Monte Carlo Simulation of Transient CSD in a Continuous Crystallizer under Stochastic Dispersion Effects

Monte Carlo simulation is a very powerful tool for simulation of transient and steady state crystal size distribution (CSD) in a continuous crystallizer under stochastic dispersion effects. In the present work, transient CSD in a continuous crystallizer has been reported when shape factor and growth rate dispersions conform to normal distribution. For the steady state run, the algorithm reported by Sen Gupta and Dutta elsewhere has been used to validate the results obtained in the present work when the steady state is reached.     

Analysis of Transient Crystal Size Distribution in a Continuous Sodium Chloride Crystallizer

This work deals with the transient analysis of crystal size distribution (CSD) in a continuous sodium chloride crystallizer. The crystallization is assumed to take place under diffusion controlled conditions and the crystal growth models reported by Sen Gupta and Dutta elsewhere have been used. Monte Carlo (MC) scheme has been employed for simulation purposes. The simulation results have been compared with the available experimental data at steady state.     

Preparation of lithium carbonate hollow spheres by spray pyrolysis

Lithium carbonate (Li₂CO₃) hollow spheres were prepared by spray pyrolysis of lithium bicarbonate (LiHCO₃) in this research. The products were characterized by X‐ray diffraction (XRD), scanning electron microscope (SEM), crystal size distribution (CSD) analysis and BET surface area measurement. The XRD figure of the product is nearly the same as the standard pattern, indicating the product achieved by spray pyrolysis has pure Li₂CO₃ crystalline phase. The SEM images show the self‐assembly hollow spheres are composed of about 200 nm primary particles. While the CSD analysis shows the macro‐volume mean crystal size ranges 4‐9 μm depending on the experimental conditions. The BET surface area of the product reaches 7.24 m²/g, which is much higher than the best value reported in the literature. The product prepared in this work has great potential application prospect in the lithium‐battery industry. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A stratified Monte Carlo simulation of CSD in a continuous crystallizer for size-dependent growth

This work deals with the prediction of crystal size distribution (CSD) in a continuous crystallizer for size-dependent growth. Crystal growth rates are described by Abegg, Stevens, and Larson (ASL) model. Stratified Monte Carlo method has been employed to evaluate the integrals involved in the classical moment equation for prediction of CSD. The simulation results have been compared with the available experimental data of K₂CO₃ · 1.5 H₂O crystals in a continuous crystall lizer.     

Application of Rosin–Rammler model for analysis of CSD in sugar crystallization

Crystal‐size distribution (CSD) is one of the most important parameters in sugar production. The objective is to grow crystals of uniform sizes or narrow CSD. CSD appears to be determined by the growth‐rate history of the crystals and the relative supersaturation (SS) of the solution from which crystals growth takes place. Three methods for preparation of nucleation seeds were described and used for industrial crystallization of raw and white sugars; these are wet milling filtered sugar (ML), agitating saturated solution (AS) and powdered sugars (PD). Rosin–Rammler (RR) and mathematical models were adopted to investigate CSD and the uniformity of the produced crystals. Higher uniformity coefficients were reported for the AS seeded crystals than the other two seeding methods. Furthermore, higher crystal contents were obtained for the AS seeded white sugar batches in comparison.     

ASL model for prediction of CSD in a continuous crystallizer

A Monte Carlo simulation scheme is proposed for crystal size distribution (CSD) in a continuous crystallizer for size dependent growth rate. Crystal growth rates are described by Abegg, Stevens, and Larson (ASL) model. The proposed model is used to predict CSD from potassium carbonate crystallizer. The agreement between theory and available data confirms the validity of the model.     

Advancements (and challenges) in the study of protein crystal nucleation and growth; thermodynamic and kinetic explanations and comparison with small-molecule crystallization

This paper reviews advancements and some novel ideas (not yet covered by reviews and monographs) concerning thermodynamics and kinetics of protein crystal nucleation and growth, as well as some outcomes resulting therefrom. By accounting the role of physical and biochemical factors, the paper aims to present a comprehensive (rather than complete) review of recent studies and efforts to elucidate the protein crystallization process. Thermodynamic rules that govern both protein and small-molecule crystallization are considered firstly. The thermodynamically substantiated EBDE method (meaning equilibration between the cohesive energy which maintains the integrity of a crystalline cluster and the destructive energies tending to tear-up it) determines the supersaturation dependent size of stable nuclei (i.e., nuclei that are doomed to grow). The size of the stable nucleus is worth-considering because it is exactly related to the size of the critical crystal nucleus, and permits calculation of the latter. Besides, merely stable nuclei grow to visible crystals, and are detected experimentally. EBDE is applied for considering protein crystal nucleation in pores and hydrophobicity assisted protein crystallization. The logistic functional kinetics of nucleation (expressed as nuclei number density vs. nucleation time) explains quantitatively important aspects of the crystallization process, such as supersaturation dependence of crystal nuclei number density at fixed nucleation time and crystal size distribution (CSD) resulting from batch crystallization. It is shown that the CSD is instigated by the crystal nucleation stage, which produces an ogee-curve shaped CSD vs. crystal birth moments. Experimental results confirm both the logistic functional nucleation kinetics and the calculated CSD. And even though Ostwald ripening modifies the latter (because the smallest crystals dissolve rendering material for the growth of larger crystals), CSD during this terminal crystallization stage retains some traces of the CSD shape inherited from the nucleation stage. Another objective of this paper is to point-out some biochemical aspects of the protein crystallization, such as bond selection mechanism (BSM) of protein crystal nucleation and growth and the effect of electric fields exerted on the process. Finally, an in-silico study on crystal polymorph selection is reviewed.     

Transient Crystal Size Distribution in DTB and FC Crystallizers

This work deals with the transient analysis of crystal size distribution (CSD) for imperfectly mixed draft tube baffled (DTB) and forced circulation (FC) crystallizers. The DTB and FC crystallizers are described by the Compartmental and Mixed models respectively. Monte Carlo (MC) scheme has been employed for simulation purposes. The simulation results have been compared with the available experimental data of BENNETT and VAN BUREN for continuous urea crystallizers.     

Effect of seeded surface area on crystal size distribution in glycine batch cooling crystallization: a seeding methodology

In batch cooling crystallization, if the seeding process is not carefully carried out, the crystal size distribution (CSD) is dispersed. The aim of this work is to determine the optimal conditions for seeding operations. Results show that the CSD is controlled if the seed surface area reaches a specific value called critical surface S_c. Nevertheless, S_c is not the only parameter to be considered. The mean crystal size of the product obtained actually depends on the size of the seeds used because of the growth rate distribution. In fact, seeds behave differently according to their crystal sizes, which accounts for the difference in crystal growth rates. Rules are proposed for seeding with the view to obtain a uni-modal CSD and a final product size predefined by the seed crystals.     

Efficient solution of a batch crystallization model with fines dissolution

In this paper, an efficient and accurate numerical method is proposed for solving a batch crystallization model with fines dissolution. The dissolution of small crystals (fines dissolution) is useful for improving the quality of a product. This effectively shifts the crystal size distribution (CSD) towards larger crystal sizes and often makes the distribution narrower. The growth rate can be size-dependent and a time-delay in the dissolution unit is also incorporated in the model. The proposed method has two parts. In the first part, a coupled system of ordinary differential equations (ODEs) for moments and solute mass is numerically solved in the time domain of interest. These discrete values are used to get growth and nucleation rates in the same time domain. In the second part, the discrete growth and nucleation rates along with the initial CSD are used to construct the final CSD. The analytical expression for CSD is obtained by applying the method of characteristics and Duhamel's principle on the given population balance model (PBM). A Gaussian quadrature method, based on orthogonal polynomials, is used for approximating integrals in the ODE-system of moments and solute mass. The efficiency and accuracy of the proposed numerical method is validated by a numerical test problem.     

Impact of agglomeration on crystalline product quality within the crystallization process chain

The quality of crystalline products, defined by e.g. purity or crystal size distribution (CSD), is primarily dominated by crystallization conditions but influenced by further downstream processes like solid‐liquid separation and drying also. Through uncontrolled agglomeration within the crystallization process chain the purity or CSD can be negatively affected. Therefore, in context of process optimization, missing knowledge of the impacts on the final product can lead to product batches out of specification. To increase the understanding of agglomeration and to provide insight into the relevance of holistic process optimization the agglomeration behavior of L‐alanine crystals is exemplarily quantified over the crystalline process chain. For the quantification the agglomeration degree (Ag) and the agglomeration degree distribution (AgD) are determined. The results show that the product quality achieved after crystallization is significantly affected by agglomeration during drying. Especially if washing after solid‐liquid separation is omitted, a broadening of the CSD is observed. Moreover, the evaluation by the AgD indicates that the final product can be ‐ despite similar characteristics of the CSD ‐ highly different. Consequently, it can be concluded that the characterization of the product quality by the CSD alone is insufficient and the quantification of agglomeration is essential for process optimization.     

Crystallization of mefenamic acid and polymorphs

The crystallization of Mefenamic Acid, (MA), which has a prevalent usage in drug formulation, was investigated. MA is a high‐dose, anti‐inflammatory, analgesic agent used for pain in menstrual disorders. Some negative properties of MA are a high hydrophobicity and propensity to stick to surfaces, which cause great problems during granulation and tabletting. To facilitate tabletability, enhance dissolution rates, and develop a stable and reproducible dosage form, investigation of the physicochemical properties of mefenamic acid is necessary. Pharmaceutical drugs are commonly crystalline materials and are therefore subject to polymorphism. Polymorphism, the ability of a substance to exist in more than one crystalline form, is a significant phenomenon in the field of chemical engineering sciences, including pharmaceutical development. Establishing the polymorphic behaviour of a drug molecule early in development minimizes the number of unsuitable candidates developed and reduces the risk of encountering issues later which may have a major financial and time impact. Mefenamic acid crystals were recrystallized from five different solvents of N, N‐dimethylformamide (DMF), acetone, N, N‐dimethylacetamide (DMA), Dimethylsulfoxide (DMS) and Ethyl Acetate (EA). In order to characterize the Mefenamic Acid crystal structure and the polymorphic forms of the crystals obtained by recrystallization, the scanning electron microscopy (SEM), Raman diffractometry and X‐ray pattern were used. From the industrial crystallization point of view, the crystal size distribution (CSD), the crystal shape, the polymorphic form and the crystallization steps are important factors that affect the quality and bioavailability of a drug. For the determination of crystal size distribution of MA, The Focused Beam Reflectance Measurement (FBRM) technique was practiced and CSD profiles were obtained. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Comparison Study of Mixing Effect on Batch Cooling Crystallization of 3‐Nitro‐1,2,4‐triazol‐5‐one (NTO) Using Mechanical Stirrer and Ultrasound Irradiation

The insensitive explosive 3‐Nitro‐1,2,4‐triazol‐5‐one (NTO) has been recrystallized from water in an effort to prepare crystals with smaller size and narrower distribution in a batch cooling crystallizer. Two mixing devices, i.e., a mechanically stirred system with and without ultrasound in aqueous media were employed to compare the mixing effect on the crystallization. Under ultrasound irradiation, the metastable zone width was significantly reduced by more than 2 fold and the crystal size was shifted from 140∼160 μm to 50∼70 μm with a narrower CSD compared to the mechanically stirred system. However in the mechanical stirrer, the mixing effect on NTO crystallization was negligible if the impeller speed was sufficient to suspend all crystals in the crystallizer. It was found that the crystal growth was not influenced by mixing. We suggest that the NTO crystals were formed by primary heterogeneous nucleation that is common in batch cooling system. Finally, the population balance model (PBM), with the empirical nucleation and growth kinetic expressions, was solved numerically to predict the crystal size and the CSD with batch time, and the results were in good agreement with the experimental data.     

Study of phosphoric acid crystallization using a focused beam reflectance measurement method

A way for restoring the crystal size distributions (CSD) from measured chord length distributions (CLD) was reported in this paper. The kinetics of phosphoric acid crystallization process was investigated in cooling mode using focused beam reflectance measurement (FBRM) and digital photo technique. In order to restore the CSD from measured CLD and verify the reliability of FBRM data, digital photo technique in real time and optical microscope were applied in large crystal size and small range, respectively. Results indicated a converting constant A existed between CLD and CSD when crystal growth follows size‐independent growth (Mcabe's ΔL law) law. It was verified by Malvern particles size analysis method. The converting constant A varied with crystal morphology. The crystal growth order increased with the stirring increasing speed during phosphoric acid crystallization process. The trend was especially notable at higher speed situations. It can illustrate that the state of phosphoric acid hemihydrate crystal growth was controlled by both diffusion and surface‐integration with the increasing stirring speed. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of process parameters on crystal size and morphology of lactose in ultrasound‐assisted crystallization

α‐lactose monohydrate is widely used as a pharmaceutical excipient. Drug delivery system requires the excipient to be of narrow particle size distribution with regular particle shape. Application of ultrasound is known to increase or decrease the growth rate of certain crystal faces and controls the crystal size distribution. In the present paper, effect of process parameters such as sonication time, anti‐solvent concentration, initial lactose concentration and initial pH of sample on lactose crystal size, shape and thermal transition temperature was studied. The parameters were set according to the L₉‐orthogonal array method at three levels and recovered lactose from whey by sonocrystallization. The recovered lactose was analyzed by particle size analyzer, scanning electron microscopy and differential scanning calorimeter. It was found that the morphology of lactose crystal was rod/needle like shape. Crystal size distribution of lactose was observed to be influenced by different process parameters. From the results of analysis of variance, the sonication time interval was found to be the most significant parameter affecting the volume median diameter of lactose with the highest percentage contribution (74.28%) among other parameters. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of Various Parameters on Crystal Size Distribution from the Cascade of two Perfectly Mixed Tanks

The influence of properties of crystallizing substance and operation parameters of simplest, two-stage cascade of mixed tanks on crystal size distribution was examined. The mathematical model of cascade was formulated to this end. The relations found enabled to decide which parameters influence the CSD. Computations were performed then with the purpose to compare the CSD from cascade and CSD from single crystallizer with the same mean retention time as in cascade and with identical input values. These computations were performed for arbitrarily chosen, but met in practice values of physico-chemical constants of crystallizing substance and parameters of crystallizers performance. It was found that for a given set of input values optimal conditions of cascade performance could be found.     

Selective etching of ZnTe in HF:H2O2:H2O solution: Interpretation of extended defect‐related etch figures

HF:H₂O₂:H₂O solution (40%wt.HF: 30wt.%H₂O₂: H₂O, 3:2:1 by volume) was used to reveal extended defects (line, face and volume defects) in bulk ZnTe crystals grown from Te solution. The etch patterns were analyzed based on their size, shape and distribution. The etch figures, both in the shape of pits and hillocks with high resolution, show forms controlled by the symmetries of the respective faces were produced. Two different sizes of pits were observed, the larger‐size pits correspond to dislocations penetrating the surface, however, the smaller‐size texture pits are produced on the defect‐free region, which serve as standard pits on respect faces. The face defects, such as grain boundaries, sub‐grain boundaries, dislocation walls, twins and stacking faults, can be all displayed clearly. Another essential feature of the etchant is that, it can effectively dissolve Te‐rich phase (Te inclusion/precipitates), which makes it promising to reveal the shape of this volume defect.     

Characterization of plasticity-induced structural changes in a Zr-based bulk metallic glass using positron annihilation spectroscopy

Changes in the free volume distribution in Zr_58.5Cu_15.6Ni_12.8Al_10.3Nb_2.8 bulk metallic glass with inhomogeneous plastic deformation and annealing were examined using positron annihilation spectroscopy. Results indicate that the size distribution of open volume sites is at least bimodal prior to deformation. The size and concentration of the larger sites, identified as flow defects, changes with processing. The size of the flow defects initially increases with deformation. More extensive deformation shifts the distribution, with a third group of much larger sites forming at the expense of flow defects. This suggests that a critical strain is required for the growth of nanovoids observed elsewhere by HRTEM. Although these observations suggest the presence of three open volume size groups, further analysis indicates that all groups have a similar distribution of chemical species around them as evidenced by the same line shape parameter. This may be due to the disordered structure of the glass and the positron affinity to particular atoms surrounding the open volume regions.     

Measurement of three‐dimensional concentration gradients around a crystal growing from its aqueous solution using laser schlieren

Schlieren measurements of the gradients of the concentration field around a KDP crystal growing from its aqueous solution are reported. The measurement of the concentration gradient field is important for crystal growth because it controls the rate of solute transport from the bulk of the solution to the crystal surface. In the crystal vicinity, the concentration gradients have a three dimensional distribution. The concentration gradient field has been imaged using monochrome schlieren technique. Four view angles, namely 0, 45, 90 and 135° have been utilized. By interpreting the schlieren images as projection data of solute concentration gradient, the three‐dimensional concentration gradient field around the crystal has been determined using an algebraic reconstruction technique. At low supersaturation levels, the growth process is accompanied by weak fluid movement during which diffusion effects are significant. At higher levels of supersaturation and large crystal size, a well‐defined convective plume around the growing crystal is observed. Reconstruction of concentration gradients around the crystal explains the preferential growth rates of various faces of the crystal. The non‐circular shape of the crystal is seen to affect the symmetry of the distribution of concentration gradients in its vicinity. The effect of crystal morphology on the orientation of convection currents rising from the crystal surface has also been brought out on the basis of the reconstructed concentration gradients distribution in the growth chamber. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Rate of sodium chloride attrition fragment generation in a mixed‐suspension crystallizer

Attrition of crystals in industrial crystallization is the major source of secondary nucleation and has strong effects on product quality. This work describes attrition in industrial crystallizers using an empirical engineering model based on dimensionless groups describing crystal properties, suspension properties, and crystallizer geometry and operating conditions. Here the attrition rate of sodium chloride crystals in a small scale mixed‐suspension crystallizer is studied, varying the following parameters: impeller speed, parent crystal size, suspension density, draft‐tube impeller clearance, off‐bottom impeller clearance, impeller type, and impeller material. It was found that the attrition rate depends on most of the variables investigated. The direction of the dependence is predictable based on intuitive modeling. An empirical power law model based on dimensionless groups predicted by Buckingham‐Pi theory (using variables mentioned above) gives a good fit to the data.