Time evolution of the PSD in crystallization operations: An analytical solution based on Ornstein‐Uhlenbeck process

Cogoni, Giuseppe; Grosso, Massimiliano; Baratti, Roberto; Romagnoli, José A.

doi:10.1002/aic.13760

Cited by 18 publications

(35 citation statements)

References 23 publications

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“…All distributions show positive skewness, in agreement with the log-normal distribution calculated from first principles by Cogoni and coworkers. 74,75 The MF/ CA ferrofluid has particles of smaller average size than the MF/OA ferrofluid due to larger populations of small diameter nanoparticles (1-4 nm). Fig.…”

Section: Particle Morphology and Sizes: Transmission Electron Microscopymentioning

confidence: 99%

High concentration aqueous magnetic fluids: structure, colloidal stability, magnetic and flow properties

et al. 2018

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This paper is an in-depth analysis devoted to two basic types of water based magnetic fluids (MFs), containing magnetite nanoparticles with electrostatic and with electro-steric stabilization, both obtained by chemical coprecipitation synthesis under atmospheric conditions. The two sets of magnetic fluid samples, one with citric acid (MF/CA) and the other with oleic acid (MF/OA) coated magnetic nanoparticles, respectively, achieved saturation magnetization values of 78.20 kA m-1 for the electrostatically and 48.73 kA m-1 for the electro-sterically stabilized aqueous ferrofluids which are among the highest reported to date. A comprehensive comparative analysis combining electron microscopy, X-ray photoelectron spectroscopy, attenuated total reflectance Fourier transform infrared spectroscopy, vibrating sample magnetometry, small-angle X-ray and neutron scattering, dynamic light scattering and magneto-rheometry revealed similarities and essential differences on the microscopic and macroscopic level between the two kinds of water-based ferrofluids. While the saturation magnetization values are quite different, the hydrodynamic volume fractions of the highest concentration MF/CA and MF/OA samples are practically the same, due to the significantly different thicknesses of the particles' coating layers. The results of volume fraction dependent structure analyses over a large concentration range by small-angle X-ray and neutron scattering, correlated with magneto-rheological investigations for the electrostatically stabilized MFs, demonstrate formation of short chains of magnetic nanoparticles which are relatively stable against coagulation with increasing concentration, while for MFs with electro-steric stabilization, magnetic field and shear rate dependent loosely bound structures are observed. These particle structures in MF/OA samples manifest themselves already at low volume fraction values, which can be attributed mainly to magnetic interactions of larger size particles, besides non-magnetic interactions mediated by excess surfactant.

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Section: Particle Morphology and Sizes: Transmission Electron Microscopymentioning

confidence: 99%

High concentration aqueous magnetic fluids: structure, colloidal stability, magnetic and flow properties

et al. 2018

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“…The magnetic diameter distribution of the nanoparticles was obtained by means of magnetogranulometry, i.e., the nonlinear regression of the magnetization curve with Ivanov and coworkers second order modified mean field theory for highly concentrated polydisperse samples [30]. The log-normal distribution was assumed for nanoparticles magnetic diameter [31],…”

Section: Characterizationsmentioning

confidence: 99%

Influence of Experimental Parameters of a Continuous Flow Process on the Properties of Very Small Iron Oxide Nanoparticles (VSION) Designed for T1-Weighted Magnetic Resonance Imaging (MRI)

et al. 2020

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This study reports the development of a continuous flow process enabling the synthesis of very small iron oxide nanoparticles (VSION) intended for T 1 -weighted magnetic resonance imaging (MRI). The influence of parameters, such as the concentration/nature of surfactants, temperature, pressure and the residence time on the thermal decomposition of iron(III) acetylacetonate in organic media was evaluated. As observed by transmission electron microscopy (TEM), the diameter of the resulting nanoparticle remains constant when modifying the residence time. However, significant differences were observed in the magnetic and relaxometric studies. This continuous flow experimental setup allowed the production of VSION with high flow rates (up to 2 mL·min −1 ), demonstrating the efficacy of such process compared to conventional batch procedure for the scale-up production of VSION.

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“…Regarding the deterministic growth term

h (y, t; θ)

, it was initially assumed to follow a logistic equation (LG), that is:

h (y, t; θ) = r y (1 - \frac{y}{K})

where

r

is the crystal growth rate constant and

K

is the equilibrium logarithmic mean size. Later, to obtain an analytical solution of the corresponding FPE, the deterministic crystal growth was reformulated through the use of a Gompertz equation (GM):

h (y, t; θ) = r' (1 - \frac{y}{K^{'}})

where

r'

is the crystal growth rate constant and

K'

is the equilibrium mean size.…”

Section: Background: Stochastic Model For Csd In Logarithmic Scalementioning

confidence: 99%

“…All previous results were obtained by applying a variable transformation to obtain a constant diffusion term in the FPE, which made easier its numerical integration. Using a linear crystal growth term this type of representation can be further simplified to allow the CSD over time in antisolvent crystallization operations to be solved analytically …”

Section: Introductionmentioning

confidence: 99%

A generalized stochastic modelling approach for crystal size distribution in antisolvent crystallization operations

2016

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A generalized formulation for the development of stochastic models to predict the crystal size distribution (CSD) in antisolvent crystallization processes is proposed. Exploiting the result of the noise induced dynamic in stochastic processes, new results are provided to represent the CSD as function of the operational parameters. The generalized formulation enables the full description of the CSD using nonlinear drift term in conjunction with multiplicative noise, i.e., state dependent diffusion. For the first time a deterministic nonlinear differential equation to represent the mean and most probable size (mode) time evolution as function of the model parameters is provided. Furthermore, the analytical solution of the asymptotic probability distribution of the CSD can also be obtained. Finally, a global model formulation is finally presented by defining relationships between the model parameters and the operating conditions. Experimental results and validations are provided using the ternary system of NaCl, water, and ethanol

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Time evolution of the PSD in crystallization operations: An analytical solution based on Ornstein‐Uhlenbeck process

Cited by 18 publications

References 23 publications

High concentration aqueous magnetic fluids: structure, colloidal stability, magnetic and flow properties

High concentration aqueous magnetic fluids: structure, colloidal stability, magnetic and flow properties

Influence of Experimental Parameters of a Continuous Flow Process on the Properties of Very Small Iron Oxide Nanoparticles (VSION) Designed for T1-Weighted Magnetic Resonance Imaging (MRI)

A generalized stochastic modelling approach for crystal size distribution in antisolvent crystallization operations

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