Particle Growth Model Research Articles

Pattern Selection in Three-Precipitate Liesegang Systems.

Liesegang patterns present a display of parallel stripes of precipitate that arise from the interdiffusion of coprecipitate ions in a gel medium. The bands observed in rocks are typical analogies of this phenomenon, and their composition is not restricted to the banded deposition of a single mineral. We here extend the study to a three-precipitate system, wherein Co2+, Ni2+, and Cd2+ cations are precipitated by the same anion (OH- from NH4OH) to form Co(OH)2, Ni(OH)2, and Cd(OH)2, respectively. The resulting pattern exhibits an alternation of compact mixed Co(OH)2 and Ni(OH)2 bands with granules of pure Cd(OH)2 between them. The obtained pattern confirms the generic type of (A + B)/C/(A + B)/C/(A + B)/C alternation conjectured analytically using the competitive particle growth (CPG) model and stability analysis.

Silica particle size and polydispersity control from fundamental practical aspects of the Stöber method

Silica-based nanoparticles have been continuously investigated for their physical and chemical properties, which have made them adaptable for a wide range of scientific purposes, from adsorption in an aqueous medium to target-specific drug delivery in biological fluids. The achievement of these properties is, in general, possible by controlling the synthesis of the nanomaterial, and the Stöber method is one of the most commonly employed approaches for silica-based nanoparticles. In this study, experiments were carried out to investigate several parameters of the Stöber method for controlling the diameter and size dispersion of silica nanoparticles. The results of these experiments were supported by and contrasted with the theoretical aspects of silica particle nucleation and growth models. In this scenery, practical aspects of the Stöber Method such as the effects of variations in catalyst concentration, colloidal stability and drying approach on particle size and polydispersity were examined in detail for providing an organized basis of experimental and theoretical data about it for who aims at work with silica nanoparticle synthesis through the Stöber Method.

Insufficient Condensable Organic Vapors Lead to Slow Growth of New Particles in an Urban Environment.

Atmospheric new particle formation significantly affects global climate and air quality after newly formed particles grow above ∼50 nm. In polluted urban atmospheres with 1-3 orders of magnitude higher new particle formation rates than those in clean atmospheres, particle growth rates are comparable or even lower for reasons that were previously unclear. Here, we address the slow growth in urban Beijing with advanced measurements of the size-resolved molecular composition of nanoparticles using the thermal desorption chemical ionization mass spectrometer and the gas precursors using the nitrate CI-APi-ToF. A particle growth model combining condensational growth and particle-phase acid-base chemistry was developed to explore the growth mechanisms. The composition of 8-40 nm particles during new particle formation events in urban Beijing is dominated by organics (∼80%) and sulfate (∼13%), and the remainder is from base compounds, nitrate, and chloride. With the increase in particle sizes, the fraction of sulfate decreases, while that of the slow-desorbed organics, organic acids, and nitrate increases. The simulated size-resolved composition and growth rates are consistent with the measured results in most cases, and they both indicate that the condensational growth of organic vapors and H2SO4 is the major growth pathway and the particle-phase acid-base reactions play a minor role. In comparison to the high concentrations of gaseous sulfuric acid and amines that cause high formation rates, the concentration of condensable organic vapors is comparably lower under the high NOx levels, while those of the relatively high-volatility nitrogen-containing oxidation products are higher. The insufficient condensable organic vapors lead to slow growth, which further causes low survival of the newly formed particles in urban environments. Thus, the low growth rates, to some extent, counteract the impact of the high formation rates on air quality and global climate in urban environments.

Immersed Lagrangian point method for predicting particle growth in Taylor–Couette flow

Direct numerical simulation of particle growth in fluid flow is still challenging, because of the limited information available in experiments. To simulate particle growth in fluid flow, fluid-particle interactions must be considered along with particle growth models in an integrated model of numerical methods. In recent times, immersed-type methods have succeeded in simulating multiple solid objects in fluid flow. Furthermore, various interaction forces on particles can be included in a simulation model. In this study, an immersed Lagrangian point method was proposed to simulate a particle growth model in fluid flow, specifically, Taylor–Couette flow. The agglomeration and deagglomeration processes of particles were described in the simulation model. The simulation model was compared against actual experiments of particle growth in fluid flow and tested using various sets of particle growth parameters. Finally, the potential and future perspectives of the suggested model were fully discussed.

Single catalyst particle growth modeling in thermocatalytic decomposition of methane

ThermoCatalytic Decomposition of methane (TCD) is studied as a method to convert natural gas into hydrogen and functional carbon. In these processes the carbon typically formed on top of a catalyst phase leading to particle growth. Therefore, the development of a particle growth model is necessary to understand the limitations of thermocatalytic decomposition of methane and to assess optimal parameters and process conditions. In this paper, a particle growth model is presented to describe the growth of functional carbon on the catalyst particle. This coupled model requires kinetic equations and information on deactivation rates which have been studied from literature. The morphology of the particle changes due to carbon formation, which leads to eventual deactivation. Therefore, these kinetic expressions are coupled to a particle growth model based on the analogy with the growth of particles in polyolefin production. To combine the effects of particle growth, kinetics, and internal heat and mass transfer, the Multi-Grain Model (MGM) was used. Results confirm that with the currently available catalysts the carbon yield is not affected by heat and mass transfer limitations, however, with the availability of more active catalysts these limitations will become important. Temperature, however, has a significant role in that it regulates the kinetic rate and thus growth rate, which in turn influences the catalyst deactivation. The optimum temperature for the production of nano-carbon, within a reasonable process time, therefore sensitively depends on the choice of catalyst. • Development of a particle growth model for Thermocatalytic decomposition of methane. • Combined mass/heat transfer, kinetics and particle growth using a multi-grain model. • Assessment of transfer limitations and temperature using available kinetic models.

Hybrid dust-tracking method for modeling Io's Tvashtar volcanic plume

A novel computational technique was used to simulate eruptions from Io's Tvashtar Catena region to better understand the origin of the visible structure of the gas/particulate plumes observed by the New Horizons spacecraft in its 2007 flyby of the Jovian system. The direct simulation Monte Carlo (DSMC) method was used to produce number density, temperature, and velocity fields for SO2 gas erupting from rectangular vents of aspect ratio 1:1, 3:1, 10:1, and 15:1. Simulations of eruptions of visible particles entrained in the gas were subsequently conducted in a separate MATLAB simulation by injecting particles at the vent and propagating them through the plume by interpolating the gas velocity fields. The temperature and number density fields were used to implement a particle growth model in which the grains grow/shrink via condensation/sublimation. With these simulations, we investigated the plume's lack of a prominent spout, how particulate structures in the vent are transformed as they move through the plume and how this could produce filamentary structure, and the origin of the traveling canopy wave observed in some of the images. Simulations showed that the presence of an observable spout in a given plume image can depend on several factors including vent aspect ratio, observer vantage point, particulate size, and eruption frequency. Several possible explanations for the lack of an observable spout in the Tvashtar images were explored, and the most plausible is that the particles are pulsed from the vent infrequently rather than being emitted in a continuous spray. The transformation of particulate structures in the vent as they travel through the plume depends primarily on vent aspect ratio and the structure's region of origin in the vent. Simulations showed that the continuous emission of particles from concentrated regions in the vent can produce filamentary structures similar to those seen in Tvashtar images, but the appearance of such structures is highly dependent on the observer's vantage point. The traveling canopy wave was replicated in simulations, to varying degrees, with two different mass flux functions: a traveling wave in the vent and the pulsing of particles out of thin cracks parallel to the vent's long axis. With a pulsing frequency of 10–15 min, the latter mass flux function was able to replicate, in a broad sense, much of the plume's interesting structure including the filaments, the traveling canopy wave, and the lack of an observable spout.

Continuous and large-scale fabrication of lecithin stabilized nanoparticles with predictable size and stability using flash nano-precipitation

Continuous and large-scale production of phospholipids stabilized emulsions and nanoparticles with controllable particle size and stability has always been a challenge. Here, we use flash nano-precipitation (FNP) to produce lecithin stabilized α-tocopheryl acetate (Vitamin E-acetate) particles at a production rate much higher than conventional batch mixing and thin-film hydration. The FNP produces particles with more homogeneous lecithin coverage comparing to conventional slow mixing. As determined by dynamic/electrophoretic light scattering, transmission electron microscope (TEM) and Quartz Crystal Microbalance with Dissipation (QCM-D), particles with low percent core are covered by thick multiple lecithin layers and aggregate easily with the coalescence of lecithin shell; particles with medium percent core content are covered with a thin layer of lecithin, which provides a high enough ζ-potential to stabilize the particle; for particles with percent core higher than 95%, the large spacing between lecithin molecules result in Ostwald ripening and aggregation. With a given composition, the particle size and stability could both be precisely predicted using the Smoluchowski's diffusion limited particle growth model and the Derjaguin-Landau, Verwey-Overbeek (DLVO) theory. This work demonstrates that the compositions affect the adsorption of phospholipid molecules at the particle surface, which further control particle size and stability.

Method for determining particle growth dynamics in a two-component alloy

The paper deals with issue of particle growth in a two-component alloy. The particle is formed from the products of chemical reactions that occur at the phase boundary. Generalized mathematical model of particle growth includes diffusion equations, mass transfer equations in boundary layer, and equation characterizing change in radius of the growing particle. The paper proposes an approach that allows reduction of the initial issue to system of PDEs and ODE that describes the state of growing particle. This approach provides basis for developing numerical method for calculating radius of growing particle as a function of time, based on the obtained equations. The computational scheme involves the finite-difference analogues of equations with an additional regularizing functional that ensure stability of the method with respect to accumulated computational error. In order to verify reliability of the proposed computational scheme and to obtain experimental error estimates of numerical solutions, computational experiments were carried out. In the experiments, radius of growing particle is determined with respect to the time via the proposed method. Also, comparative analysis of the calculated radius with test values was carried out and experimental estimates of deviations of the calculated radius from the test functions were obtained. The results of the experiment presented in the work indicate sufficient accuracy of the developed numerical method.

Method for Determining Particle Growth Dynamics in a Two-Component Alloy

The paper deals with the issue of particle growth in a two-component alloy. The particle is formed from chemical reaction products that occur at the phase boundary. A generalized mathematical model of particle growth includes diffusion equations, mass transfer equations in the boundary layer, and equations characterizing a change in the growing particle radius. The paper proposes an approach that reduces issues to the system of PDEs and ODE that describes the state of growing particle. This approach provides a basis for developing a numerical method for calculating the growing particle radius as a function of time, based on the obtained equations. The computational scheme involves the finite-difference analogues of equations with an additional regularizing functional that ensure method stability with respect to accumulated computational error. In order to verify reliability of the proposed computational scheme and to obtain experimental error estimates of numerical solutions, computational experiments were carried out. In the experiments, the growing particle radius is determined with respect to the time via the proposed method. Also, comparative analysis of the calculated radius with test values was carried out and experimental estimates of deviations of the calculated radius from the test functions were obtained. The experiment results presented in the work indicate sufficient accuracy of the developed numerical method.

Synthesis of Poly(N-vinylcaprolactam)-Based Microgels by Precipitation Polymerization: Pseudo-Bulk Model for Particle Growth and Size Distribution.

Particle size distribution and in particular the mean particle size are key properties of microgels, which are determined by synthesis conditions. To describe particle growth and particle size distribution over the progress of synthesis of poly(N-vinylcaprolactam)-based microgels, a pseudo-bulk model for precipitation copolymerization with cross-linking is formulated. The model is fitted and compared to experimental data from reaction calorimetry and dynamic light scattering, showing good agreement with polymerization progress, final particle size, and narrow particle size distribution. Predictions of particle growth and reaction progress for different experimental setups are compared to the corresponding experimental data, demonstrating the predictive capability and limitations of the model. The comparison to reaction calorimetry measurements shows the strength in the prediction of the overall polymerization progress. The results for the prediction of the particle radii reveal significant deviations and highlight the demand for further investigation, including additional data.

Model for UV induced growth of semiconductor nanoparticles in polymer films

A theoretical macrokinetic model for photoinduced growth of semiconductor nanoparticles was developed with allowance for specific features of their optical properties in the near ultraviolet region. In [A. A. Smirnov et al., Optical Materials Express, 8 (2018) 1603–1612] the Polymethylmethacrylate (PMMA) film containing good soluble CdS precursors [Cd(N(SCNEt2)2)2] (TEDBCd) was irradiated by an ultraviolet light emitting diode (UV LED) with a central wavelength of 365 nm at different fixed temperatures and at different fixed intensities. The authors in situ followed the evolution of absorbance at a wavelength of 405 nm where the film is initially transparent. The corresponding photon energy is larger than the bandgap of the bulk CdS crystals. The increase in absorbance of the irradiated film at this wavelength was associated with the CdS nanoparticle growth. The main result is that at a given temperature, the effect of UV radiation on the sample is determined by the exposure (dose) rather than the light intensity and the irradiation time separately. The presented paper aims at constructing a model of the semiconductor particle growth initiated by the light-induced destruction of good soluble precursor molecules and fitting this model to the experimental data, making it possible to estimate the most important parameters of the process. The photoinduced formation of CdS nanoparticles is a complicated process that includes photo-mediated destruction of the precursor molecules followed by diffusion-assisted growth of nanoclusters. The feature of the growing semiconductor nanoparticles is that rather small particles do not absorb radiation at a particular wavelength because of the quantum confinement. The theory also takes into account the finite thickness of the sample and the nonlinear effects of radiation shielding.

A spatio-temporal point process model for particle growth

AbstractA spatio-temporal model of particle or star growth is defined, whereby new unit masses arrive sequentially in discrete time. These unit masses are referred to as candidate stars, which tend to arrive in mass-dense regions and then either form a new star or are absorbed by some neighbouring star of high mass. We analyse the system as time increases, and derive the asymptotic growth rate of the number of stars as well as the size of a randomly chosen star. We also prove that the size-biased mass distribution converges to a Poisson–Dirichlet distribution. This is achieved by embedding our model into a continuous-time Markov process, so that new stars arrive according to a marked Poisson process, with locations as marks, whereas existing stars grow as independent Yule processes. Our approach can be interpreted as a Hoppe-type urn scheme with a spatial structure. We discuss its relevance for and connection to models of population genetics, particle aggregation, image segmentation, epidemic spread, and random graphs with preferential attachment.

Numerical simulation of particle growth process in a polysilicon fluidized bed reactor

An Eulerian–Eulerian model coupled with a population balance model (PBM) is adopted to investigate the growth process of polysilicon particles in a polysilicon fluidized bed reactor. A novel particle growth model, considering the effect of interphase velocity difference, is proposed and incorporated into PBM. The interphase mass transfer rate and particle growth rate are obtained based on the modified PBM. The effects of operating velocity and silane mole fraction on the particle growth rate and deposition efficiency are also analyzed. The results show that silicon fines scavenging occurs in the solid phase, especially in central and near-wall regions. Moreover, the increases of operating velocity and silane mole fraction lead to the decrease in the deposition efficiency.

Microstructural Features of Ternary Powder Compacts

In this study the microstructure features of ternary powder compacts of different size ratios and various volume fractions are investigated. Particle compacts are generated by particle growth model using a discrete element method approach. The particles of three different sizes are placed randomly without overlap in a 3D box at given volume fractions. Then, the particle sizes increase to reach the desired particle size. The microstructural properties of powder compacts are analysed using a radical Voronoi tessellation. The obtained results confirm that microstructural characteristics of powder compacts are influenced by size ratios and volume fractions of large, medium and small components of the ternary mixture.

A Telescoping View of Solute Architectures in a Complex Fluid System.

Short- and long-range correlations between solutes in solvents can influence the macroscopic chemistry and physical properties of solutions in ways that are not fully understood. The class of liquids known as complex (structured) fluids—containing multiscale aggregates resulting from weak self-assembly—are especially important in energy-relevant systems employed for a variety of chemical- and biological-based purification, separation, and catalytic processes. In these, solute (mass) transfer across liquid–liquid (water, oil) phase boundaries is the core function. Oftentimes the operational success of phase transfer chemistry is dependent upon the bulk fluid structures for which a common functional motif and an archetype aggregate is the micelle. In particular, there is an emerging consensus that mass transfer and bulk organic phase behaviors—notably the critical phenomenon of phase splitting—are impacted by the effects of micellar-like aggregates in water-in-oil microemulsions. In this study, we elucidate the microscopic structures and mesoscopic architectures of metal-, water-, and acid-loaded organic phases using a combination of X-ray and neutron experimentation as well as density functional theory and molecular dynamics simulations. The key conclusion is that the transfer of metal ions between an aqueous phase and an organic one involves the formation of small mononuclear clusters typical of metal–ligand coordination chemistry, at one extreme, in the organic phase, and their aggregation to multinuclear primary clusters that self-assemble to form even larger superclusters typical of supramolecular chemistry, at the other. Our metrical results add an orthogonal perspective to the energetics-based view of phase splitting in chemical separations known as the micellar model—founded upon the interpretation of small-angle neutron scattering data—with respect to a more general phase-space (gas–liquid) model of soft matter self-assembly and particle growth. The structure hierarchy observed in the aggregation of our quinary (zirconium nitrate–nitric acid–water–tri-n-butyl phosphate–n-octane) system is relevant to understanding solution phase transitions, in general, and the function of engineered fluids with metalloamphiphiles, in particular, for mass transfer applications, such as demixing in separation and synthesis in catalysis science.

Evaluation of ECMWF-IFS (version 41R1) operational model forecasts of aerosol transport by using ceilometer network measurements

Abstract. In this paper, we present a comparison of model simulations of aerosol profiles with measurements of the ceilometer network operated by the German Weather Service (DWD) over 1 year from September 2015 to August 2016. The aerosol forecasts are produced by the Copernicus Atmosphere Monitoring Service (CAMS) using the aerosol module developed within the Global and regional Earth-system Monitoring using Satellite and in-situ data (GEMS) and Monitoring Atmospheric Composition and Climate (MACC) projects and coupled into the European Centre for Medium-Range Weather Forecasts Integrated Forecasting System (ECMWF-IFS). As the model output provides mass mixing ratios of different types of aerosol, whereas the ceilometers do not, it is necessary to determine a common physical quantity for the comparison. We have chosen the attenuated backscatter β∗ for this purpose. The β∗ profiles are calculated from the mass mixing ratios of the model output assuming the inherent aerosol microphysical properties. Comparison of the attenuated backscatter averaged between an altitude of 0.2 km (typical overlap range of ceilometers) and 1 km in general shows similar annual average values. However, the standard deviation of the difference between model and observation is larger than the average in 8 out of 12 sites. To investigate possible reasons for the differences, we have examined the role of the hygroscopic growth of particles and the particle shape. Our results show that using a more recent particle growth model would result in a ∼22 % reduction of particle backscatter for sea salt aerosols, corresponding to a 10 % reduction of the total backscatter signal on average. Accounting for nonspherical dust particles in the model would reduce attenuated backscatter of dust particles by ∼30 %. As the concentration of dust aerosol is in general very low in Germany, a significant effect on the total backscatter signal is restricted to dust episodes. In summary, consideration of both effects tends to improve the agreement between model and observations but without leading to a perfect consistency. In addition, a strong Saharan dust event was investigated to study the agreement of the spatiotemporal distribution of particles. It was found that the arrival time of the dust layer and its vertical extent very well agree between model and ceilometer measurements for several stations. This underlines the potential of a network of ceilometers to validate the dispersion of aerosol layers.

Variational iteration method and projection method solution of the spatially distributed population balance equation

In this work, two major hydrodynamic parameters, the holdup of the dispersed phase and the Sauter diameter, are considered. This is done for describing the hydrodynamics of interacting liquid–liquid dispersions using different particle breakage, coalescence and growth models in a particle population balance model. Based on the semi-analytical solution method of the population balance, namely, the variational iteration method (VIM), different process cases have been performed, and it is possible to find the exact solution or a closed approximate solution of a problem. For the simultaneous growth and coalescence terms comparisons between the present method and projection method which include discontinuous Galerkin and collocation techniques are made, respectively. The VIM technique overcomes the difficulties of discretization of the variables, introduces an efficient algorithm that improves the standard discretization method and is able to handle quite successful these process of population balance equations.The results are encouraging and the new method has proven to be suitable to predict holdup and Sauter diameter profiles.

Character of crystallization particle in bitten transfer pump

In order to understand the flow pattern of salt-out particles in a bittern transfer pump, the population balance model (PBM) coupled with mixture two-phase was applied to calculate the particle flow. User-defined particle growth and nucleation models were used in this study to consider the actual dynamic behavior of the crystallization particle, such as particle growth, nucleation, aggregation and breakage. The result shows that the average particle size is smaller and more evenly distributed among area of the impeller inlet. The size of crystal particles is different at different regions in the impeller passages with the characteristics of small crystal particles near suction side and large crystal particles near pressure side. In addition, the distribution of average particle size near pressure and suction side has an upward trend from inlet to outlet. The distribution of crystal particles on the blade near the tongue is different from other blades whether it is in the pressure surface or suction surface.

Nucleation and growth of Y2O3 nanoparticles in a RF-ICTP reactor: a discrete sectional study based on CFD simulation supported with experiments

Synthesis of yttria (Y2O3) nanoparticles in an atmospheric pressure radiofrequency inductively coupled thermal plasma (RF-ICTP) reactor has been investigated using the discrete-sectional (DS) model of particle nucleation and growth with argon as the plasma gas. Thermal and fluid dynamic information necessary for the investigation have been extracted through rigorous computational fluid dynamic (CFD) study of the system with coupled electromagnetic equations under the extended field approach. The theoretical framework has been benchmarked against published data first, and then applied to investigate the nucleation and growth process of yttrium oxide nanoparticles in the plasma reactor using the discrete-sectional (DS) model. While a variety of nucleation and growth mechanisms are suggested in literature, the study finds that the theory of homogeneous nucleation fits well with the features observed experimentally. Significant influences of the feed rate and quench rate on the distribution of particles sizes are observed. Theoretically obtained size distribution of the particles agrees well with that observed in the experiment. Different thermo-fluid dynamic environments with varied quench rates, encountered by the propagating vapor front inside the reactor under different operating conditions are found to be primarily responsible for variations in the width of the size distribution.

Experimental investigation on mechanisms of fine particles generation for the Borealis Borstar multistage olefin polymerization process

ABSTRACTSimultaneous production of large amount of undesired fine particles is a big trouble in the Borstar multistage olefin polymerization process. Aiming at reducing the fine particles, the formation mechanism and formation location of the fine particles were thus studied. First, the influence of catalyst nature was considered. Second, the ash content, bulk density, morphology, and molecular weight distribution of polyethylene with different particle sizes from the small‐scale loop prepolymerization reactor, supercritical loop reactor, and gas phase fluidized bed reactor were studied, respectively. In combination with particle growth model, scanning electron microscope, gel permeation chromatography, and laser particle size analyzer, the particle morphology and growth kinetics were investigated. The results showed that fine particles were mostly generated in the supercritical loop reactor, and were significantly affected by the particle size distribution, residence time distribution, and particle fragmentation of the catalyst. Furthermore, scanning electron microscope images showed the catalysts with low activity tended to generate more fine particles. Based on these results, several strategies for reducing the amount of fine particles were proposed, which could be applied in the industrial process. © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2018, 135, 46589.