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The phase diagrams of tetragonal hen egg white lysozyme containing besides thermodynamic (solubility) also kinetic (nucleation) data were determined for pH values of 4.4, 5.0, and 6.0, 3 to 7 wt % sodium chloride concentrations and lysozyme concentrations from 5 to 70 mg/mL by the use of a turbidity technique. This new technique offers a rapid, precise and reliable determination of nucleation and solubility points. These points can be obtained simultaneously within 6 h. The errors of measurements are less than ±0.9 °C for the solubility temperature and less than ±1.0 °C for the nucleation temperature. The solubility data obtained could be extended and described by a good correlation with literature data. The solubility of lysozyme was found to decrease with increasing salt concentration while the nucleation points were observed more early with respect to salt addition; as a consequence the metastable zone is more narrow. The solubility of lysozyme is slightly reduced at higher values of the pH, and the nu...

Cocoa butter equivalent (CBE) was produced from a blend of mango kernel fat (MKF) and palm oil mid-fraction (PMF). Five fat blends with different ratios of MKF/PMF (90/10, 80/20, 70/30, 60/40 and 50/50 (%wt)) and pure MKF, PMF and cocoa butter (CB) were characterized. Similar to CB, all fat blends contained palmitic (P), stearic (S) and oleic (O) acids as the main fatty acid components. The triglyceride compositions of all blends were significantly different from CB. However, blend 80/20, which contained higher content of SOS, similar content of POP and lower content of POS compared to CB, exhibited a slip melting point, crystallization and melting behavior most similar to CB and hence it was recommended as CBE. The chosen CBE was then mixed with CB in a ratio of 1:5.64 (wt), mimicking that of typical dark chocolate where 5 % of CBE is added to the finished product. The crystallization behavior, the crystal morphology and bloom behavior of the mixture was investigated and was found to be not significantly different from CB.

Anionic surfactants, commonly used in household products and the detergency industry, tend to precipitate with divalent counterions in hard water. The unsightly soap scum thus formed also removes the surfactant from the cleaning action. The current research has improved prediction of the precipitation phase boundary for mixtures of surfactants in hard water in two ways: firstly, an accurate value of the solubility product (KSP) has been determined for the calcium salt of 4-octylbenzene sulfonate, and accurate temperature dependent KSP values have been determined for the calcium salts of dodecyl sulfate and decyl sulfate; secondly, improvements in prediction of the precipitation phase boundary have been achieved using an improved model. The KSP values of the decyl sulfate and dodecyl sulfate salts strongly increase with increasing temperature, with the shorter chain surfactant having significantly higher KSP than its longer chain analogue. At 30 °C the KSP of the 4-octylbenzenesulfonate salt is similar to that of the dodecyl sulfate salt, perhaps due to the similarity in the length of their hydrocarbon tails. A recent counterion binding model proposed by our research group and micellization models have been used to model the precipitation phase boundaries for both single anionic surfactant and binary mixed anionic surfactant systems, improving thermodynamic modeling of the precipitation phase boundary of single and binary mixed anionic surfactant systems. In particular, the improved model of counterion binding has allowed the model to predict the phase boundary accurately over a range of temperatures.

The current research has produced an accurate model of the non-nucleating seeded batch crystallization of glucose monohydrate which includes complex phenomena including crystal growth rate dispersion and the effect of the mutarotation reaction. The model is able to predict the population density of crystals in the batch as a function of particle size and batch time, n=n(L,t) as well as total glucose concentration in the mother liquor and the fraction of glucose in the α-d-glucopyranose form. A previous model of similar systems was limited by considering only systems with monosize seed crystals, and where growth rate dispersion had a negligible effect on the particle size distribution. Because of the nature of the ‘common history’ crystals that are produced by the growth of glucose monohydrate, the modifications required to the model to account for these additions to the model are remarkably simple. By predicting the full population density the model produces an accurate mass balance for the crystallization process, since the second moment of the crystal size distribution (CSD) may be calculated analytically at every point in the simulation. This enables the competitive kinetics between the rate of crystal mass deposition of α-glucose and the rate of production of α-glucose via the mutarotation reaction to be more accurately accounted for, and hence the significance of the mutarotation reaction on the crystal growth to be more accurately predicted.

The induction time for precipitation of pure sodium dodecylsulfate (NaDS) solutions by CaCl2 both below and above the cmc at a specific temperature depends only on the supersaturation ratio of the precipitating species in the bulk solution, rather than the means of achieving the supersaturation (changes in calcium ion concentration or in surfactant concentration). For mixed NaDS/sodium decylsulfate (NaDeS) systems precipitated by CaCl2, the induction time is only a function of the supersaturation ratio calculated based on Ca(DS)2, which is formed from these solutions, since its solubility product is orders of magnitude less than that of Ca(DeS)2. The increase in induction time in mixtures of these surfactants, compared to pure systems of the same total surfactant content, is only due to the change in the concentration of the precipitating species (DS) because of changes in the molar ratio of the surfactants present and thermodynamic changes due to mixed micellization. For mixed NaDS/sodium octylbenzenesul...

Competitive counterion binding of sodium and calcium to micelles, and mixed micellization have been investigated in the systems sodium dodecylsulfate (NaDS)/sodium decylsulfate (NaDeS) and NaDS/sodium 4-octylbenzenesulfonate (NaOBS) in order to accurately model the activity of the relevant species in solution. The critical micelle concentration (CMC) and equilibrium micelle compositions of mixtures of these anionic surfactants, which is necessary for determining fractional counterion binding measurements, is thermodynamically modeled by regular solution theory. The mixed micelle is ideal (the regular solution parameter β(M)=0) for the NaDS/NaOBS system, while the mixed micelle for NaDS/NaDeS has β(M)=-1.05 indicating a slight synergistic interaction. Counterion binding of sodium to the micelle is influenced by the calcium ion concentration, and vice versa. However, the total degree of counterion binding is essentially constant at approximately 0.65 charge negation at the micelle's surface. The counterion binding coefficients can be quantitatively modeled using a simple equilibrium model relating concentrations of bound and unbound counterions.

The Secondary Nucleation Threshold (SNT) of γ- dl -methionine ( dl -met) in aqueous solution was measured for the temperature range 10–61 °C. The width of the SNT is weakly temperature dependent with slightly smaller induction times at higher temperatures. Seeded batch crystallizations of γ- dl -met were performed isothermally at 10, 25, and 40 °C in an agitated batch crystallizer, and within the SNT region to avoid nucleation. The effect of the initial supersaturation and seed mass on crystal growth were also studied at 25 °C. The initial growth rate (during the first 20 min of the batch) is significantly higher than subsequent crystal growth, a phenomenon previously seen with other species. The measured growth rates are independent of seed mass, as expected, for the usable portion of the growth rate data. The growth rates were found to linearly depend on the relative supersaturation of the total dl -met in the system. The growth rate constants increase with increasing temperature and follow an Arrhenius relationship. The growth kinetics of the γ- dl -met will be used to study in order to begin characterization of the polymorphic transformations and the overall crystallization rate of dl -met.

This article analyzes a collection of recent research on a recently discovered feedback mechanism between the crystal growth rate and the surface features of the crystal, and the ramifications the mechanism has on crystallization in general and also on the design and analysis of industrial crystallizers. It has been found that growth under high supersaturations degrades the crystal surface, causing a roughening that is probably due to imperfect incorporation of growth clusters into the surface of the crystal. The effect becomes more pronounced under higher growth rate conditions, and for higher residence times under such conditions. The mechanism only occurs if the supersaturation is increased above a critical level known as the macroscopic roughening transition, although this level is typically quite low; for sucrose it has been measured as a relative supersaturation between 2.5 and 3.9% which is in the range used in many industrial crystallizations. The mechanism appears to be associated with the surface energy of the crystal, with the surface of high surface energy crystals being degraded at lower values of the supersaturation, and such crystals also have larger reductions in growth rate after the roughening has occurred. The mechanism also appears related to growth rate dispersion (GRD), since it gives a mechanism for variation in growth rates in batches of crystals, and also because GRD also appears to be more significant in species having a higher value of the surface energy. The mechanism also causes an increase in the impurity incorporation in the crystal, thus leading to reduced product crystal purities. The mechanism for the impurity incorporation is probably due to enhanced adsorption of impurity molecules due to large crystal surface areas (due to the roughening) and also larger numbers of adsorption sites. The mechanism also complicates measurement of crystal growth kinetics, and thus makes efficient design of industrial crystallization units more difficult.

The effect of crystallization conditions on the dextran partition coefficient between impure syrup and sugar crystal has been investigated in a batch crystallizer. The crystallizer is operated isothermally at temperatures of 30, 40, and 50 °C, at constant relative supersaturations of 0.05, 0.07, and 0.09, and with mother liquor dextran concentrations of 1000 and 2000 ppm/Brix. The dextran content has been determined by the CSR method. A 1:1 mass ratio of high-fraction dextran (approximately 250,000 Da) and low-fraction dextran (60,000–90,000 Da) is used to represent a wide range of dextran contamination. It is seen that the dextran partition coefficient in sucrose crystallization increases with both increasing supersaturation and increasing crystallization temperature. However it appears that these are secondary effects, with the partition coefficient strongly correlating with crystal growth rate alone, despite the regressed data having large variations in temperature, mother liquor dextran content, and supersaturation. Dextran incorporation into the sugar crystal results from both dextran adsorption onto the crystal surface and mother liquor inclusions. The explanation for the variation in the dextran content in sugar crystal with respect to the growth rate is due to increased adsorption due to the higher surface roughness of crystals grown at high growth rates. Although the dextran concentration in the solution affects the dextran content in the crystal, it does not strongly affect the dextran partition coefficient.

This research numerically simulates the two-phase (liquid and vapor) flow in a 1 m3 draft tube baffle (DTB) crystallizer with fines removal streams. The computational fluid dynamics (CFD) commercial software ANSYS CFX-10.0 was employed to perform 3-D simulation using the finite volume method with an unstructured mesh topology. The influence of hydrodynamics in the crystallizer, as characterized by the momentum source strength and fines removal flow, on the flow characteristics and the classification of crystals are investigated. The results showed the liquid flow is fully uniform in the main body of the crystallizer studied for momentum sources larger than or equal to 19.63 kg · m/s2. The uniformity of the suspension will strongly affect the product crystal size distribution. Momentum source strengths and fines removal flow rates also have a significant effect on the fines removal cut-size due to varying up-flow velocities in the fines removal section, altering the size at which particles are carried out ...

The moment form of the population balance is a very popular method of modeling the evolution of particle size in many particulate systems. In many cases the moments of the particle size distribution are sufficient to characterize the system for engineering purposes, however in some cases an approximation to the particle size distribution itself is desired. The traditional method to achieve this approximation is to write the set of (known) moments in matrix form, μ = A.n, and then solve this equation, via matrix inversion, to obtain the population density, n, in a finite number of size classes. The method of matrix inversion may result in a poor approximation, particularly if the distribution is too complex to be represented by a small set of finite width pulses. Several alternative methods are discussed including a similar method based on the central moments, and fitting the moments to known types of distribution functions, the gamma distribution in particular. The inversion method involving central moments improves the conditioning of the matrix. This did not improve the result when small numbers of moments (six or less) were used, because accurate inverses of the matrix for the moments about the origin could be achieved. Fitting moments to known distributions is computationally more difficult than the inversion technique because of the optimization required, but this is not a significant drawback due to the widespread availability of computation mathematical programs. This method was particularly successful in reproducing accurate distributions.

Investigation of the secondary nucleation threshold (SNT) of alpha-glucose monohydrate was conducted in aqueous solutions in agitated batch systems for the temperature range 10 to 40 degrees C. The width of the SNT decreased as the induction time increased and was found to be temperature independent when supersaturation was based on the absolute concentration driving force. Nonnucleating seeded batch bulk crystallizations of this sugar were performed isothermally in the same temperature range as the SNT experiments, and within the SNT region to avoid nucleation. The growth kinetics were found to be linearly dependent on the supersaturation of total glucose in the system when the mutarotation reaction is not rate limiting. The growth rate constant increases with increasing temperature and follows an Arrhenius relationship with an activation energy of 50 +/- 2 kJ/mol. alpha-Glucose monohydrate shows significant crystal growth rate dispersion (GRD). For the seeds used, the 95% range of growth rates was within a factor of 6 for seeds with a narrow particle size distribution, and 8 for seeds with a wider distribution that was used at 25 degrees C. The results will be used to model the significance of the mutarotation reaction on the overall crystallization rate of D-glucose in industrial crystallization.

The effect of a crystal's growth rate history on the current growth behavior was investigated as a cause of crystal growth rate dispersion (GRD), which is a significant problem in crystallizer design and modeling. The solute used in the experiments was sucrose, a high production commodity still crystallized mainly in batch crystallizers, where GRD is most significant. The results show that the growth history of a crystal has a significant effect on the crystal growth rate of that crystal. In particular, a history of rapid crystal growth under high supersaturation causes a roughening of the crystal surface, apparently due to poor surface integration, and subsequent growth occurs at lower rates than would be expected without this growth history. The process of crystal surface healing occurs at low levels of supersaturation over periods of several hours of growth and results in the crystals again reaching their normal growth rate levels. The growth layer formed to heal the surface of the crystal is greater t...

Commercial crystalline fructose is currently prepared by chromatographic separation of aqueous solutions of fructose and glucose followed by crystallization in either aqueous or aqueous−ethanol solutions. It may be possible to use one or more crystallization steps instead of the chromatographic process, thus producing crystalline product more directly. In this study the solubility, refractive index, and viscosity of solutions of fructose + glucose + ethanol + water were measured at 30 °C, and the densities of solutions with solvent concentrations of 40, 60, and 80 mass % ethanol were measured at 25 °C. These properties will be useful for crystallization studies for this system.

The growth of fructose crystals from aqueous ethanolic solutions was studied using a 1-L seeded batch crystallizer. The growth kinetics were found to linearly depend on the relative supersaturation of the crystallizing tautomer (beta-D-fructopyranose). The growth-rate constant increased slightly with increasing temperature and increasing solvent ethanol content. The growth rates are lower than those for aqueous solutions of comparable supersaturations. Fructose displays significant growth-rate dispersion (q = 0.35) when crystallized from aqueous ethanolic solutions. The growth-rate dispersion is independent of solvent composition and temperature within the range studied, although it is slightly higher than is seen in crystallization from aqueous solutions.

Nutrient stewardship is emerging as an issue of global importance, which will drive the development of nutrient recovery in the near to medium future. This will impact wastewater treatment practices, environmental protection, sustainable agriculture and global food security. A modelling framework for precipitation-based nutrient recovery systems has been developed, incorporating non-ideal solution thermodynamics, a dynamic mass balance and a dynamic population balance to track the development of the precipitating particles. The mechanisms of crystal nucleation and growth and, importantly, aggregation are considered. A novel approach to the population balance embeds the nucleation rate into the model, enabling direct regression of its kinetic parameters. The case study chosen for the modelling framework is that of struvite precipitation, given its wide interest and commercial promise as one possible nutrient recovery pathway. Power law kinetic parameters for nucleation, crystal growth and particle aggregation rates were regressed from an ensemble data set generated from 14 laboratory seeded batch experiments using synthetic solutions. These experiments were highly repeatable, giving confidence to the regressed parameter values. The model successfully describes the dynamic responses of solution pH, the evolving particle size distribution subject to nucleation, growth and aggregation effects and the aqueous magnesium concentration in the liquid phase. The proposed modelling framework could well be extended to other, more complex systems, leading to an improved understanding and commensurately greater confidence in the design, operation and optimisation of large-scale nutrient recovery processes from complex effluents.

Fructose may be recovered from aqueous syrups by crystallization through the addition of ethanol, which reduces the solubility of the fructose. The solubility of fructose in ethanol + water was det...

The current study investigated a potential mechanism of growth rate dispersion (GRD) by determining the effect of a crystal’s “growth rate history” on its current crystal growth, for sucrose, potash alum, potassium dihydrogen phosphate (KDP), and potassium sulfate crystals, using a combination of growth kinetic analysis and surface analysis via atomic force microscopy (AFM) and scanning electron microscopy (SEM). The growth history of a crystal had a significant effect on the future crystal growth rate: if a crystal had a period of high growth in a high supersaturation environment, the subsequent growth of the crystal in a lower supersaturation had a lower rate than a crystal that had been kept in the lower supersaturation environment. These results can be explained by the effect of high growth rates on the growing surface of a crystal: crystals grown in high supersaturation solutions had a rougher surface (on a macroscopic rather than molecular scale) than those grown in low supersaturation solutions. Th...

International audience; The occurrence of concentration and temperature gradients in saline microdroplets evaporating directly in air makes them unsuitable for nucleation studies where homogeneous composition is required. This can be addressed by immersing the droplet in oil under regulated humidity and reducing the volume to the picoliter range. However, the evaporation dynamics of such a system is not well understood. In this work, we present evaporation models applicable for arrays of sessile microdroplets with dissolved solute submerged in a thin layer of oil. Our model accounts for the variable diffusion distance due to the presence of the oil film separating the droplet and air, the diffusive interaction of neighboring droplets, as well as the variation of the solution density and water activity due to the evolving solute concentration. Our model shows excellent agreement with experimental data for both pure water and NaCl solution. With this model, we demonstrate that assuming a constant evaporation rate and neglecting the diffusive interactions can lead to severe inaccuracies in the measurement of droplet concentration particularly during nucleation experiments. Given the significance of droplet evaporation in a wide array of scientific and industrial applications, the models and insights presented herein would be of great value to many fields of interest.