Aggregation Process Of Particles Research Articles

CHALCONE ANALOGUES AS POTENTIAL MEDICINES OF PATHOGENETIC THERAPY OF ALZHEIMER'S DISEASE: IN VITRO SCREENING

Introduction. Alzheimer's disease is one of the most common forms of dementia, the pathogenesis of which is based on the accumulation of β–amyloid plaques in brain structures and the development of cholinergic deficiency. The aim of the study was to evaluate the effect of chalcone analogues on the change in acetylcholinesterase activity and the process of β-amyloid aggregation in vitro. Material and methods. The tested compounds were six bis-substituted chalcone analogues, which were dissolved in dimethylsulfoxide during the analysis to obtain double dilutions. The effect of the studied substances on the activity of acetylcholinesterase was evaluated by the modified Ellman method. The change in the aggregation process of β-amyloid particles was determined in reaction with congo red after 3, 6 and 9 days of incubation. Based on the obtained results of the «% inhibition- concentration» relationships, the IC50 index was calculated, which was expressed in mmol/ml. Results. In the course of the study, it was shown that the analyzed chalcone analogues inhibit the aggregation of β-amyloid particles starting from the 6th day of incubation with a maximum on the 9th day. At the same time, the compounds that showed the highest level of activity were trimethoxy-substituted substances under the codes AZBAX4 and AZBAX6, whose IC50 on the 9th day of the study was 21.4±0.928 mmol/ml and 32.4±0.456 mmol/ml, respectively. Also, a high level of anticholinesterase properties was established for these compounds with IC50 of 35.9±0.991mmol/ml and 25.1±0.261 mmol/ml, respectively. The rest of the tested compounds showed a lower level of activity. Conclusion. The study showed that chalcone analogues under the codes AZBAX4 and AZBAX6 inhibit the activity of acetylcholinesterase and the pro-cess of aggregation of β-amyloid in vitro, which makes these compounds promising for further study in order to develop medicines for the pathogenet-ic treatment of Alzheimer's disease.

Combustion of iron particles in solid propellants at elevated pressure

Metal fuels, such as aluminum (Al) and iron (Fe), can be added to composite solid propellants to improve their performance, such as specific impulse, density, and burning rate. In comparison to aluminum, iron can theoretically provide improved density specific impulse and higher flame temperatures; reduce condensed combustion product (CCP) concentration and the associated two-phase flow losses; and eliminate hydrochloric acid (HCl) in the exhaust products. A fundamental and quantitative understanding of metal particle aggregation and agglomeration processes in solid propellants is required to understand the underlying combustion mechanisms in these systems. In the current study, composite strand and laminate AP/HTPB/AP propellant samples loaded with Fe microparticles (∼45 μm in diameter) were burned at elevated pressures in an optically accessible strand bomb. Combustion processes were monitored with transient pressure diagnostics and a high-speed camera fitted with a high-magnification lens system (3.83 μm/pixel resolution) for the laminate propellant experiments. An automated image processing algorithm was developed to measure burning rates and ejected particle/agglomerate sizes and velocities. Time-resolved statistical distributions of both particle size and velocity are presented at elevated pressure for multiple laminate propellant experiments with a high degree of repeatability and low measurement error estimated as < ±5% and < ±1.5% for particle size and velocity, respectively. The incorporation of iron microparticles into the composite strand propellants yielded over a 20% increase in the global burning rate over the range of pressures evaluated (3.45–13.8 MPa). Similarly, the addition of iron to the fuel lamina in laminate propellant samples led to an approximately 30% increase in the global burning rate at the evaluated pressure (3.45 MPa). Additive particles were observed to eject near the oxidizer/fuel interface, or to melt, aggregate, coalesce, and agglomerate on the fuel lamina surface prior to ejection. Particle velocities are controlled by a balance of gravitational forces, drag forces imparted by expanding combustion product gases, and particle inertia. The observed combustion enhancements are attributed to the combined effects of catalytic mechanisms, increased radiation heat transfer, and local energy release from reacting iron particles. In addition, discussions on the image processing methods developed in the current study, corresponding potential sources of error, and prospective areas of improvement are provided. The experimental approach developed enables high-speed and high-magnification visualization of propellant combustion at high pressures and can be utilized to better understand the fundamental combustion behavior of energetic systems.

Structure evolution of porous alumina during aging process and its support effect on PtSn/Al2O3 catalyzed propane dehydrogenation

Precise control of porous alumina microstructures is always challenging due to the diversity and complexity of the growth process-related alumina crystalline phase and surface properties. In this work, we established a bottom-up synthesis route with a combination of rapid precipitation at high supersaturation and high-temperature aging in terms of enhancing particle aggregation kinetics. Surprisingly, we discovered that there were two distinct growth stages of alumina precursor (ammonium aluminum carbonate hydroxide) during the aging procedure, that is, oriented attachment at the early stage of crystallization and subsequent Oswald ripening. High-temperature aging can effectively strengthen the aggregation kinetics between the particles and produce large mesoporous (∼16 nm) and a remarkable number of defect sites with the exposure of up to 14 % unsaturated pentacoordinate aluminum ions. Owing to the presence of strong metal-support interactions, the alumina-supported PtSn catalyst exhibited excellent catalytic activity in the propane dehydrogenation reaction with propylene formation with 99 % selectivity and superior stability with a low deactivation rate of 0.007 h−1 over 24 h. These results suggested that it was feasible and instructive to achieve precise control of the structure and surface properties of alumina by manipulating the aggregation process of the initial particles during the aging stage.

Thermal treatment effect on the particle size distribution of alkaline earth metals hydroxyapatite

Hydroxyapatites of certain alkaline earth metals were synthesised, and their phase composition was determined using X-ray phase analysis. Thermal modification of the studied compounds was performed at temperatures not exceeding 800°C. The laser diffraction method determined the size distribution of the samples subjected to thermal treatment. It was found that the mean particle size ranged from 5,48±1,28 to 126,71±3,68 μm. It has been demonstrated that particle aggregation and fragmentation processes are possible depending on the synthesised compounds' qualitative and quantitative phase composition and the modification temperature.

Aggregation behavior and mechanism of kaolin particles suspension in the presence of Xanthan gum and Fe(III)

Aggregation is an economical and widely existing method to in fine particles dewatering, but the mechanism of composite applications of inorganic coagulants/flocculants remains unclear. In this work, the aggregation process of kaolin particles using Fe(III) and xanthan gum (XG) was investigated by settling testing. The results shows that the combination XG and Fe(III) was effective in the flocculation of kaolin, which due to the self-assembly multilayers built onto the surface of kaolin. Further, density functional theory (DFT) calculations and X-ray photoelectron spectroscopy (XPS) analyses were performed to detect the flocculation mechanism. It was found that [Fe(Ⅲ)(OH)]2+, [Fe(Ⅲ)(H2O)6]3+ and [Fe(Ⅲ)(OH)2]+ were the dominant species, which could complex with the XG on kaolin surface by the Fe-O adsorption site. However, the precipitate Fe(OH)3(s) covered on the kaolin surface is difficult to combine XG by coordination reaction under alkaline conditions. The research elucidated a new insight into of composite applications of inorganic coagulants and flocculants which could expand our knowledge of aggregation process, further define the relationship between coagulation and flocculation for enhancing colloidal particle settling in practical application.

Morphology and aggregation process of natural rubber particles

Natural rubber particles (NRPs) are the main place of natural rubber biosynthesis and storage which exist as the organelle in the latex tube cells of rubber trees. Here, we observed the aggregation process from the morphology of rubber particles and correlated the aggregate structure with the mechanical properties. The rubber particle sizes were first examined by optical microscopy, and the distribution showed a Gaussian curve with an average diameter of 1200 nm. Scanning electron microscopy (SEM) was then used to photograph the smaller particles, which supported a Gaussian distribution for NRPs smaller than 200 nm in diameter. They collectively indicated a bimodal distribution of NRP size, consistent with the results of the laser particle size analyzer. The percentage of the small rubber particles was measured to be 68.3 % and 31.7 % for the large rubber particles. The aggregation process of NRPs was observed as membrane fusion, superimposed aggregation, followed by the concavity of the inner core from the outside, and finally the formation of aggregated state rubber. Subsequently, the natural rubber latex films were obtained by spreading the latex at room temperature. The green strength was tested in its naturally dried stacked aggregated state, reaching a notable strength of 8 MPa. This was about 7 times higher than that of the ribbed smoked sheet (RSS). In contrast, when the naturally dried rubber film was processed by high-temperature molding and low-temperature setting, its green strength dropped to the level of the RSS. It thus supports that the processing methods, such as high temperature and shearing, could significantly impact the structure and performance of natural rubber (NR). Consequently, excellent performance of elastomeric materials might be reached under low-temperature drying and normal-temperature vulcanization processing methods.

THE EFFECT OF NITROGEN AND PHOSPHORUS ON THE AGGREGATION OF SOIL COLLOIDAL PARTICLES IN THE THREE GORGES RESERVOIR AREA

Nitrogen (N) and phosphorus (P) concentrations in tributaries and bays of the Three Gorges Reservoir area increase significantly after impoundment. It will affect processes such as coalescence/dispersion of soil colloidal particles, which in turn will affect the ecological safety of the reservoir water bodies. We analyzed the aggregation process of purple soil colloidal particles, and found that aggregation was controlled by the interaction of N and P. With the increase of N and P concentration in the water body, purple soil colloidal particles transformed from slow aggregation (represented by linear growth) to fast aggregation (represented with a power function). We chose three forms of purple soil (acidic, calcareous, and alkaline) to check how interactions between nutrients and physical aggregation processes may vary across soil types. Average aggregation rate (TAA) of the three purple soils differed significantly, and the critical coalescence concentration (CCC) of neutral, alkaline, and acidic purple soils was 220.14, 117.49, and 47.20[Formula: see text]mmol[Formula: see text]L[Formula: see text] and 507.49, 437.15, 328.30[Formula: see text]mmol[Formula: see text]L[Formula: see text], respectively. Compared to phosphorus, the nitrogen system has higher TAA and lower CCC, indicating that nitrogen is more effective in triggering colloidal aggregation of purple soils. In the N and P systems, the surface potentials of neutral, alkaline and acidic purple soils decreased from −172.85[Formula: see text]mV to −70.28[Formula: see text]mV and −187.65[Formula: see text]mV to −81.98[Formula: see text]mV, respectively. With the increase of N and P concentrations, the surface charge density and the absolute surface potential values of the three purple soil colloids decreased, the surface potentials of the three purple soil colloids (absolute values) at the same concentration showed that P was greater than N. Meanwhile, the activation energy of interaction of all three purple soil colloids decreased continuously with the increase of N and P concentrations, and the activation energy of interaction in the N system was significantly lower than that in the P system under the same concentration conditions. Theoretical calculations showed that N and P changed the surface charge properties of the soil and increased the net gravitational force between colloidal particles, which made the net force behave as attraction and colloidal particles were more likely to agglomerate. When the N and P concentrations increased to 0.2, 0.1, 0.05[Formula: see text]mol[Formula: see text]L[Formula: see text], and 0.5, 0.4, 0.3[Formula: see text]mol[Formula: see text]L[Formula: see text], respectively, they were basically consistent with their CCC values. The net force between the three purple soil particles was negative and behaved as attraction. The surface potentials at the corresponding concentrations were all about −125[Formula: see text]mV. This study showed that N and P in the water body ultimately affected the aggregation process of soil colloids by changing the surface charge properties of particles, which in turn causes changes in the interaction forces and activation energy between colloidal particles.

Diffusion/Reaction Limited Aggregation Approach for Microstructure Evolution and Condensation Kinetics during Synthesis of Silica-Based Alcogels.

A base-catalysed methyltrimethoxysilane (MTMS) colloidal gel formation was implemented as a cellular automaton (CA) system, specifically diffusion and/or reaction-limited aggregation. The initial characteristic model parameters were determined based on experimental synthesis of MTMS-based, ambient-pressure-dried aerogels. The applicability of the numerical approach to the prediction of gels' condensation kinetics and their structure was evaluated. The developed model reflects the kinetics properly within the investigated chemical composition range (in strongly reaction-limited aggregation conditions) and, to a slightly lesser extent, the structural properties of aggregates. Ultimately, a relatively simple numerical model reflecting silica-based gel formation was obtained and verified experimentally. The CA simulations have proved valid for understanding the relation between the initial chemical composition and kinetics constants of MTMS-based synthesis and their impact on secondary particle aggregation process kinetics.

Model of the aggregation process of fine ferromagnetic particles

The most important result of the effect of interparticle interactions of ferromagnetic particles in suspensions is the formation of aggregates and modification of their physical properties, which allows changing the kinetics of separation processes. The interest of the authors to this problem is dictated by both its theoretical content and purely applied aspects within mineral processing. Based on the block-structural approach to technological equipment modeling within the framework of the ideal mixing model, a mathematical model of processes occurring in the working volumes of apparatuses using magnetic forces to intensify the separation of mineral suspensions was created. The use of the MATHCAD software has allowed obtaining analytical solutions of the differential equations system of the model and predictions of the kinetics of aggregation of ferromagnetic particles and physical properties of the formed aggregates, such as coarseness, density, deposition velocity in the gravity field as functions of medium parameters and external magnetic fields. The analytical solutions are necessary for developing simulation models of magnetic separation processes in strong, weak, uniform and non-uniform magnetic fields, magnetic deslammers and filters.

A nanoparticle formation model considering layered motion based on an electrical explosion experiment with Al wires

To study the evolution of nanoparticles during Al wire electrical explosion, a nanoparticle formation model that considered layered motion was developed, and an experimental system was set up to carry out electrical explosion experiments using 0.1 mm and 0.2 mm Al wires. The characteristic parameters and evolution process during the formation of nanoparticles were calculated and analyzed. The results show that the maximum velocities of the innermost and outermost layers are about 1200 m·s−1 and 1600 m·s−1, and the velocity of the middle layer is about 1400 m·s−1, respectively. Most of the nanoparticles are formed in the temperature range of 2600 K‒2500 K. The characteristic temperature for the formation of Al nanoparticles is ∼2520 K, which is also the characteristic temperature of other parameters. The size distribution range of the formed nanoparticles is 18 to 110 nm, and most of them are around 22 nm. The variation of saturated vapor pressure determines the temperature distribution range of particle nucleation. There is a minimum critical diameter of particles (∼25 nm); particles smaller than the critical diameter can grow into larger particles during surface growth. Particle motion has an effect on the surface growth and aggregation process of particles, and also on the distribution area of larger-diameter particles. The simulation results are in good agreement with the experiments. We provide a method to estimate the size and distribution of nanoparticles, which is of great significance to understand the formation process of particles during the evolution of wire electrical explosion.

Aggregation and charging of natural allophane particles in the presence of oxyanions

Allophane is a typical clay mineral in young volcanic ash soil with special and complex structures and properties. The aggregation-dispersion and charging behaviors of natural allophane may have implications on sustainable agriculture and environment. Oxyanions, such as phosphate and arsenate, may also be related to many environmental resource problems. To investigate the aggregation and charging behaviors of allophane in the presence of oxyanions, the stability ratio (W) and electrophoretic mobility (EPM) of allophane were measured. The results of EPM, W and the values of CCCs show ion specific effect, which is not explicitly considered by the Derjaguin, Landau, Verwey and Overbeek (DLVO) theory. However, the relationship between critical coagulation ionic strength (CCIS) and surface charge density from EPM based on DLVO theory with the Debye-Huckel (DH) approximation is in good agreement with the experimental CCIS. This agreement indicates that the DLVO forces controlled by ionic strength and electrokinetic charge are the driving forces in the aggregation process of natural allophane particles in the presence of oxyanions.

Physics-informed deep learning for modelling particle aggregation and breakage processes

Particle aggregation and breakage phenomena are widely found in various industries such as chemical, agricultural and pharmaceutical processes. In this study, a physics-informed neural network is developed for solving both the forward and inverse problems of particle aggregation and breakage processes. In this method, the population balance equation is directly embedded in the loss function of a neural network so that the network can be trained efficiently and fulfil physical constraints. For the forward problems, solutions of population balance equations are obtained through the optimization of the neural network where the predictions well match the analytical solutions. In the inverse modelling, the data-driven discovery of model parameters of population balance equations is investigated. The sensitivity regarding the selection of different neural network structures is also investigated. The developed population balance equations embedded with neural network approach is promising for solving inverse problems of particle aggregation and breakage processes with noisy observation data.

Evaluation of direct quadrature method of moment for the internally circulating fluidized bed simulation with ultrafine particles

In the framework of the Euler-Euler gas–solid two-fluid model, the particle population balance equation is solved by the direct quadrature method of moment. The dynamic process of ultrafine particle movement and aggregation in an internally circulating fluidized bed is simulated. The distribution of the concentration and velocity of the agglomerates in the flow process is given, and the changes of the moments in the bed are shown. The effects of different breakage coefficients and inlet gas rates on the concentration distribution of agglomerates are compared. The results show that the particle size decreases with the increase of breakage coefficient, and the time required to reach steady fluidization state increases; the higher the inlet velocity, the better the effect of circulating particles in the bed. When there is a certain gas velocity difference between the two sides, the effect of circulating particles in the bed is better.

Cellular Automata Modeling of Silica Aerogel Condensation Kinetics.

The formation of silica aerogels and the kinetics of condensation were investigated numerically. The influence of the reaction-limited to the diffusion-limited aggregation (RLA to DLA) transition on the reaction kinetics curves and the evolution of the aggregate size distribution during condensation were examined. The 2D cellular automaton was developed and applied to reflect the process of secondary particle aggregation. Several tendencies were observed due to the adjustment of the model parameters: the probability of condensation reaction and the particles’ concentration. The final wet-gel structures’ visualizations proves that the structure becomes more dense and compact due to entering the RLA regime. The simulation time (associated with the gelation time) decreased along with the increase in both model parameters. The lower the collision probability, the slower reaction becomes, and particles are more likely to penetrate the structure deeper until they finally join the aggregate. The developed model reflects the condensation process’s nature and its mechanisms properly and indicates a significant potential for further aerogel synthesis investigations and for the prediction of wet-gel properties according to condensation parameters.

Genesis of electric field assisted microparticle assemblage in a dielectric fluid

Abstract

Stickiness of extracellular polymeric substances on different surfaces via magnetic tweezers

Organic particle dynamics in the surface ocean plays a critical part in the marine carbon cycle. Aggregation of marine organic particles drives their downward transport to support various marine organisms on their transit to the sediments. Extracellular polymeric substances (EPS) from various microbes are a major contributor to the oceanic organic particle pool. The stickiness of EPS is expected to play a determining role in the aggregation process of particles; however, stickiness parameters are usually indirectly estimated through data fitting without direct assessment. Here a magnetic tweezer method was developed to quantitatively assess the stickiness of three model EPS produced by: Amphora sp., (diatom), Emiliania huxleyi (coccolithophore), and Sagittula stellata (bacteria), under different in vitro environmental conditions (salinity or EDTA complexed cations) and surface matrices (EPS-EPS and bare glass). Our results showed the stickiness of three microbial EPS decreasing for S. stellata > E. huxleyi > Amphora sp., in line with their decreasing protein-to-carbohydrate (P/C) ratios (related to their relative hydrophobicity). The data not only emphasize the importance of hydrophobicity on EPS stickiness, but also demonstrates that salinity and the nature of the substrate surface can influence the stickiness. Furthermore, we investigated stickiness between various types of EPS, and the observed selective stickiness of EPS between species may shed light on the interactions among heterogeneous marine microorganisms. Overall, this newly developed system provides a platform to assess the EPS stickiness to advance our understanding of the aggregation and sedimentation process of organic particles that are critical for the fate of organic carbon as well as for biofilm formation and microbial colonization of surfaces in the ocean.

Physical and Aerodynamic Characterization of Particle Clusters at Sakurajima Volcano (Japan)

The process of particle aggregation significantly affects ash settling dynamics associated with volcanic explosive eruptions. Several experiments have been carried out to investigate the physics of ash aggregation and dedicated numerical schemes have been developed to produce more accurate forecasting of ash dispersal and sedimentation. However, numerical description of particle aggregation is complicated by the lack of complete datasets on natural samples required for model validation and calibration. Here we present a first comprehensive dataset for the internal structure, aerodynamical properties (e.g., size, density, terminal velocity) and grain size of constituting particles of a variety of aggregate types collected in the natural laboratory of Sakurajima Volcano (Japan). Even though the described particle clusters represent the most common types of aggregates associated with ash-rich fallouts, they are of difficult characterization due to the very low potential of preservation in tephra-fallout deposits. Properties were, therefore, derived based on a combination of high-resolution-high-speed videos of tephra fallout, scanning electron microscope analysis of aggregates collected on adhesive paper and analysis of tephra samples collected in dedicated trays. Three main types of particle clusters were recognized and quantitively characterized: cored clusters (PC3), coated particles (PC2), and ash clusters (PC1) (in order of abundance). A wide range of terminal velocities (0.5–4 m/s) has been observed for these aggregates, with most values varying between 1 and 2 m/s, while aggregate size varies between 200 and 1,200 µm. PC1, PC2, and PC3 have densities between 250 and 500, 1,500 and 2,000, and 500 and 1,500 kg/m3, respectively. The size of the aggregate core, where present, varies between 200 and 750 µm and increases with aggregate size. Grain size of tephra samples was deconvoluted into a fine and a coarse Gaussian subpopulation, well correlated with the grain size of shells and of the internal cores of aggregates, respectively. This aspect, together with the revealed abundance of PC3 aggregates, reconciles the presence of a large amount of fine ash (aggregate shells) with coarse ash (aggregate cores) and better explains the grain size distribution bimodality, the high settling velocity with respect to typical PC1 velocities and the low settling velocities of large aggregates with respect to typical PC2 velocity. Furthermore, ash forming the aggregates was shown to be always finer than 45 µm, confirming the key role played by aggregation processes in fine ash deposition at Sakurajima.

Evaporation and particle deposition of bi-component colloidal droplets on a superhydrophobic surface

Droplet evaporation is not only a natural phenomenon occurring on a daily basis, but also a novel approach to pattern microscopic structures using small colloids via the evaporative self-assembly. In this work, we carry out a comparative investigation of the evaporation kinetics and particle deposition dynamics of diverse bi-component colloidal droplets on a superhydrophobic surface. We found that the evaporation modes of a drying droplet are determined by both the added volatile component and dispersed colloidal particles, which affect the droplet-surface interactions and thus the contact line motion. While increasing the concentration of the volatile component significantly accelerates the evaporation, no apparent influence was observed for the presence of colloidal particles on droplet lifetime, and the evaporation rate of bi-component droplets in the constant contact angle and constant contact radius modes can still be described by their classical theories for single component droplets. Three types of deposition patterns, namely, a thin disk, a three-dimensional cap and a circular ring, were obtained after evaporation. By direct visualizing the particle aggregation process and analyzing the evaporation flux distribution around sessile droplets, we demonstrate that the residual colloidal structures are regulated by the capillary flows developed in the evaporating droplets.

Combustion synthesis of SiO2 nanoparticles using flat premixed flame

Recently, numerous researches have actively progressed for producing nanoparticles such as SiO2, TiO2, and Al2O3 used in various commercial applications. In particular, SiO2 nanoparticle is widely used for the fiber optics, pigment and dye, ceramic semiconductor industries. Synthesis of SiO2 by combustion process using gas-phase silane as a precursor is very attractive because the flame aerosol method can be easily scaled up to mass production and economically feasible. Therefore it is necessary to investigate the fundamental research such as nuclei inception, coagulation, coalescence, and morphology during combustion synthesis for the nanoparticle formation. In this study, we performed experimental research to generate the SiO2 nanoparticle using the methane - hydrogen flat premixed flame which can show the effect of hydrogen on the formation of SiO2 nanoparticles especially. We found out the effect of the H2 content in the fuel mixture on the characteristics of SiO2 particle formation when the optimum condition of the flat surface flame is satisfied. Measurements of the particle morphology and size by TEM (Transmission Electron Microscopy) showed that the hydrogen enhancement in fuel mixture was likely to prevent aggregation process of SiO2 primary particles effectively.

Investigation of Fe–Mn particle aggregation and growth processes in molten slag

ABSTRACTThe aggregation and growth behaviours of Fe–Mn particles in the direct alloying process were investigated using the high-temperature experiment. The manganese-rich slag was used as a source of manganese to make into the briquette for the alloying process, and the quaternary slag was prepared using an analytical reagent. To monitor the aggregation and growth process of metal particles and its chemical reactions, some test methods, such as XRD, TDA SEM and EDS, were applied. The results showed that after the briquette is added into the melted slag, because the heat is transferred from the outer layer of the briquette to its interior, the growth process of metal particles can be divided into three stages: nucleation period, aggregation period and growth period. In the first two stages, the Fe particles are first reduced as the nucleation for the alloying process, while the Mn particles are nucleated by Fe particles and formed Fe–Mn particles. Finally, the Fe–Mn particles gradually grow up. In addition, the statistical model was developed for describing the growth process of Fe–Mn particle, and it shows a good relationship with the measured value.