Modeling Nucleation, Growth, and Ostwald Ripening in Crystallization Processes: A Comparison between Population Balance and Kinetic Rate Equation

Vetter, Thomas; Iggland, Martin; Ochsenbein, David R.; Hänseler, Flurin; Mazzotti, Marco

doi:10.1021/cg4010714

Cited by 118 publications

(118 citation statements)

References 53 publications

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“…23 A clean surface structure can easily undergo Ostwald ripening because of the lack of protecting ligand on the surface. 30 The transition between ripening and growth is caused by the relationship of particle size and particle size distribution (PSD), as well as the time dimension. 24 The aggregation of many small spheres can construct a big sphere, however, if the stabilities of the spheres in big sphere are different, after ripening, only the most stable spheres will remain.…”

Section: Ostwald Ripeningmentioning

confidence: 99%

Nanostructure formation via post growth of particles

Wang

2015

CrystEngComm

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Post growth of particles will lead to new nanostructure formation, and blur the boundaries of crystal growth and molecular chemistry as well. The driving force of post growth usually stems from the inherent stabilities of the nanoparticles (NPs) and the environmental changes, which results in the transformation of the pristine nanostructures. One type of post growth driven by thermodynamic stability is Ostwald ripening, which usually leads to the elimination of small particles, and can be utilized to prepare hollow structures. By sophisticatedly controlling the reaction conditions, the NPs may undergo oriented attachment to form nanostructures with more complexity. This process is different from the random aggregation of nanoparticles; the final morphologies can be ingeniously controlled, and the kinetics resemble polymerization in some cases. If the chemical bonding during the oriented attachment process is replaced by non-covalent bonding, self-assembly of the NPs is achieved. Self-assembly of NPs further extends the diversity of nanostructures, as well as the understanding of crystallization. Post growth of particles is also a feasible strategy to fabricate heterostructures. The wetting behaviour sheds light on the final morphologies of the heterostructures. Meanwhile, seed mediated growth enables an alternative method to control pre-formed NPs. Another heterostructure of atomically-thin layered sheets connected via van der Waals forces also extends the potential of nanomaterials. The driving forces of the post growth of particles are divergent, and the applications are various. It can be utilized to prepare homogeneous and heterogeneous structures. CrystEngCommThis journal is

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Section: Ostwald Ripeningmentioning

confidence: 99%

Nanostructure formation via post growth of particles

Wang

2015

CrystEngComm

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“…47,48 As mentioned above, the feed flow (transporting out of the crystallizer, heating up to the unsaturated temperature then feed to membrane module) decreases the crystal density in the crystallizer; meanwhile, the retentate steam provides the nuclei generated in the membrane interface, which performed as the crystal seed resource of the crystallization process besides the HON nucleation in the crystallizer. These two factors are different from the conventional batch crystallization.…”

mentioning

confidence: 99%

Membrane assisted cooling crystallization: Process model, nucleation, metastable zone, and crystal size distribution

Jiang

Xiao

et al. 2015

AIChE Journal

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The membrane assisted cooling crystallization was proposed and investigated by the simulation and experiments. The developed process model concerned the supersaturation evolution on the membrane interface, the combined nucleation rate in the crystallizer. The impact of different membrane on reducing the nucleation barrier was investigated by introducing the metastable zone width theory. The influence of membrane distillation conditions on the crystal nucleation and growth kinetic was uncovered based on the simulation and experiments results. The experimental results indicated that membrane assisted cooling mode with optimized profiles did improve the crystal size distribution and crystal habit comparing with conventional cooling mode. Terminal coefficient of variation decreased from 55.4 to 33.9 under similar mean crystal growth rate, 2.27 3 10 27 m s 21 (conventional cooling) and 1.98 3 10 27 m s 21 (membrane assisted cooling). Finally, the brief summary on the advantages and key issues of this propose membrane assisted crystallization operation were concluded. V C 2015 American Institute of Chemical Engineers AIChE J, 62: [829][830][831][832][833][834][835][836][837][838][839][840][841] 2016

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“…[31,32] However, in the case of Ostwald ripening, [33] particles with intermediate sizes begin to grow and then dissolve, leading to non-monotonous characteristic curves. [34] In another work, PBM was discussed with a non-monotonous growth process (termed a reaction process) and nucleation process (termed an activation process) in biochemical engineering [35] when the internal variable (concentration of protein) showed non-monotonous behaviour versus time. However, the characteristic curves followed only the translational phenomenon (i.e.…”

Section: Introductionmentioning

confidence: 99%

Population balances in case of crossing characteristic curves: Application to T‐cells immune response

Ali

Elkamel

Gruy³

et al. 2016

Can J Chem Eng

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The progression of a cell population where each individual is characterized by the value of an internal variable varying with time (e.g. size, mass, and protein concentration) is typically modelled by a population balance equation, a first-order linear hyperbolic partial differential equation that is shared by all T-cells is involved. At these crossing points, the linear advection equation is not possible by using the hyperbolic conservation laws in a classical way. Therefore, a new transport method is introduced in this article that is able to find the population density function for such processes. A multi-scale mathematical modelling framework is employed. At the first scale, two processes, which are termed as the activation and reaction terms (assimilated as nucleation and growth in chemical processes), are studied as independent processes. At the second scale, the dynamic variation in the population density of activated T-cells is investigated in the presence of activation and reaction terms. The newly-developed transport method is shown to work in the case of crossing and to provide a smooth solution at the crossing points in contrast to the classical PDF techniques.2

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Modeling Nucleation, Growth, and Ostwald Ripening in Crystallization Processes: A Comparison between Population Balance and Kinetic Rate Equation

Cited by 118 publications

References 53 publications

Nanostructure formation via post growth of particles

Nanostructure formation via post growth of particles

Membrane assisted cooling crystallization: Process model, nucleation, metastable zone, and crystal size distribution

Population balances in case of crossing characteristic curves: Application to T‐cells immune response

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