Sonocrystallization and crystallization with gassing of adipic acid

Sonocrystallization is widely used to control nucleation and, therewith, improve the product quality. For this purpose, power ultrasound is turned on within the metastable zone during the crystallization process. But the mechanism by which power ultrasound induces nucleation is still unclear. Efforts have been made to identify the mechanism. It is assumed that nucleation is induced due to the bubble surface provided acting itself as nucleation center so that the mechanism seems to be a heterogeneous one. To prove this assumption, gassing has been investigated to induce nucleation during batch cooling crystallization. The gas bubbles are just expanding not collapsing. This study focuses on the investigation of the crystallization behavior of adipic acid during sonocrystallization and, furthermore, during the crystallization with gassing. During sonocrystallization experiments the insonation period, the ultrasonic frequency and the initial supersaturation ratio were varied. The results show that the metastable-zone width can be reduced and the crystal-size distribution, which turns out to be bimodal, can be narrowed the longer the insonation period and the higher the initial supersaturation ratio is. The crystals formed were identified as agglomerates, whereas the agglomeration can be reduced by power ultrasound. The gassing experiments demonstrated that the crystallization behavior of adipic acid can be affected similar to the application of power ultrasound. It can be concluded that gassing is an alternative to power ultrasound.     

Modeling ultrasound-induced nucleation during cooling crystallization

A model to simulate cooling crystallization processes with ultrasound is proposed by introducing an additional kinetic expression for nucleation mechanism due to the ultrasound irradiation. Applying the model to predict the concentration profiles, nucleation rates, and crystal-size distribution during the sonocrystallization process shows that the key parameter for understanding induced nucleation seems to be the reduction of the nucleation work, which verifies the assumption of a heterogeneous-nucleation mechanism. Hence, the specific foreign surfaces of the cavitation bubbles as well as the adsorption properties of the forming crystals on the cavitation bubbles play important roles in qualitative prediction of the number of induced nuclei. Furthermore, enhanced diffusion due to ultrasonic waves seems to have a minor effect on the nucleation mechanism.     

A new technique to determine rate constants for growth and agglomeration with size- and time-dependent nuclei formation

Fluidized bed spray agglomeration is a particle size enlargement process where particles stick together with the help of spraying binder. High impact forces between particles lead to attrition. Attrition may be modeled as poly-disperse nucleation. Furthermore, particulate event like over-spray leads to the formation of particles in a wide range of volume. A new technique for the determination of agglomeration, growth and nucleation parameters is presented in this work. The model is based on a previous approach which takes mono disperse nuclei formation in the smallest class into account. Frequently in crystallization processes, nucleation is assumed to be mono-disperse. The technique presented here incorporates nuclei formation in a certain range of volume. It is quite general and applicable to consider size- and time-dependent nuclei formation. For two particular cases of growth and agglomeration including size-dependent nuclei formation, simulation data was generated by continuous feeding of nuclei in a certain range to demonstrate the capability of parameter extraction of the model. Further, the new technique is applied to extract rate constants from experimental data measured during fluidized bed spray agglomeration. This technique is also useful for the prediction of bimodal behavior of particle size distributions (PSD).     

Population balance model for nucleation,growth, aggregation,and breakage of hydrate particles in turbulent flow

This article describes a computational model for the size evolution of hydrate particles in a pipeline‐pump system with turbulent flow. The model is based on the population balance principle, and the simulation results were validated with data from an experimental study of a flow loop containing hydrate particles reported in the literature. It is found that the particle size is significantly influenced by aggregation and breakage, related to shear in the flow, and that these effects are comparable to those of growth and nucleation, related to diffusional processes. Two different approaches for hydrate growth and nucleation, one of continuous nucleation during the process and one of only an initial nucleation‐pulse, were used. This was done to compare the aggregation and breakage parameters which come out when fitting the models output to experiment. These two approaches are found to give rise to similar aggregation/breakage parameters, lending credence to the pbm‐based modeling. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Metastable zone determination of lipid systems: Ultrasound velocity versus optical back‐reflectance measurements

The metastable zone width (MZW) of a multi‐component system as influenced by the process parameters cooling rate, agitation speed, and additive concentration was determined via ultrasound velocity measurements. The results were compared with those obtained by optical back‐reflectance measurements (ORM) using coconut oil as a model substance. Increasing the cooling rate led to the shift of the nucleation point to lower temperatures. This tendency was better visualized by the ultrasonic curves while a significant disturbance of the ORM signal could be observed. Agitation led to an increase of the nucleation temperature and hence a narrower metastable zone. The influence of an additive on the MZW was found to strongly depend on its concentration. The MZW detected by the ultrasound technique was narrower compared to that obtained by the ORM method, indicating the faster response to the phase transition of the ultrasound technique. Another advantage of the ultrasound technique was the in situ evaluation of the experimental data, while ORM needed a linear fitting to estimate the saturation temperature. Furthermore, ultrasound velocity measurements are based on density determination of the medium whereas the ORM sensor is able to detect only particles that are located within the measuring zone and possess a well‐defined size. Practical applications: MZW is one of the most important parameters that determine the characteristics of crystalline products. However, a proper technique that can be used in MZW detection in fat systems has rarely been reported, due to the difficulties in dealing with natural fats. The findings of this study can greatly help those who are involved in the field of fat crystallization from both the academic and the practical point of view. This is due to the fact that new and promising techniques for the online and in situ determination of the MZW of fats, with high accuracy, and reproducibility, under most process conditions, were clarified in this work. The readers can easily follow the procedure developed in this paper. Also information about the influence of process parameters and additives on the MZW is included.     

Electrodeposition of Al,Mn, and Al–Mn Alloy on aluminum electrodes from molten salt (AlCl<Subscript>3</Subscript>–NaCl–KCl)

Electrochemical deposition of aluminum and manganese from basic and acidic molten AlCl₃–NaCl–KCl mixture on an aluminum electrode at 180 °C was studied by the methods of voltammetry, and potential and current transient. The deposition of aluminum was found to proceed via a nucleation/growth mechanism in basic melt, while the deposition of manganese was found to be diffusion controlled in basic melt. The diffusion coefficient of Mn²⁺ ions in basic melt, as derived by voltammetry was in agreement with the deductions of transient methods. Analysis of the chronoamperograms indicates that the deposition of manganese on Al was controlled by 3D diffusion controlled nucleation and growth. The processes are manifested as peaks on a decaying chronoamperogram. Non-linear fitting methods were applied to obtain the kinetic parameters from theoretical formulae proposed to describe this system. It is also found that under more cathodic potentials, the saturation number density of the manganese nuclei and also the efficiency of use of the available surface nucleation sites increased.     

Parameterization of population balance models for polythermal auto seeded preferential crystallization of enantiomers

For analysis, design and model-based control of crystallization processes typically population balance models or reduced models derived therefrom are used. Usually the kinetic parameters in these models are determined analyzing measured concentration trajectories and/or particle size distributions using parameter estimation procedures. In the case of preferential crystallization of enantiomers the analysis of experiments is complex since there are two “competing” crystal populations. In this field often batch processes are performed using seeds of the desired enantiomer. Currently, it is in particular challenging to quantify and optimize a new concept: e.g. the so-called “auto seeded programmed polythermal preferential crystallization” (“as3pc” [Coquerel, G., Petit, M.-N., Bouaziz, R., 2000. Method of resolution of two enantiomers by crystallization. United States Patent, Patent number: 6,022,409]). In order to design and optimize this process the temperature dependent kinetic constants for crystal growth, nucleation and dissolution have to be known. In this work a reduced model for this auto seeded process is presented. The general identifiability of the model parameters is investigated along with some suggestions on how to reparameterize the kinetic terms involved. The values of the identified key parameters are estimated using conventional least square optimization using experimental data determined for the model system threonine/water. Parameter confidence and cross correlation are discussed and finally the model is validated using experiments not used for parameter estimation.     

Ultrasound assisted crystallization of cephalexin monohydrate:Nucleation mechanism and crystal habit control

With the high-quality requirements for cephalexin monohydrate,developing a robust and practical crys-tallization process to produce cephalexin monohydrate with good crystal habit,appropriate aspect ratio and high bulk density as well as suitable flowability is urgently needed.This research has explored the influence of ultrasound on crystallization of cephalexin monohydrate in terms of nucleation mechanism and crystal habit control.The results of metastable zone width and induction time measurement showed the presence of ultrasound irradiation can narrow the metastable zone and shorten induction time.Cavitation phenomena generated by ultrasound were used to qualitatively explain the mechanism of ultrasound promoting nucleation of cephalexin monohydrate.Furthermore,on the basis of classical nucleation theory and induction time data,a series of nucleation-related parameters (such as crystal-liquid interfacial tension,radius of the critical nucleus and etc.) were calculated and showed a decreasing trend under ultrasound irradiation.The diffusion coefficient of the studied system was also determined to increase by 72.73％ under ultrasound.The changes in these parameters have quantitatively confirmed the mechanism of ultrasound influence on the nucleation process.In further,the calculated surface entropy factor has confirmed that the growth of cephalexin monohydrate follows continuous growth mechanism under the research conditions of this work.Through the exploration of crystallization conditions,it is found that suitable ultrasonic treatment,seeding,supersaturation control and removal of fine crystals are conducive to improving the quality of cephalexin monohydrate product.Optimizing the crystalliza-tion process coupled continuous ultrasound irradiation with fine-crystal dissolution policy has achieved the controllable production of monodisperse cephalexin monohydrate crystal with good performance.     

Phenomena and Modeling of Hydrophobic Interaction Chromatography

Comprehension of the mechanisms of hydrophobic interaction chromatography is not as deep as for other chromatographic steps. This article shows the combination of modeling and experimental model parameter determination. Original mammalian cell culture is applied for validation instead of often-used test systems with for example, three pure proteins. This approach can have a huge benefit for process development and optimization of production processes under project conditions. To simulate the separation by hydrophobic interaction chromatography, a distributed plug flow model with inner pore diffusion is applied. The needed model parameters are determined by small scale experiments on a 1 ml column to reduce feed amount consumption and experimental procedure. Effects caused by system setup are optimized in relation to the volume. Gradient experiments are performed for the determination of isotherm parameters. The model parameters determined are experimentally validated at different set-ups of operation parameters as well as scaled up to 10 ml columns. The practicability of the proposed stepwise procedure of physico-chemical modeling in combination with laboratory scale experiments for the prediction of separation performance of original mammalian cell culture is proved. A model parameter determination directly with fermentation mixture is as well feasible.     

Robust identification and control of batch processes

An approach is proposed for the robust identification and control of batch and semibatch processes. The batch experiments used for model identification are designed by minimizing the magnitude of the parameter uncertainties, and the effect of these uncertainties on the product quality achievable by optimal control is used as a stopping criterion for the identification procedure. The optimal control approach incorporates a quantification of the impact of both parameter and control implementation uncertainties on the performance of the optimal control policy. The approach is applied to the nucleation and growth of crystals with multiple characteristic dimensions, where the nominal parameters used in the simulation study are quantified from experimental data.     

Simulation of batch crystallization

The closed mathematical model of a well-mixed batch crystallizer has been presented. This model takes into consideration crystals growth rate fluctuations producing an increased spread of crystal sizes. The numerical methods for solving partial integro-differential system of this model equations are proposed for the cases of when growth rate is expressible as product of supersaturation and size functions.Simultaneous population and mass balance equations have been calculated together with power law kinetics of nucleation and growth to determine crystal-size distribution functions (CSD), variation coefficients (CV), produced crystal sizes and numbers. The case of size-dependent crystal growth determined by sequential processes of diffusion and surface reaction is also investigated.The computer results are presented in the dimensionless form as functions on both diffusion and fluctuation Peclet numbers and dimensionless cooling rate. In particular, it has been established that the CV of weight CSD increases approximately twice due to fluctuations and becomes close to 40%; the CV also increases owing to the decrease of cooling rate and approaches 28%. Some formulae are suggested for predicting the kinetics of crystallization (or precipitation) and determining the kinetic parameters of crystals growth and nucleation.     

Parameterbestimmung bei linearen chemischen Prozessen

Determination of Parameters in Linear Chemical Processes . The authors describe a straightforward and extremely reliable method for determination of the physicochemical parameters occurring in mathematical models of chemical processes. It is based on the restrictive assumption that the system considered is linear and the number of parameters is small. These assumptions permit a detailed eigenvalue analysis of the system, permitting a complete insight into its behaviour. The eigenvalues λ_k and the factors a_k of the corresponding exponential functions are determined by curve fitting. These in turn are determined by system parameters and thus afford relations from which the latter can be calculated. Use of the proposed model requires the design of experiments which can be described by approximately linear models. This is indeed possible in many cases.     

Establishment of nucleation and growth model of silica nanostructured particles and comparison with experimental data

A mathematical model is developed for the calculation of the nucleation and growth process of silica nanostructured particles prepared by using the drop-by-drop method,and the calculation results of the proposed model is compared with the experimental value obtained from SAXS data.The model provides a non-ideal improvement in the supersaturation calculation and considers the impact of both mass transfer and surface reaction on the particle growth rate.The nucleation and growth rates are coupled ...     

Modelling particle size distributions and secondary particle formation in emulsion polymerisation

An extensive model is given for the particle size distribution (PSD), particle number, particle size and amount of secondary nucleation in emulsion polymerisations. This incorporates what are thought to be all of the complex competing processes: aqueous phase kinetics for all radical species arising from both initiator and from exit (desorption), radical balance inside the particles, particle formation by both micellar and homogeneous nucleation mechanisms, and coagulation (the rate of which is obtained using the Healy–Hogg extension of DLVO theory). The predictions of the model are compared to extensive experimental results on rates, time evolution of the particle size distribution, and relative amounts of secondary nucleation, for styrene initiated by persulfate with sodium dodecyl sulfate and with sodium dihexyl sulfosuccinate as surfactants. For this system values of almost all of the many parameters needed for the model are available from independent measurements, and thus no significant parameter adjustment is plausible. Accord with experiment is imperfect but quite acceptable, supporting the validity of the various mechanisms in the model. Effects such as the experimental variation of particle number with ionic strength, as well as calculated coagulation rate coefficients as functions of particle size, suggest that coagulation of precursor (i.e., newly-formed) particles is a significant effect, even above the cmc. The modelling also suggests why secondary nucleation occurs readily in systems stabilised with polymeric surfactant.     

Low‐temperature aging of baddeleyite‐based Ca‐TZP ceramics

The aging kinetics during low‐temperature aging of calcia‐stabilized tetragonal zirconia polycrystal (Ca‐TZP) ceramics prepared by high‐energy milling of natural zirconia mineral (baddeleyite) was studied by X‐ray diffraction under hydrothermal treatment conditions. Aging kinetics was investigated for ceramics with different contents of calcia. It was found that the kinetics may be well‐described within Johnson‐Mehl‐Avrami‐Kolmogorov model. Model parameters were determined by data fitting procedure. Change in exponential factor within Johnson‐Mehl‐Avrami‐Kolmogorov model with time is shown. Analytical model to describe aging kinetics is proposed. The transformation nucleation rate, initial diameter, and depth of the transformed areas and their growth rates are estimated. Degradation of hardness and fracture toughness is also reported for Ca‐TZP after low‐temperature aging for different contents of the stabilizer.     

MULTIPLICITY AND STABILITY ANALYSIS OF AGGLOMERATION CONTROLLED PRECIPITATION

The possibility of multiplicity in continuous isothermal MSMPR precipitators has been explored for agglomeration controlled conditions and general criteria, independent of nucleation kinetics, are developed for stability and multiplicity of the steady states. For the Volmer model of primary nucleation and the magma dependent power law model of secondary nucleation, parameter regions are determined in which multiple steady states exist, and their linear stability is analyzed. The analysis holds in general for all types of agglomeration kernel. For the Volmer nucleation kinetics three steady states exist in the region of multiplicity with the “middle” one always being unstable. The analysis for magma dependent power law model showed multiplicity regions having as many as four steady states, the number depending on magma and kinetic order. Unlike the case of molecular growth control, limit cycle behaviour is not possible, and the approach to the steady state is always asymptotic     

A new hydration kinetics model of composite cementitious materials,part 1: Hydration kinetic model of Portland cement

This work is the first part of an overall research project that aims to model the hydration kinetics of modern composite cementitious materials. The aim of this part is to build a hydration kinetic model to characterize the hydration behavior of cement at all ages. In this paper, the nucleation and growth of CSH and the diffusion of water are described by a modified BNG model and a modified Jander's model. The kinetic parameters are obtained by simulative fitting of the model to the experimental data. The linear functions between the nucleation and growth rates and the W/C ratios are given in this paper. The apparent activation energy of the nucleation rate constant, growth rate constant, and generalized diffusion constant are approximately 36.0, 37.5, and 42.0 kJ/mol, respectively. Finally, the phase compositions of hardened cement paste are calculated according to the kinetic model and the reaction formula of cement.     

MULTIPLICITY AND STABILITY ANALYSIS OF AGGLOMERATION CONTROLLED PRECIPITATION

The possibility of multiplicity in continuous isothermal MSMPR precipitators has been explored for agglomeration controlled conditions and general criteria, independent of nucleation kinetics, are developed for stability and multiplicity of the steady states. For the Volmer model of primary nucleation and the magma dependent power law model of secondary nucleation, parameter regions are determined in which multiple steady states exist, and their linear stability is analyzed. The analysis holds in general for all types of agglomeration kernel. For the Volmer nucleation kinetics three steady states exist in the region of multiplicity with the “middle” one always being unstable. The analysis for magma dependent power law model showed multiplicity regions having as many as four steady states, the number depending on magma and kinetic order. Unlike the case of molecular growth control, limit cycle behaviour is not possible, and the approach to the steady state is always asymptotic     

逆向法测定酮洛芬对映体在Chiralpak AD柱上的吸附等温线

模拟移动床（SMB）色谱分离与纯化的操作过程复杂,对其进行设计与优化需要使用数值模拟方法,准确测定竞争型吸附等温线具有重要意义。采用逆向法确定了25℃下酮洛芬对映体在直链淀粉手性固定相（Chiralpak AD）上的竞争吸附等温线,先用高效液相色谱测得酮洛芬对映体在Chiralpak AD 柱上的过载流出曲线,再通过拟合实验测得的流出曲线确定吸附等温线模型及其参数。研究中采用平衡扩散模型描述酮洛芬对映体在色谱柱上流出的瞬态过程。参数拟合过程中,首先用非支配基因算法（NSGA-Ⅱ）在较广的参数空间内搜索吸附等温线模型参数,再以所得结果作为初值,使用Levenberg-Marquardt 算法（LMA）对参数进一步优化。比较了4种不同竞争吸附等温线模型对实验测得的流出曲线的拟合结果,其中五参数的Bi-Langmuir 模型拟合程度最好。测量了不同进料浓度和进料量条件下的流出曲线,并通过与模型预测结果的对照验证了所确定吸附等温线模型和参数。     

A new hydration kinetics model of composite cementitious materials,Part 2: Physical effect of SCMs

This paper is the second part of an overall research project that aims to model the hydration kinetics of composite cementitious materials. The new hydration kinetic model of Portland cement was constructed in the first part of this research project. The aim of this part is to characterize the physical effect of SCMs by modifying some kinetic parameters of the hydration kinetic model of cement. In this paper, the filler effect of SCMs is attributed to the “dilution effect”, “nucleation effect” and “accelerated dissolution effect”. The dilution effect is considered by introducing the actual water/cement ratio into the kinetic model. The nucleation surface area, nucleation and growth rates are modified to account for the nucleation effect and accelerated dissolution effect of fillers. The simulative fit results show that the extra contribution of SCMs due to their filler effect on hydration of cement at early ages has an upper limit: at most 20% extra nucleation surface area, 30% extra nucleation ratio and 40% extra growth ratio of calcium silicate hydrate (CSH). The new modified kinetic model and the value-taking method of the newly introduced parameters are verified by simulative fitting to the kinetic data from reference. The apparent activation energies of the nucleation rate, growth rate, and diffusion rate are approximately 35 kJ/mol, 36 kJ/mol and 38.5 kJ/mol, which are slightly smaller than those of the pure Portland cement reported in the first part of this research project.