Random particle packing with large particle size variations using reduced-dimension algorithms

We present a reduced-dimension, ballistic deposition, Monte Carlo particle packing algorithm and discuss its application to the analysis of the microstructure of hard-sphere systems with broad particle size distributions.We extend our earlier approach (the “central string”algorithm) to a reduced-dimension, quasi-3D approach. Our results for monomodal hard-sphere packs exhibit a calculated packing fraction that is slightly less than the generally accepted value for a maximally random jammed state. The pair distribution functions obtained from simulations of composite structures with large particle size differences demonstrate that the algorithm provides information heretofore not attainable with existing simulation methods, and yields detailed understanding of the microstructure of these composite systems.     

颗粒尺寸分布对SiC-Si粉体体系密度的影响

研究了两种粒径颗粒的级配对SiC粉体自由堆积密度的影响 ,并与理论模型进行比较 ,发现当粗细颗粒的粒径比 >3且粗颗粒的质量分数在6 0 %～ 70 %之间时 ,体系的自由堆积密度较大。探讨了SiC -Si混合料中SiC的颗粒尺寸分布和Si粉含量对自由堆积密度、压实密度和压缩比的影响 ,表明Si粉量为 30 %时体系的较佳压实密度为2 .0 9g·cm- 3。     

Role of TiO2 nanoparticles in the dry deposition of NiO micro-sized particles at room temperature

A room-temperature dry-deposition method with TiO₂ powder was used to deposit NiO particles onto a fluorine-doped tin oxide (FTO) substrate. Initially, in the absence of TiO₂ powder, we observed that the NiO particles did not adhere to the substrate; however, the addition of TiO₂ particles facilitated NiO deposition. The volume percentage (vol%) deposition of NiO particles increased with the TiO₂ particle concentration. The inability of the NiO particles to adhere to the FTO substrate was attributed to the absence of deformation and fragmentation in the substrate. This is related to the lower hardness of the FTO substrate, compared with that of the NiO particles. However, the addition of the TiO₂ particles at different vol% during NiO deposition induced deposition, possibly due to the lower hardness of the TiO₂ particles compared with the FTO substrate. The minimum TiO₂ fraction that enabled NiO powder deposition was ~4.8 vol%. Microstructural analysis revealed that TiO₂ powder agglomerates tended to break up as the NiO particles impacted the substrate surface, creating a “deposition complement” from the excess kinetic energy. The deposition mechanism was investigated using microstructural analysis, electron probe microanalysis, and Brunauer–Emmett–Teller (BET) measurements; the results confirmed the influence of the TiO₂ powders on NiO powder deposition, specifically, an improvement in the adhesion and density of the NiO powder and a decrease in the surface roughness of the coating. Therefore, we demonstrated NiO deposition with TiO₂ particles at room temperature, providing potential applications to the supercapacitor and battery industries.     

Pore size distribution from challenge coreflood testing by colloidal flow

The transport of colloidal and suspension particles and the resultant particle retention occur in a wide range of porous media. The micro scale pore throat size distribution is an important characteristic of porous media, allowing for evaluation of important transport properties. An effective method based on micro scale modelling for the determination of overall pore throat size distribution (PSD) by injection of colloidal particle suspensions into engineered porous media with monitored inlet and breakthrough particle concentrations is developed. The treatment of inlet and outlet colloidal particle concentrations obtained in coreflooding results in a good agreement between the modelling and experimental data. Yet, some deviation was observed between the obtained PSD and that calculated by the Monte Carlo simulation based on the Descartes’ theorem.     

Analysis of size distribution functions of diamond crystallites formed in the early stages of chemical vapour deposition

Size distribution functions of diamond particles formed in the early stages of chemical vapour deposition (CVD) can be used to distinguish between seeding and heterogeneous nucleation on the basis of their shape and of the d_max/d_min ratio, d_max and d_min being the maximum and the minimum diameters, respectively. A monomodal size distribution function with a d_max/d_min ratio much greater than 1.2–1.3 indicates diamond formation to occur via heterogeneous nucleation. In this case the nucleation kinetics can be calculated once the growth law of the crystallites has been established. The nucleation kinetics at copper substrates have been derived from distribution functions and described by a new kinetic model which includes the generation of nucleation sites.     

Time-resolved particle emission and size distribution characteristics during dynamic engine operation conditions with ethanol-blended fuels

The effect of ethanol-blended gasoline fuels on the characteristics of time-resolved particle concentration and size distribution was investigated in a gasoline engine and in a flexible fuel vehicle. Particle concentration levels from the vehicle running on ethanol-blended gasoline were compared to those of diesel vehicles with and without diesel particulate filter (DPF). In the engine test, particle size distribution and number concentration using E0 and E10 fuels were analyzed with a differential mobility spectrometer (DMS500) at dynamic engine operation conditions. In the vehicle emission test, time-resolved particle concentrations with ethanol blending contents (E0, E10, and E85) during a new European driving cycle (NEDC) were analyzed with a golden particle measurement system (GPMS) as recommended by the particle measurement programme (PMP). As the excess air ratio is shifted to lean conditions and as the spark and intake valve opening timing are retarded, particle number levels were reduced with both E0 and E10. The particle concentration from ethanol-blended gasoline was slightly decreased regardless of engine operating conditions. From the driving test results, the total particle concentration from the spark ignition and the diesel vehicle with a DPF was decreased by two orders of magnitude compared to a non-DPF diesel vehicle. As the oxygenated component is increased, particle emissions decreased. The total particle concentration for E85 was reduced by 37% compared to E0.     

Modeling of particle deposition in a vertical turbulent pipe flow at a reduced probability of particle sticking to the wall

Particle deposition on the wall in a dilute turbulent vertical pipe flow is modeled. The different mechanisms of particle transport to the wall are considered, i.e., Brownian motion, turbulent diffusion and turbophoresis. The Saffman lift force, the electrostatic force, the virtual mass effect and wall surface roughness are taken into account in the model developed. A boundary condition that accounts for the probability of particle sticking to the wall is suggested. An analytical solution for deposition of small Brownian particles is obtained. A particle relaxation time range, where the model developed is reliably applicable, is evaluated. Computational results obtained at different particle-wall sticking probabilities in the wide particle relaxation time range are presented and discussed.     

Modeling and simulation of polypropylene particle size distribution in industrial horizontal stirred bed reactors

This work aims at developing a steady-state particle size distribution (PSD) model for predicting the size distribution of polypropylene particles in the outflow streams of propylene gas-phase horizontal stirred bed reactors (HSBR), on the one hand and investigating the effect of the catalyst residence time distribution (RTD) on the polymer PSD, on the other hand. The polymer multilayer model (PMLM) is used to describe the growth of a single particle. Knowing the PSD and RTD of a Ziegler–Natta type of catalyst and polymerization kinetics, this model allows calculating the polymer PSD of propylene polymerization in the HSBRs. The calculated polypropylene PSDs agree well with those obtained from the industrial reactors. The results reveal that both the PSD and the RTD of the catalyst affect the polymer PSD but in different manners. The effect of RTD on the PSD is less significant in the case of a nonuniform size catalyst feed. This model also allows investigating the effects of other process parameters on the polymer PSD under steady-state conditions, including intraparticle mass- and heat-transfer limitations, initial catalyst size, and polymer crystallinity. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Predictive control of particle size distribution in particulate processes

In this work, we focus on the development and application of predictive-based strategies for control of particle size distribution (PSD) in continuous and batch particulate processes described by population balance models (PBMs). The control algorithms are designed on the basis of reduced-order models, utilize measurements of principle moments of the PSD, and are tailored to address different control objectives for the continuous and batch processes. For continuous particulate processes, we develop a hybrid predictive control strategy to stabilize a continuous crystallizer at an open-loop unstable steady-state. The hybrid predictive control strategy employs logic-based switching between model predictive control (MPC) and a fall-back bounded controller with a well-defined stability region. The strategy is shown to provide a safety net for the implementation of MPC algorithms with guaranteed stability closed-loop region. For batch particulate processes, the control objective is to achieve a final PSD with desired characteristics subject to both manipulated input and product quality constraints. An optimization-based predictive control strategy that incorporates these constraints explicitly in the controller design is formulated and applied to a seeded batch crystallizer. The strategy is shown to be able to reduce the total volume of the fines by 13.4% compared to a linear cooling strategy, and is shown to be robust with respect to modeling errors.     

Part I: Dynamic evolution of the particle size distribution in particulate processes undergoing combined particle growth and aggregation

The present study provides a comprehensive investigation on the numerical problems arising in the solution of dynamic population balance equations (PBEs) for particulate processes undergoing simultaneous particle growth and aggregation. The general PBE was numerically solved in both the continuous and its equivalent discrete form using the orthogonal collocation on finite elements (OCFE) and the discretized PBE method (DPBE), respectively. A detailed investigation on the effect of different particle growth rate functions on the calculated PSD was carried out over a wide range of variation of dimensionless aggregation and growth times. The performance (i.e., accuracy and stability) of the employed numerical methods was assessed by a direct comparison of predicted PSDs or/and their respective moments to available analytical solutions. It was found that the OCFE method was in general more accurate than the discretized PBE method but was susceptible to numerical instabilities. On the other hand, for growth dominated systems, the discretized PBE method was very robust but suffered from poor accuracy. For both methods, discretization of the volume domain was found to affect significantly the performance of the numerical solution. The optimal discretization of the volume domain was closely related with the satisfactory resolution of the time-varying PSD. Finally, it was shown that, in specific cases, further improvement of the numerical results could be obtained with the addition of an artificial diffusion term or the use of a moment-weighting method to correct the calculated PSD.     

Control of particle size distribution of ultrafine iron particles in the gas phase reaction

Experiments on the synthesis of ultrafine iron particles have been made for the control of particle size distribution using the gas phase reduction of ferrous chloride with hydrogen. The previous studies were focused on the control of particle size of ultrafine particles with the variation of the partial pressure of reactants, residence time of feed, and reaction temperature. However, it is also very important to control the size distribution of ultrafine particles. In this study, the control of particle size distribution was investigated from the standpoint of nucleation. The variation of evaporating condition at the same evaporation rate of ferrous chloride, and of the temperature gradient of reactants between preheating zone and reaction zone were adopted as experimental variables. Ultrafine iron particles having uniform size distribution could be produced under the control of evaporating condition such as the change of the surface area at constant evaporating temperature. As the temperature gradient decreased, particle size distribution became uniform and average particle sizes were also decreased.     

Part II: Dynamic evolution of the particle size distribution in particulate processes undergoing simultaneous particle nucleation, growth and aggregation

The present study provides a comprehensive investigation on the solution of the dynamic population balance equation (PBE) for particulate processes undergoing simultaneous particle nucleation, growth and aggregation. The general PBE was numerically solved in both the continuous and its equivalent discrete form using the orthogonal collocation on finite elements and the discretized PBE method, respectively. A detailed investigation on the effect of particle nucleation rate on the calculated particle size distribution (PSD) was carried out over a wide range of variation of dimensionless aggregation, nucleation and growth times. The performance (i.e., accuracy and stability) of the two numerical methods was assessed by a direct comparison of predicted PSDs and/or their respective moments to available analytical solutions. For combined aggregation and nucleation problems, the numerical error scaled with the product of the dimensionless aggregation and nucleation times. On the other hand, for combined growth and nucleation problems, the numerical error scaled only with the dimensionless growth time. For particulate systems with minimal particle growth, constant particle nucleation rate and Brownian aggregation, the total particle number approached a “steady-state” value characterized by the equilibrium of particle aggregation and nucleation rates. When the particle nucleation rate followed a pulse-like function, the PSD converged to a self-similar distribution after the end of particle nucleation. Moreover, for particulate systems exhibiting a constant particle nucleation rate and a Brownian-type particle aggregation kernel, an increase in the particle growth rate resulted in a decrease in the final total number of particles. On the other hand, for a constant particle nucleation rate and an electrostatically stabilized Brownian aggregation kernel, an increase in the particle growth rate can lead to an increase in the final total number of particles.     

A generalized population balance model for the prediction of particle size distribution in suspension polymerization reactors

In the present study, a comprehensive population balance model is developed to predict the dynamic evolution of the particle size distribution in high hold-up (e.g., 40%) non-reactive liquid-liquid dispersions and reactive liquid(solid)-liquid suspension polymerization systems. Semiempirical and phenomenological expressions are employed to describe the breakage and coalescence rates of dispersed monomer droplets in terms of the type and concentration of suspending agent, quality of agitation, and evolution of the physical, thermodynamic and transport properties of the polymerization system. The fixed pivot (FPT) numerical method is applied for solving the population balance equation. The predictive capabilities of the present model are demonstrated by a direct comparison of model predictions with experimental data on average mean diameter and droplet/particle size distributions for both non-reactive liquid-liquid dispersions and the free-radical suspension polymerization of styrene and VCM monomers.     

Measurement methods of particle size distribution in emulsion polymerization

The particle size distribution of polymer always develops in emulsion polymerization systems, and certain key phenomena/mechanisms as well as properties of the final product are significantly affected by this distribution. This review mainly focuses on the measurement methods of particle size distribution rather than average particle size during the emulsion polymerization process, including the existing off-line, on-line, and in-line measurement methods. Moreover, the principle, resolution, performance, advantages, and drawbacks of various methods for evaluating particle size distribution are contrasted and illustrated. Besides, several possible development directions or solutions of the in-line measurement technology are explored     

锂离子电池异构建模及内部传质机理探究：粒径分布的影响

锂离子电池是目前应用较广的储能设备,具有能量密度高、使用寿命长等特点。随着锂离子电池正极材料实际能量密度接近理论值,电池组装工艺参数的优化成了提升其性能的重要途径,其中电极颗粒粒径及分布是十分重要的参数。因此,本文针对石墨-LiFePO₄体系锂离子电池,利用异构模型构建单粒径和双粒径电极的几何结构,再结合Newman模型模拟其放电过程,定量研究了正极材料粒径分布对锂离子电池性能的影响,探究了存在粒径分布的电极中不同粒径的颗粒在充放电过程的作用机制。模拟结果表明,粒径的减小可以减小固相扩散系数对电池性能的影响,但会增加液相扩散阻力;而粒径的分布可以促进锂离子在电解液中的扩散,提高小粒径颗粒的锂嵌入量,但会引起极化增大,导致大颗粒的锂嵌入量降低。粒径分布宽度越大,总体粒度越大,锂离子电池的能量密度越小。选择合适的粒径分布宽度,适当减小总体粒度的大小,能有效提升电极的能量密度。研究结果对于锂离子电池电极活性材料颗粒粒径分布的选择提供了有益的基础知识和指导。     

Magnetic effects in particle adhesion. Part II. The influence of particle composition and size on deposition in a magnetic field

The effects of a magnetic field on the deposition of particles of various compositions, sizes, shapes (spherical and rod-like) on steel beads of different kinds and sizes in an aqueous environment are described. In the systems studied, the particles and the collector bear a negative charge. If both interacting bodies have a sufficiently high magnetic moment, the magnetic force causes an enhancement in the particle attachment. The process is very sensitive to the size of the depositing solids; larger particles adhere much faster. Interpretation of the results is based on the shape of the total interaction energy function consisting of electrostatic, dispersion, and magnetic contributions. The major influence of the magnetic field is in the formation of a deep secondary minimum in which the particles, moving toward the surface, are accumulated. The magnetic force enhances the flux of these particles and deepens the minimum, causing an increase in the retention efficiency.     

Particle size distribution control in emulsion polymerization

Effects of the operating policies—the initial initiator amount; the initial emulsifier amount; the monomer addition mode: batch or semibatch; and the monomer addition rate under “monomer‐starved conditions” for the control of particle size distribution (PSD)—were studied through a model that simulates batch and semibatch reactor operations in conventional emulsion polymerization. The population balance model incorporates both the nucleation stage and the growth stage. The full PSDs were reported, which have normally been omitted in earlier studies. It was shown through simulations that the broadness of the distributions, both initial (obtained after the end of nucleation) and final (after complete conversion of monomer), can be controlled by the initial initiator amount and the emulsifier amount. The higher initiator amounts and the lower emulsifier amounts favor narrower initial and final distributions. The shape of the initial PSDs and the trends in the average size and range were preserved with subsequent addition of monomer in the batch or in the semibatch mode, although the final PSD was always considerably narrower than that of the initial PSD. The addition of monomer in the semibatch mode gave narrower distribution compared to that of the batch mode, and also, lower monomer addition rates gave narrower distributions (larger average sizes), which was a new result. It was further shown through simulations that, under monomer‐starved conditions, the reaction rate closely matched the monomer feed rate. These conclusions are explained (1) qualitatively—the shorter the length of the nucleation stage and the larger the length of the growth stage (provided the number of particles remains the same), the narrower is the distribution; and (2) mathematically—in terms of the “self‐sharpening” effect. Experimental evidence in favor of the self‐sharpening effect was given by analyzing the experimental particle size distributions in detail. The practical significance of this work was proposed. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 92: 2884–2902, 2004     

A particle analyser for measuring particle size distribution and shape,on-line or in the laboratory

Norsk Hydro has developed a Particle Analyser for on-line or laboratory use, which measures particle size, size distribution and the deviation from sphericity (called nonspherical).The principle for this system is that the particles fall in a monolayer curtain in front of a high resolution CCD camera. The computer unit in the analyser measures and calculates the particle size and a sphericity factor for each particle. The data are presented as four real time trend curves, shown simultaneously for the on-line version. These curves show % oversize and fines, d₅₀ and the percentage nonspherical particles. For the laboratory version the data are presented in table and cumulative form.The on-line particle analyser has been installed in two of Norsk Hydro's prilling plants in Norway. The analyser has in both plants improved the product quality during the two years of installation.     

应用灰色系统优化水泥颗粒分布的方法研究

应用灰色关联分析方法研究了水泥颗粒级配与水泥强度之间的关系，结果表明：用原始测试数据直接进行关联度分析和均值化变换后再进行关联度分析，后者更符合水泥水化理论。