layers grow, rotation rate should be increased to make up the insufficient solute supply resulting from the decreasing linear speed. The optimal parameters for rapid and high-quality capping of large size Z-cut plates are suggested, the relevant simulation results are also presented.

Toward the Understanding of KDP Crystal Surface Height Variation by a Rapid Growth Technique

Numerical simulations are performed to understand the variation of KDP crystal surface height by a rapid growth technique. The theoretical models used in numerical simulations couple the macroscopic transport of solute and impurities with the microscopic interfacial kinetics processes. Studies are specifically made to growth rate fluctuation at each growth interface subject to variations in crystal size, bulk supersaturation, rotation rate of the stirring paddle, and impurities. It is found that predicted interface moving speeds, equivalent to the growth rate, are uniformly distributed normal to each pyramidal and prismatic faces at macroscale by taking into account the interfacial kinetics process; however, they fluctuate wavily at microscale. The amplitude of growth rate fluctuation is on the order of micrometer. The fluctuation in growth rate will cause KDP crystal surface height variation and lead to the formation of micron-sized and nanosized inclusions in the crystals. Increasing crystal size and bu...

Iron carbonate formation kinetics onto corroding and pre-filmed carbon steel surfaces in carbon dioxide corrosion environments

This work investigates the Corrosion Layer Accumulation Rate (CLAR) of iron carbonate (FeCO3) onto X65 carbon steel in carbon dioxide containing environments using the direct method of corrosion layer mass gain measurement. Glass cell experiments were performed at 80 °C and pH 6.3 or 6.8 over a range of bulk FeCO3 saturation ratios using both actively corroding carbon steel and steel pre-filmed with FeCO3. The CLARs obtained from experiments using actively corroding samples displayed strong agreement with the most recently developed precipitation model by Sun and Nesic at high supersaturation for pH 6.3 and 6.8, but a disparity at low supersaturation for the solution at pH 6.8. The observed discrepancy was attributed to the significant difference in surface saturation ratio between the two conditions when the steel is actively corroding. CLARs determined for pre-FeCO3 filmed carbon steel show that the kinetics of FeCO3 formation reduce significantly once the film establishes a protective barrier at lower values of bulk supersaturation. The results highlight the contrast between surface layer accumulation kinetics in the early stages of growth and those encountered in the long-term after the development of a protective film.

Growth of high-quality metastable crystal of acetaminophen using solution-mediated phase transformation at low supersaturation

We improved the crystal quality of the metastable phase of a pharmaceutical compound acetaminophen (form II) using solution-mediated phase transformation (SMPT) combined with the control of supersaturation and crystal size. Form II crystals grew at low supersaturation via SMPT of the trihydrate at low temperature (10 °C). While crystal growth rate was low compared to the 20 °C condition, crystals had many defects such as solution inclusions or cracks at 20 °C, but few at 10 °C. The ratio of form II crystals with any defects was small (12%), about 1/3 that of the 20 °C condition. Since the concentration gradient on the crystal surface was relatively small at low bulk supersaturation, high-quality crystals grew uniformly. However, large crystals (>∼0.8 mm) were still defective even at low supersaturation, because concentration gradient is large on large surfaces. Using a new seed-dipping process, obtained crystals were small and uniform in size (∼0.4 mm), and the ratio of defective crystals was reduced to 6%. Powder X-ray diffraction analysis revealed that form II crystals were ∼6 times more temporally stable than in the 20 °C condition. We found that high-quality crystals of metastable phase with high temporal stability could be realized by low supersaturation and reduction of the crystal size via SMPT.

The early stages of FeCO3 scale formation kinetics in CO2 corrosion

In a carbon dioxide (CO2) corrosive environment, when the product of the local concentrations of iron (Fe2+) and carbonate (CO32−) ions exceed the solubility limit, the precipitation of iron carbonate (FeCO3) on the internal walls of carbon steel pipelines can significantly reduce the corrosion rate. In the following work, static glass cell corrosion experiments were conducted to understand the precipitation behavior in the early stages of FeCO3 development and the factors favorable to protective film formation. The corrosion and precipitation rates were followed using a combination of mass gain, mass loss, electrochemistry and surface analysis techniques. At the conditions studied, the protectiveness and the rate of film formation was observed to vary significantly. The results indicated that the early stages of FeCO3 precipitation consists of a complex simultaneous nucleation and growth process. FeCO3 precipitation is shown to be dependent on surface species concentrations which can be significantly different to that of the bulk solution. Additionally, the role of crystal surface coverage and the blocking of actively corroding sites on the steel surface is examined and is shown to play a critical role in reducing precipitation kinetics at low levels of bulk super-saturation.

Mechanisms and Nucleation Rate of Methane Hydrate by Dynamical Nonequilibrium Molecular Dynamics

We investigate the effects of high solvated-methane concentration on methane-hydrate nucleation at 250 K and 500 atm. We consider solutions at four levels of methane molar fraction in the initial H2O–CH4 solution, χCH4 = 0.038, 0.044, 0.052, and 0.058, which are higher than (metastable) bulk supersaturation. χCH4 is controlled independently of the temperature and pressure thanks to the use of special simulation techniques [Phys. Chem. Chem. Phys. 2011, 13, 13177]. These conditions mimic a possible increase of local methane concentration beyond supersaturation induced, for example, by freeze concentration or thermal fluctuations. The nucleation mechanism and kinetics are investigated using the dynamical approach to nonequilibrium molecular dynamics. We demonstrate a hydrate-forming/-ordering process of solvated methane and water molecules in a manner consistent with both the “blob” hypothesis and “cage adsorption hypothesis”: the system initially forms an amorphous nucleus at high methane concentration, wh...

Experimental study on the effect of polysaccharides on incipient membrane scaling during desalination

Experimental results are reported on the effect of polysaccharides in the early stage of membrane scaling. Sodium alginate at small concentration (2 and 10mg/L) was employed as typical polysaccharide. Synthetic solutions, characterized by small bulk supersaturation ratio S in calcium sulfate (S~1.4), were filtered through a desalination membrane in dead-end cells under agitation. Three types of tests were performed; i.e. membrane scaling in absence of alginates (as reference), combined fouling-scaling (i.e. scaling in presence of alginates) and scaling tests after a fouling layer was formed on the membrane. Examination of various deposits by Scanning Electron Microscopy (SEM) and determination of calcium on membrane deposits and in filtered solids (from retentate and feed-fluid samples) provide useful insights including clear evidence that alginates tend to inhibit CaSO4 crystallization, likely due to calcium binding with carboxylates of alginate macromolecules and formation of gel deposits. The inhibition effect, manifested in the reduced deposit-mass density on membranes and crystallization–rate, as well as in crystal-shape modification, is stronger at the higher alginate concentration. Similarly, incipient membrane scaling, pretreated with alginate foulant solution, appears to be significantly inhibited compared to clean membranes. Under the conditions tested, membrane salt rejection was unaffected.

Seeded Crystallization of β-l-Glutamic Acid in a Continuous Oscillatory Baffled Crystallizer

A continuously seeded l-glutamic acid cooling crystallization process, in a continuous oscillatory baffled crystallizer, was designed and operated to deliver control over polymorphic form. Different feed solution concentrations and seed loadings of β-l-glutamic acid crystals were examined. Steady-state operation, based on particle size distribution and polymorphic form, was demonstrated consistently after two residence times. Where bulk supersaturation remained in the range 2–3, the polymorphic phase purity of the thermodynamically stable β polymorph was retained. However, when the bulk supersaturation exceeded this range to values of 3–8, primary nucleation of the metastable α polymorph was observed, and product crystals were a mixed phase. In the absence of seeding the system could not be operated without significant encrustation to the vessel surface thus leading to loss of control, whereas a continuously seeded approach allowed robust processing for at least 10 h.

RACORO continental boundary layer cloud investigations: 2. Large‐eddy simulations of cumulus clouds and evaluation with in situ and ground‐based observations

AbstractA 60 h case study of continental boundary layer cumulus clouds is examined using two large‐eddy simulation (LES) models. The case is based on observations obtained during the RACORO Campaign (Routine Atmospheric Radiation Measurement (ARM) Aerial Facility (AAF) Clouds with Low Optical Water Depths (CLOWD) Optical Radiative Observations) at the ARM Climate Research Facility's Southern Great Plains site. The LES models are driven by continuous large‐scale and surface forcings and are constrained by multimodal and temporally varying aerosol number size distribution profiles derived from aircraft observations. We compare simulated cloud macrophysical and microphysical properties with ground‐based remote sensing and aircraft observations. The LES simulations capture the observed transitions of the evolving cumulus‐topped boundary layers during the three daytime periods and generally reproduce variations of droplet number concentration with liquid water content (LWC), corresponding to the gradient between the cloud centers and cloud edges at given heights. The observed LWC values fall within the range of simulated values; the observed droplet number concentrations are commonly higher than simulated, but differences remain on par with potential estimation errors in the aircraft measurements. Sensitivity studies examine the influences of bin microphysics versus bulk microphysics, aerosol advection, supersaturation treatment, and aerosol hygroscopicity. Simulated macrophysical cloud properties are found to be insensitive in this nonprecipitating case, but microphysical properties are especially sensitive to bulk microphysics supersaturation treatment and aerosol hygroscopicity.

Incipient crystallization of calcium carbonate on desalination membranes: dead-end filtration with agitation

The development of reliable criteria for determining the onset of scaling on desalination membranes is of high practical value. A novel approach to systematically investigate incipient membrane crystallization and scale-particle evolution was recently reported by this laboratory, involving modeling-relevant phenomena during membrane desalination and experiments, in well-controlled pressure cells operating in dead-end mode with no agitation. However, parallel studies have shown that flow conditions equivalent to those prevailing in real desalination membrane modules are obtained in pressure cells with agitation. Therefore, this work aims to employ the aforementioned approach to the more realistic case of membrane CaCO3 scaling in dead-end desalination with agitation. Detailed data regarding incipient CaCO3 scaling of desalination membranes were obtained, by analyzing scanning electron microscopy (SEM) images, for small bulk supersaturation ratios S = 1 to 4 and short filtration times (~30–90 min). Mean shear stresses at the membrane surface were similar to those prevailing in desalination modules. The data show that concentration polarization due to salt rejection strongly affects scale-particle growth rate, insignificantly influencing particle-number surface density. There is no evidence of a significant induction period in the nucleation and growth of scale-particles on the membrane surface. The initial CaCO3 deposit flux, in mg/(m2 min), exhibits a strong dependence on membrane surface supersaturation. Experimental data on the supersaturation-dependent scale evolution appear to significantly differ from predictions based on classical concepts of heterogeneous nucleation and growth, thus indicating that non-conventional nucleation is the dominant mechanism of the membrane-scale development.

Effect of bulk pH and supersaturation on the growth behavior of silica biomorphs in alkaline solutions

Under certain conditions, mineralization of barium carbonate in silica-containing media at high pH results in the formation of complex crystal aggregates called “silica biomorphs”. These self-assembled, purely inorganic materials exhibit hierarchical structure and curved morphologies much reminiscent of certain living forms, thus constituting an interesting model system for the study of the biomineralization processes. In this paper, we report on the influence of the bulk pH on the morphogenesis of silica biomorphs in alkaline solutions. To that end, crystallization experiments were carried out at initial pH values between about 9.8 and 11.9, using atmospheric CO2 as a carbonate source. Formed aggregates were characterized quantitatively by statistical analyses of their morphology, number and size. Corresponding data evidence that well-developed polycrystalline architectures with elaborate shapes occur only when the starting pH is adjusted to values within a rather narrow corridor, ranging roughly from 10.2 to 11.1. Otherwise, merely ill-defined, globular or dumbbell-shaped particles were obtained. In addition, the pH of the mother solutions was monitored continuously during growth and correlated with time-dependent Ba2+ concentration profiles determined by in-situ X-ray fluorescence spectroscopy. By combining the collected data, temporal progressions of the bulk supersaturation were estimated for different conditions and used to re-evaluate the role of pH in the formation of silica biomorphs, particularly with regard to the recently proposed model of the growth mechanism. It is shown that a suitable starting pH is required not only to allow for dynamically coupled co-precipitation of the components, but also to maintain continuous CO2 uptake and hence adequate levels of supersaturation over extended periods of time during growth. Our experiments rationalize previous observations concerning the effect of pH on the formation of silica biomorphs, and disclose fundamental differences between growth in solutions and gels.

Dissolution and Precipitation Behavior of Amorphous Solid Dispersions

Amorphous solid dispersions (ASDs) are widely utilized in the pharmaceutical industry for bioavailability enhancement of low solubility drugs. The important factors governing the dissolution behavior of these systems are still far from adequately understood. As a consequence, it is of interest to investigate the behavior of these systems during the dissolution process. The purpose of this research was twofold. First, the degree of supersaturation generated upon dissolution as a function of drug-polymer composition was investigated. Second, an investigation was conducted to correlate physical behavior upon dissolution with polymer loading. Felodipine and indomethacin were selected as model drugs and hydroxypropylmethylcellulose (HPMC) and polyvinylpyrrolidone (PVP) were used to form the dispersions. Diffusion and nuclear magnetic resonance spectroscopy experiments revealed that the extent of bulk supersaturation generated on dissolution of the ASD did not depend on the drug-polymer ratio. Interestingly, the maximum supersaturation generated was similar to the predicted amorphous solubility advantage. However, dynamic light scattering measurements revealed that particles on the submicron scale were generated during dissolution of the solid dispersions containing 90% polymer, whereas solid dispersions at a 50% polymer loading did not yield these nanoparticles. The nanoparticles were found to result in anomalous concentration measurements when using in situ ultraviolet spectroscopy. The supersaturation generated upon dissolution of the solid dispersions was maintained for biologically relevant timeframes for the HPMC dispersions, whereas PVP appeared to be a less effective crystallization inhibitor.

3D numerical simulation for single crystal growth of potassium dihydrogen phosphate in a new solution growth system

A new system for improving the growth of KDP crystal with rotary flow field and stationary crystal is proposed. The 3D numerical simulation for flow and mass transfer shows that the rotation rate is the key factor that has a significant effect on the surface supersaturation and surface homogeneity. Especially for the high rotation rate, higher surface supersaturation and better surface homogeneity can be gained. Bulk supersaturation and inlet velocity also affect surface supersaturation and surface homogeneity to a certain extent. The surface shear stress increases with enhancing the rotation rate or the inlet velocity. The optimization for the configuration has also been discussed, which is helpful for the surface homogeneity.

Incipient crystallization of sparingly soluble salts on membrane surfaces: The case of dead-end filtration with no agitation

This paper aims at contributing to development of reliable criteria for determining the onset of scaling on desalination membranes. A novel approach is proposed to investigate incipient crystallization on membranes through modeling and RO filtration experiments. The evolution of membrane surface concentration of rejected ionic species (e.g. Ca 2+, CO 3 2−) is theoretically determined, and coupled with a detailed kinetic model for nucleation and growth of particles on the membrane. Model results contribute to our understanding of this problem and are in general accord with experimental data on membrane surface crystal density and mean size. Experimental data and model results show that incipient crystallization on RO membrane surfaces, when the bulk supersaturation ratio is maintained near its critical value (S ~ 1), is controlled by fluid permeation, and that the “induction time” may be insignificant under typical RO conditions. This work also suggests that the ability to determine the onset of crystallization on membranes is dependent on the combined sensitivity and adequate spatial resolution of the experimental technique employed, which explains the significant uncertainty associated with the reported in literature “induction period” data of different origin. Directions for future research are discussed.

Computational analysis of three-dimensional flow and mass transfer in a non-standard configuration for growth of a KDP crystal

Computational analysis of three-dimensional flow and mass transfer in a non-standard configuration for growth of a KDP crystal was conducted. The results show that the surface shear stress is mainly affected by the inlet velocity, and the distribution of the surface supersaturation is determined by the bulk supersaturation and the inlet velocity. By adjusting the inlet velocity, the homogeneity of surface supersaturation can be improved, which is helpful for reducing the occurrence of inclusions and enhancing the crystal quality. The thickness of solute boundary layer is closely related to the flow intensity, but it is almost free from the impact of the bulk supersaturation.

Supersaturation tracking for the development, optimization and control of crystallization processes

Supersaturation is the key driving force in crystallization operations, determining nucleation and growth kinetics, and heavily influencing physical mechanisms such as agglomeration. Therefore, knowledge of the bulk supersaturation during crystallization can greatly enhance process understanding and optimization. In this paper, a method which facilitates the calibration-free use of in situ ATR-FTIR for crystallization development and control is presented. This methodology uses solute-specific ATR-FTIR absorption peak heights to describe solute solubility and dissolved concentration and, in turn, supersaturation, for the optimization of cooling crystallizations of an active pharmaceutical ingredient (API) and benzoic acid. The approach presented facilitates rapid process understanding, design and optimization. Specifically, the potential to significantly reduce cycle time for both systems studies is demonstrated. In addition, the potential of the method to form the basis of a process control strategy for batch crystallization is successfully demonstrated.

Effect of Rate of Crystallization on the Continuous Reactive Crystallization of Nanoscale 6-Line Ferrihydrite

Altering the rate of 6-line ferrihydrite continuous reactive crystallization from the control conditions of pH 3.6 and 85 °C was investigated by varying the pH, feed concentration, and mean residence time. In these experiments, the rate of precipitation changed the relative proportion of 6-line ferrihydrite and goethite nanoparticles in precipitates and the aggregatesʼ physical properties of surface area, impurity concentration, filtration rate, and particle size. Although increasing the rate of precipitation had a negligible effect on bulk supersaturation, it is thought to locally increase the supersaturation at the FeIII feed inlet and precipitate 6-line ferrihydrite and for goethite precipitation to occur in the bulk. Alternatively, decreasing the rate of precipitation increased the relative proportion of goethite in precipitates, and the formation of smaller aggregates with higher impurity concentrations and surface areas. A reduction in pH also increased the proportion of goethite in precipitates and reduced the aggregates particle size distribution. The increased solubility at lower pH is believed to promote goethite formation by improved dilution of the feed solution. This work has demonstrated that the physical properties of 6-line ferrihydrite and goethite precipitates can only be altered via the way primary crystals aggregate and not through altering their crystallinity.

Engineering the oil binding capacity and crystallinity of self-assembled fibrillar networks of in edible oils.

The crystallinity and oil binding capacity of 12-hydroxystearic acid (12HSA)-vegetable oil organogels was modified by changing the post-crystallization annealing temperature from 5 °C to 30 °C for 24 h. The gels stored at 5 °C had a highly branched crystalline structure with small uniform pores, as determined by cryo-scanning electron microscopy. Large T2proton relaxation peaks at 50 to 70 ms determined by pulse nuclear magnetic resonance (pNMR) suggested the presence of highly immobilized oil at 5 °C. When the gels were stored at 30 °C, longer fibers and a less branched network were observed. At 30 °C, the 12HSA network's crystallinity was enhanced with fewer inclusions of liquid oil as determined by pNMR. When the gels were stored at 30 °C, a significantly shorter T2 relaxation peak was observed. The increased crystallinity, at 30 °C, was attributed to a reduction in bulk supersaturation, resulting in a very high crystallographic mismatch nucleation barrier (ΔG*) which favored one-dimensional fiber growth. However, at a lower crystallization temperature of 5 °C, there is an increase in the supersaturation and hence the crystallographic mismatch barrier is significantly lower, increasing fiber tip branching. The nucleation-growth-branching-growth model for self-assembled fibrillar networks explains the differences in crystallinity, pore size and oil syneresis observed for the 12HSA-vegetable oil organogels. It was found that the gels stored at 30 °C syneresised 1.35 times faster than the gels stored at 5 °C. Furthermore, the change in the T2 relaxations and the ratio of the complex viscosity/pore radius were 1.35 and 1.30 respectively.