Particle Size Distribution Behavior Research Articles

RETRACTED: Zhong et al. Fractal Behavior of Particle Size Distribution in the Rare Earth Tailings Crushing Process under High Stress Condition. Appl. Sci. 2018, 8, 1058

The Applied Sciences Editorial office retracts the article “Fractal Behavior of Particle Size Distribution in the Rare Earth Tailings Crushing Process under High Stress Condition” [...]

Discrete Element Modelling of Fractal Behavior of Particle Size Distribution and Breakage of Ballast under Monotonic Loading

Breakage of particles has a great influence on the particle size distribution (PSD) and the associated mechanical behavior of ballast under train loads. A discrete element method (DEM) simulation of triaxial testing under monotonic loading was carried out using FRM (fragment replacement method) breakable particles as ballast and a flexible shell model as membrane. The coupled model was validated by comparing the load-deformation responses with those measured in previous experiments and was then used to analyze the contact orientations and the distribution of particle breakage from a micromechanical perspective. The simulation results show that higher confining pressure and larger axial strain may increase the grain breakage (Bg) and the fractal dimension (D) of ballast. It was observed that most breakage was first-generation breakage, and that the proportions of the second- to fifth-generation breakage decreased successively. Moreover, as the axial strain or confining pressure increased, the percentage of small particle fragments increased in correspondence with the PSD curves that remained concave upwards, as the fractal dimension D of PSD increased. In addition, the evolution of D exhibited a linear correlation with grain breakage Bg. Contrarily, a quadratic curve relation between D and volumetric strain was exhibited under different axial strain stages. Therefore, D has the potential to be a key indicator to evaluate the degree of ballast crushing and PSD degradation, which may contribute to better decision making concerning track bed maintenance.

Comparing multifractal characteristics of soil particle size distributions calculated by Mie and Fraunhofer models from laser diffraction measurements

Particle size distribution (PSD) is a basic soil property, closely related to main soil physical and chemical attributes. Soil PSD determined by laser diffraction (LD) may provide additional information to soil texture determined by traditional methods. In turn, LD may be implemented using either Mie or Fraunhofer calculation methods, based on different assumptions. The multifractal approach has been demonstrated to be useful for characterizing the inner structure of soil PSD. We analysed the PSDs of 18 soil horizons sampled on the most characteristic soil types from Argentina with a wide range of textural classes, from clayey to sandy, mainly developed over loess material. Our aims were to assess the multifractality between PSDs computed using either Mie scattering or Fraunhofer diffraction models, and to compare the scaling properties and multifractal behavior of PSDs from soils with contrasting textures. Fraunhofer model provided PSD curves, which were shifted toward coarser particles compared to those obtained with Mie model. Regardless calculation method, all the PSDs studied displayed a well-defined multifractal structure, as shown by singularity, f(α) versus α, and by Rènyi spectra, Dqvs q. Moreover, all singularity spectra were strong asymmetric, right deviating curves, which is consistent with a greater heterogeneity of the low values of volume frequencies for all the PSDs analysed. Soil PSDs computed by Fraunhofer model showed higher asymmetry than those computed by Mie model for 16 out of 18 horizons studied; this suggests that scaling heterogeneity mainly depends on the support length, which is larger for the PSDs computed by Mie. In addition, other features of the PSDs stemming from soil processes such as weathering intensity of loess materials may also influence multifractality. Stronger correlations were found between multifractal parameters from PSDs calculated by the two models for the most positive q moments of singularity and Renyi spectra, i.e. α10, D10, than for those gathered from the central and negative q moments. The entropy dimension, D1, significantly (P<0.05) increased with increasing clay content, in contrast to previous findings; this may be due either to differences in the inner structure of various PSD data sets compared, or to shortcomings of standard PSD measurement and calculation procedures.

RETRACTED: Fractal Behavior of Particle Size Distribution in the Rare Earth Tailings Crushing Process under High Stress Condition

To disclose the fractal transformation mechanism of the size distribution of rare earth tailing particles, this paper utilizes the side confined uniaxial compression test to study the evolution rule of the particle size distribution of the rare earth tailing and the particle breakage features under the high stress condition. The fractal behavior of the particle size distribution in the crushing process is studied based on the fractal model and the particle size distribution. The experimental results show that, under the high stress condition, the particle size distribution tends towards fractal distribution due to the particle breakage of the rare earth tailing. The crushing process is closely related to the breakage amount of the particles and can be described with the increased fractal dimension. Although the initial distribution and particle size of the rare earth tailings are different, the measured data of the particle size distribution with the fractal dimension greater than 2.2 shows fairly strict self-similarity, and this value can be taken as the lower limit value of the fractal dimension when the particle size distribution tends towards fractal distribution. When the particle size distribution becomes a fractal distribution due to the particle breakage, the ratio between the volumetric strain and the relative breakage rate remains constant and is slightly affected by the initial distribution uniformity and particle size.

Modeling and simulation of particle size distribution behavior in gas–liquid–solid polyethylene fluidized bed reactors

In this work, population balance model (PBM) that describes particle size distribution (PSD) and liquid vaporization modeling scheme (VMS) (including the heat transfer model and droplet vaporization model), which describes liquid evaporation, were incorporated into a three-fluid computational fluid dynamics (CFD) model to analyze PSD behavior in an industrial–scale gas–liquid–solid three–phase polyethylene fluidized bed reactor (FBR). The validation of this CFD–VMS–PBM coupled model was conducted through comparing results with industrial and calculated data, which then was applied to discuss the characteristics of PSD behavior in terms of the effects of particle kinetics, node number, and condensed liquid content. Unlike gas–solid polyethylene conventional FBRs, although the PSD behavior was dominated by particle agglomeration, particle breakage kinetics exerted a great impact on PSD, especially at the initial polymerization period when it competed with aggregates to decrease the defluidization risk of the reactor. Furthermore, the number of nodes strongly affected PSD simulation results, and using three nodes was the best configuration. In this three–phase system, the increase in the condensed liquid content improved the particle growth rate, which affected the reactor's productivity and product's properties, such as mean particle size and final PSD.

The Asymptotic Behavior of Particle Size Distribution Undergoing Brownian Coagulation Based on the Spline-Based Method and TEMOM Model

In this paper, the particle size distribution is reconstructed using finite moments based on a converted spline-based method, in which the number of linear system of equations to be solved reduced from 4m × 4m to (m + 3) × (m + 3) for (m + 1) nodes by using cubic spline compared to the original method. The results are verified by comparing with the reference firstly. Then coupling with the Taylor-series expansion moment method, the evolution of particle size distribution undergoing Brownian coagulation and its asymptotic behavior are investigated.

Response of suspended sediment particle size distributions to changes in water chemistry at an Andean mountain stream confluence receiving arsenic rich acid drainage

AbstractAcid drainage is an important water quality issue in Andean watersheds, affecting the sustainability of urban, agricultural, and industrial activities. Mixing zones receiving acid drainage are critical sites where changes in pH and chemical environment promote the formation and dissolution of iron and aluminum oxy/hydroxides. These particles can significantly change the speciation of toxic metals and metalloids throughout drainage networks via sorption, desorption, and settling processes. However, little is known about the behavior of particle size distributions (PSDs) in streams affected by acid drainage and their relationship to metal speciation. This work studied: (a) the PSDs for a wide range of mixing ratios found at a fluvial confluence affected by acid drainage, and (b) the response of PSDs and arsenic speciation to environmental changes found when the particles approach complete mixing conditions. The confluence between the Azufre River (pH ~ 2, high concentration of dissolved metals) and Caracarani River (pH = 8.6, low concentration of dissolved metals) was used as a representative model for study. Field measurements show a bimodal PSD with modal diameters of ~50 and 300 μm. At shorter distances from the junction, the smaller modes with smaller particle volumes were dominant across the stream cross‐sections. A systematic shift towards larger particle sizes and larger particle volumes occurred downstream. The analysis of laboratory PSDs for Azufre/Caracarani mixing ratios between 0.01 and 0.5 (pH from 6.2 to 2.3) showed a bimodal trend with ~15 and 50 μm characteristic diameters; larger particles formed at pH&gt;4. When particle suspensions were transferred in laboratory experiments from very low pH to full mixing conditions (pH ~ 2.8 and mixing ratio ~ 0.25) particle sizes varied, and the dissolved arsenic concentration decreased. The observed reaction kinetics were slow compared to the time scale of advective transport, creating opportunities for engineered controls for arsenic. This work contributes to a better understanding of the chemical‐hydrodynamic interactions in watersheds affected by mining, and identifying opportunities to improve water quality at points of use.

Size Distribution Behavior of Metallic Iron Particles in Coal-Based Reduction Products of an Oolitic Iron Ore

The size distribution of metallic iron particles is important to better understand the coal-based reduction mechanisms of refractory iron ores. This study was focused on the particle size distribution behavior of metallic iron in coal-based reduction products of an oolitic iron ore. The size of metallic iron particles was measured using image analysis, and the data obtained were analyzed using frequency and cumulative distributions. The curves of the size-frequency distribution and cumulative passing percentage of metallic iron particles exhibited nearly the same trend with respect to particle size. The particle size distribution of metallic iron particles was markedly influenced by both reduction time and temperature. The number of metallic iron particles with large size increased with the reduction time and temperature. Goodness-of-fit tests indicated that the power function and the cumulative distribution function (CDF) of the log-normal distribution best fitted the experimental data of size frequency distribution and cumulative passing percentage of metallic iron particles, respectively.

Particle size distribution of metallic iron during coal-based reduction of an oolitic iron ore

The objective of this study was to evaluate the effect of reduction temperature, reduction time and binary basicity on the size of metallic iron particles in coal-based reduction products of an oolitic iron ore. The particle size distribution behavior (i.e., cumulative passing percentage and mean size of metallic iron particles) during reduction was investigated in detail. Results showed that the particle size distribution of metallic iron particles was strongly influenced by reduction temperature, reduction time and binary basicity. The cumulative passing percentage and mean size significantly increased with reduction temperature and time in the entire range of the experiments. All curves of cumulative passing percentage versus particle size under different conditions demonstrated a similar trend (continuous increase). The size distribution parameters and mean size slightly increased with increasing binary basicity and significantly decreased when the binary basicity exceeded 1.0. The size of metallic iron particles could be controlled by adjusting the reduction conditions during coal-based reduction.

Evolution of particle size distribution in air in the rainfall process via the moment method

Population balance equation is converted to three moment equations to describe the dynamical behavior of particle size distribution in air in the rainfall. The scavenging coefficient is expressed as a polynomial function of the particle diameter, the raindrop diameter and the raindrop velocity. The evolutions of particle size distribution are simulated numerically and the effects of the raindrop size distribution on particle size distribution are studied. The results show that the raindrops with smaller geometric mean diameter and geometric standard deviation of size remove particles much more efficiently. The particles which fall in the ?greenfield gap? are the most difficult to be scavenged from the air.

Multi-Scale Modeling and Inventory Control of Particle Growth Processes

In this paper, we develop a multi-scale model to describe the particle growth in a fluidized bed reactor. Population balance model is presented to describe the dynamical behavior of particle size distribution. Stability analysis is derived to determine the control configuration for the complex particulate process. Inventory control strategy is applied to control the particle size distribution.

Macroscale and microscale evolutions of mechanically alloyed Fe [sbnd]Zn systems

The present work aims to correlate, in time, macroscale and microscale phenomenological evolutions of the microstructure of Fe and Fe Zn alloys processed by mechanical milling (MM) and alloying (MA), respectively. Powders were characterized for particle size distribution (PSD), particle morphology (optical microscopy, OM, scanning electron microscopy, SEM), microhardness, crystallite size, differential scanning calometry (DSC) and transmission electron microscopy (TEM). Two macroscopic regimes of PSD behavior were distinguished: the first one dominated by the cold welding process; and, the other where both fracture and agglomeration play a significant role. Solid solubilization of Zn on bcc Fe was found to reduce the final microhardness as well as increase the lattice parameter and is very well predicted by Miedema's thermodynamical approach. Microhardness and solid solution formation kinetics were correlated in time and both could be precisely described by a logistic function. After 5 h of planetary milling, microhardness and the lattice parameter become stable as well as the PSD and particle morphology, indicating that the system has already reached steady state. Indeed, this condition can be monitored by both macroscopic and microscopic parameters. Prior to an homogeneous powder, DSC results suggest an endothermic solid-state amorphization reaction for samples processed for up to 1 h as a result of the formation of clean Fe/Zn interfaces during MA.

Stochastic Modeling of Dynamic Behavior of Particle Size Distribution in Continuous Emulsion Polymerization

To gain a better understanding of the dynamic behavior of continuous emulsion polymerization, the authors developed a simple stochastic model which considers the competitive interaction between polymerization reaction and aggregation of latex particles. The numerical results were then compared with the experimental data from continuous emulsion polymerization of vinyl acetate carried out under various operating conditions. The numerical and experimental results showed satisfactory agreement. It was found that the dynamic behavior of particle size distribution is affected by latex particle aggregation and the feed flow rate.

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).

Solution of population balance equation with pure aggregation in a fully developed turbulent pipe flow

This paper presents our preliminary effort in predicting particle size distributions in particulate processes in turbulent flow systems. The focus has been on processes of pure aggregation, occurring in a turbulent environment. A remarkably simple strategy has been used to solve the population balance equation (PBE) for spatially dependent pure aggregation with insignificant diffusive transport of particles in turbulent flow systems. The method makes use of the solution of a batch PBE through a mathematical transformation linking time to spatial variables. Furthermore, we investigate the self-similar solution of batch aggregation to show scaling behavior of particle size distributions in such flow systems using spatially dependent average particle sizes. Average particle sizes across the pipe cross section have been computed using both averaged frequencies as well as spatially varying frequencies. Comparison of the two solutions shows significant differences between them, establishing the sheer inappropriateness of the use of average aggregation frequencies in the prediction of absolute particle size distribution as done in the past.

Experimental study of particle flow in a gas–solid separator with baffles using PDPA

Particle flow behavior in a gas–solid separator with a guide baffle and separation baffles developed by the Institute of Process Engineering (IPE) for cocurrent down-flow reactors has been studied with a Phase Doppler Particle Analyzer (PDPA), which allows to measure the particle size and velocity simultaneously. Profiles of particle velocities, particle size and particle number density at different heights in the separator were obtained. Analysis of the velocity profile indicates that the particle inertia has a significant effect on the behavior of particles in different size groups: the trajectories of the smaller particles are more influenced by the gas stream in relation to the larger, more heavier, particles. Experimental results reveal that the guide baffle together with the separation baffles plays a role of guidance as well as particle concentrators. Particles entrained by the gas flowing upward along the top side of the separation baffle may mainly come from the regions far from the guide baffle surface. Small particles are gradually dispersed toward the periphery of the two-phase flow field after being ejected from the rectangular nozzle, giving rise to a bimodal behavior of particle size distributions in the region far from the guide baffle.

Effect of the Emulsifier on the Dynamic Behavior of Particle Size Distribution in Continuous Emulsion Polymerization of Vinyl Acetate

The purpose of this research is to elucidate the effect of the emulsifier on the dynamic behavior of particle size distribution (PSD) in continuous emulsion polymerization. Emulsion polymerization of vinyl acetate was performed in a continuous stirred tank reactor. An anionic surfactant (sodium dodecyl sulfate: SDS) was used as an emulsifier. The initial emulsifier concentration in the reactor and that in the feed was varied as a control parameter. In order to vary the colloidal stability of latex particles, a nonionic surfactant (polyoxyethylene sorbitan monooleate: Tween80) was added in some cases. It has been found that PSD varies with time even while the constant monomer conversion is maintained at a steady state in all cases. Compared with the case of using only SDS, however, using a mixture of anionic surfactant and nonionic surfactant can effectively suppress this time-dependent behavior.

Behavior of Particle Size Distributions, Means and BET Values in Ideal and Non-Ideal Morphology Systems in a TEM

Abstract Historically, one of the first jobs performed by the new instrument called a “transmission electron microscope” (TEM) was the determination of particle size and distribution. Particle size is still important in controlling the properties of sub-micron and nanoparticle products. The width and average particle size can determine the light scattering properties of a pigment like TiO2, for example. The cost of installing a TEM facility and TEM sample preparation issues makes TEM analysis expensive and labor intensive. So decades ago, nitrogen BET (Brunauer, Emmett, and Teller) surface area determinations were used on sub-micron powders and pigments to minimize these costs. The BET measurement of the exposed external surface area of a material is made by detecting and measuring the amount of nitrogen given off after absorption, assuming one atomic layer of nitrogen is adsorbed.

Particle size distributions and viscosity of suspensions undergoing shear-induced coagulation and fragmentation

The dynamic behavior of concentrated suspensions (up to a solids volume fraction of 20%) of non-spherical particles is investigated theoretically by coupling a rheological law to a population balance model accounting for coagulation and fragmentation of the detailed particle size distribution. In these suspensions, the immobilization of matrix liquid renders the viscosity dependent on the particle aggregation state. The effect of initial solids volume concentration and shear rate on the transient behavior of particle size distribution and suspension viscosity is examined. Power law correlations for the equilibrium flow curves of aggregating suspensions are deduced and compared to experimental data. Steady-state or equilibrium particle size distributions are found to be self-preserving with respect to solids volume fraction and shear rate.

Particle Size Distribution in the Radial Direction of the Spray Cone and its Influence on the Formation of Porosity in Fe-6%Si Alloy Processed by Spray Forming

The spray forming process consists of atomizing a molten metal flux by a high velocity gas stream to generate small droplets. These are accelerated and simultaneously refrigerated / solidified by the atomization gas during their trajectory onto the substrate, upon which they consolidate, forming a coherent and dense pre-formed deposit. The present work consisted of investigating the behavior of particle size distribution in the radial direction of the spray cone, and its influence on the porosity of the deposited material. It was found that the size distribution curves were dislocated to the region of the smallest particle size when the radial distance was increased, leading to a decrease in the mean particle size and increasing the percentage of volumetric porosity in the material deposited in this direction.