Numerical simulation of nanoparticle synthesis in diffusion flame reactor

A computational model combining the fluid dynamics with the particle kinetics was employed to study TiO₂ nanoparticle synthesis in a diffusion flame reactor. A one-step chemical kinetics approach was used to model titanium tetraisopropoxide (TTIP) decomposition that leads to homogeneous nucleation and particle formation. The momentum, heat, and mass transfer, Brownian coagulation and diffusion, surface growth, coalescence and thermophoresis have been taken into account. Based on the particle size distributions, an efficient quadrature method of moments was allowed to approximate the general dynamics equation of particle, and the eddy dissipation concept (EDC) combustion model was used to estimate the flame temperature field. Excellent agreements between the model predictions and experimental data, with respect to the flame temperature distribution and particle kinetics, are reached. By taking the particle size and surface area as independent variables, the full distributions of volume equivalent diameters, evolution of the agglomerate number, the geometric standard deviation based on volume and agglomerate fractal nature, mean primary particle size and the number of primary particles per agglomerate are revealed. The variation of oxygen flow rate has an important influence on the temperature distribution and hence on the particle kinetics accordingly.     

Experimental and theoretical determination of the particle size of hydrotreating catalysts of different shapes

Equations for calculating the total geometric volume and external area of lobe-shaped catalytic particles as a function of easy-to-determine geometric parameters are presented in this work. Particle density was experimentally determined by the ASTM C-128 standard method, which, together with the average weight of various particles, was used to estimate the total external volume. The calculated total geometric volume was then compared with that obtained by the proposed equations for the purpose of validation. A variety of porous and non-porous particles with different shapes and sizes were employed for validation of both the experimental method and the proposed equations. In the absence of an experimental approach to determine external area, the corresponding equations were validated indirectly by comparing bulk densities determined by the ASTM C-29 experimental method with those calculated with particle density and bed void fraction. Calculated values of external volume and surface were in good agreement with experimental data.     

Analysis of non-spherical polydisperse particle growth in a two-dimensional tubular reactor

Polydisperse aggregate particle growth considering coalescence, coagulation, generation and spatial transport processes is studied in a two-dimensional reactor for the first time. Effects of two-dimensional spatial transport processes, such as convection, diffusion, deposition and thermophoresis as well as nucleation, coagulation and coalescence are of primary interests. An efficient particle dynamics model based on two sets of coupled sectional equations (J. Aerosol Sci. 32 (2001) 565) is used to facilitate the severe computation loads for analyzing the growth of non-spherical polydisperse particles in an axi-symmetric two-dimensional geometry. Fluid dynamics calculations indicate the existence of non-uniform distributions of temperature and flow fields in the radial direction as well as in the axial direction inside the reactor. Particle dynamics simulations also demonstrate the significant inhomogeneous spatial distributions of the characteristics of aggregate particles. The present two dimensional calculations for reactor temperatures and particle size distributions are in agreement with the previous experimental data. The validity of simplified one-dimensional analysis is also evaluated against the present two-dimensional analysis. While the one-dimensional analysis agreed well with the spatially two-dimensional one for the cases of low flow rates, it resulted in significant errors for high flow rates.     

Gloss control additives for PVC

Matte finishes are characterized by a lack of specular (mirror-like) reflectance. Using equations from the literature which relate surface roughness to specular reflectance, surface roughness values were calculated for various particle size inclusions assuming that the particles protruded half in half out of the surface and that 20% of the surface area is covered by the particles. Specular reflectance values at 85 deg illumination were calculated from the surface roughness calculated data. Based on these calculations, a series of large particle size monodispersed emulsion polymers was prepared using Ugelatad polymerization techniques and evaluated for their surface altering effects in PVC. Considering that the model contained many approximations, excellent agreement was found between the predicted and measured particle size effect on the surface gloss.     

Computational Modeling of Silicon Nanoparticle Synthesis: II. A Two-Dimensional Bivariate Model for Silicon Nanoparticle Synthesis in a Laser-Driven Reactor Including Finite-Rate Coalescence

In this work, a two-dimensional model was developed for silicon nanoparticle synthesis by silane thermal decomposition in a six-way cross laser-driven aerosol reactor. This two-dimensional model incorporates fluid dynamics, laser heating, gas phase and surface phase chemical reactions, and aerosol dynamics, with particle transport and evolution by convection, diffusion, thermophoresis, nucleation, surface growth, coagulation, and coalescence processes. Because of the complexity of the problem at hand, the simulation was carried out via several sub-models. First, the chemically reacting flow inside the reactor was simulated in three dimensions in full geometric detail, but with no aerosol dynamics and with highly simplified chemistry. Second, the reaction zone was simulated using an axisymmetric two-dimensional CFD model, whose boundary conditions were obtained from the first step. Last, a two-dimensional aerosol dynamics model was used to study the silicon nanoparticle formation using more complete silane decomposition chemistry, together with the temperature and velocities extracted from the reaction zone CFD simulation. A bivariate model was used to describe the evolution of particle size and morphology. The aggregates were modeled by a moment method, assuming a lognormal distribution in particle volume. This was augmented by a single balance equation for primary particles that assumed locally equal number of primary particles per aggregate and fractal dimension. The model predicted the position and size at which the primary particle size is frozen in, and showed that increasing the peak temperature was a more effective means of improving particle yield than increasing silane concentration or flowrate.     

On-line measurement of ultrafine aggregate surface area and volume distributions by electrical mobility analysis: I. Theoretical analysis

Electrical mobility analyzers are usually calibrated for spherical particles, and provide number, area and volume distributions for spherical particles. However, these instruments cannot be directly used to obtain the surface area and volume distributions for aggregates. Aggregates are important in technological applications, such as the manufacture of fine powdered materials, and in air pollution and atmospheric sciences. Thus, nanoparticle chain aggregates of low fractal dimension are another important limiting case, in addition to spheres; a method is described which makes it possible to relate aggregate surface area and volume distributions to the electrical mobility diameter. This is accomplished by equating the migration velocity of an aggregate to that of a sphere. Particles of equal migration velocities will trace similar paths in the mobility analyzer and have the same mobility diameter (neglecting the Brownian diffusive spread). By equating the migration velocities of a sphere and aggregate, the number and size of the primary particles composing the aggregate can be related to the diameter of a sphere with the same migration velocity.The calculation of aggregate surface areas and volumes requires two theoretical “modules”, one for the drag on the aggregates and the other for aggregate charging efficiency. Two modules selected from the literature were used. The results indicate that the surface area distributions of aggregates with random orientation are somewhat over-predicted when calculated directly from the mobility diameter. However, the volume distributions are greatly over-predicted, up to a factor of ten compared with values based on the mobility diameter. The affect of aggregate orientation on surface area estimates was also examined.     

Particle Size Distribution of Coprecipitated Mn-Zn Ferrite Powders

The particle size distribution of 0.07- to 0.35-μm powders was measured by quantitative electron microscopy using an areal analysis. Measurements of at least 15 particles were required to characterize each size distribution. The specific surface area calculated from the size distributions satisfactorily agreed with that measured by the BET method. For the powders with surface area of 4.4 to 9.7 m²/g, the particle size distributions were generally narrow. In many cases the distributions were near log normal.     

Computational Modeling of Silicon Nanoparticle Synthesis: I. A General Two-Dimensional Model

A two-dimensional model has been developed for silicon nanoparticle synthesis by silane thermal decomposition driven by laser heating in a tubular reactor. This fully coupled model includes fluid dynamics, laser heating, gas phase and surface phase chemical reactions, and aerosol dynamics which includes particle transport and evolution by convection, diffusion, thermophoresis, nucleation, surface growth, and coagulation processes. A moment method, based upon a lognormal particle size distribution, and a sectional method are used to model the aerosol dynamics. The simulation results obtained by the two methods are compared. The sectional method is capable of capturing the bimodal behavior that occurs locally during the process, while the moment method is computationally more efficient. The effect of operating parameters, such as precursor concentration, gas phase composition, inlet gas velocity and laser power input, on the characteristics of the particles produced are investigated. Higher temperature generates more large particles with higher precursor conversion. Shorter residence time, from high inlet velocity, produces more small particles at the cost of lower precursor conversion. Increasing H₂ concentration suppresses particle formation by reducing the rates of gas phase and surface reactions, leading to fewer and smaller particles. In addition, the relative importance of the interconnected mechanisms involved in the particle formation is considered. The results make clear that spatial variations in reaction conditions are the primary source of size polydispersity and generation of non lognormal overall size distributions in a laser-driven process like that considered here.     

Numerical analysis of particle mixing in a rotating fluidized bed

This paper describes the numerical analysis of particle mixing in a rotating fluidized bed (RFB). A two-dimensional discrete element method (DEM) and computational fluid dynamics (CFD) coupling model were proposed to analyze the radial particle mixing in the RFB. Spherical polyethylene particles (Geldart group B particles) were used as model particles under the assumptions that they were cohesionless and mono-disperse with their diameter of 0.5 mm.The validity of the proposed model was confirmed by the comparison between the calculated degree of particle mixing and the experimental one, which was obtained by measuring the lightness of the recorded image taken by a high-speed video camera. Effects of the operating parameters (gas velocity, centrifugal acceleration, particle bed height, and vessel radius) on the radial particle mixing rate were numerically analyzed. The radial particle mixing rate was found to be strongly affected by the bubble characteristics, especially by the bubble size. The mathematical model for the rate coefficient of particle mixing as functions of operating parameters was empirically proposed. The radial particle mixing rate in a RFB could be well correlated by the three dimensionless numbers: dimensionless acceleration (Ac), bubble Froude number (Fr_b), and dimensionless radius on the surface of particle bed (β_s).     

Study of the rheology of aqueous radiation curable polyurethane dispersions modified with associative thickeners

The chemistry of radiation curable polyurethane dispersions is outlined with an emphasis on the microstructure of the aqueous polymer dispersion and the possible interactions with associative thickeners. The steady-shear flow was studied for two model dispersions prepared from the same unsaturated polyurethane but showing significantly different particle size distributions. A hydrophobically modified ethoxylated urethane (HEUR) associative thickener with a linear structure was incorporated at different amounts to the dispersions with varying particle volume fractions. The steady-state viscosity at 25 and 10 °C was always reached quickly after instant flow rate changes so that no significant thixotropic effects were reported within the experimental timescale. Without thickener, the flow curves of the two model dispersions exhibited a Newtonian behavior except at the highest volume fractions where shear thinning became apparent. The maximum packing values determined from the Krieger–Dougherty relationship were essentially the same for the two systems. In the presence of thickener, the flow curves were characterized by a Newtonian plateau followed by a marked shear thinning region even at low particle volume fractions. This behavior typically suggests the formation of a physical network between polyurethane particles and thickener molecules partly adsorbed onto the polymer surface. The zero-shear viscosity of the two dispersions was compared with respect to: (i) particle volume fraction and (ii) particle surface area at different HEUR concentrations. At a given volume fraction, the particle size affects the viscosity of thickened models. As a corollary, a relationship is found between the particles size and the level of thickener required to reach a target viscosity. This study offers practically relevant data in terms of application conditions and provides a better insight into the thickening protocol.     

On-line measurement of ultrafine aggregate surface area and volume distributions by electrical mobility analysis: II. Comparison of measurements and theory

Differential mobility analyzers (DMAs) are sometimes used to characterize aerosols that contain aggregates of low fractal dimension. However, these instruments are normally calibrated for spherical particles and the calibrations are not directly applicable to aggregates. A method proposed by Lall and Friedlander [(2006). On-line measurement of ultrafine aggregate surface area and volume distributions by electrical mobility analysis, I: Theoretical analysis. Journal of Aerosol Science, in press] for characterizing ultrafine aggregate number, surface area and volume distributions by electrical mobility measurements was tested experimentally. The method is best applied to idealized aggregates composed of uniform primary particles smaller than the mean free path of the gas. It relates the number and size of the primary particles that compose the aggregate to the mobility diameter of a spherical particle. Aggregate number distributions were obtained by calculations based on aggregate drag and aggregate charging efficiency; surface area and volume were obtained by summing over the primary particles that compose the aggregate.The theory was tested experimentally using silver aggregates generated by an evaporation–condensation method. Primary particle diameter was $18.5\pm 3.5\mathrm{nm}$. To obtain distributions with respect to particle volume, aggregates were sintered to form spheres. It was assumed that the aggregate volume does not change upon sintering and coagulation was neglected. Thus the number of aggregates in a given volume range (number distribution, $\mathrm{d}N/\mathrm{dlog}v$ vs. $v$) should not change after sintering. Agreement between aggregate number distribution based on idealized aggregates and the values measured for spheres of sintered aggregates was good. The agreement also indicates that the aggregate volumes based on idealized aggregates were accurate. The aggregate number distribution and volume based on the conventional calibration for spheres were significantly overpredicted. A separate experimental test of the theory was made using literature data for diesel aggregates. Primary particle diameter was $31.9\pm 7.2\mathrm{nm}$. Aggregate volumes calculated from theory agreed well with aggregate volumes measured by transmission electron microscope analysis.     

Intraparticle effects in char combustion. III transient studies

Unsteady state mass and energy balance equations along with a probabilistic model to predict the surface area evolution, constitute the model developed to study the dynamics of single particle char combustion. The transients and the ignition-extinction phenomenon are analyzed with the aid of the pseudo-steady state structure of the problem. There exists a critical particle size, ambient temperature, ambient oxygen concentration and boundary layer thickness above which the particle ignites. There is an optimum particle size for which the burning time is a minimum. Experimentally observed extinction phenomenon of artificially ignited particles is predicted by the model. Also, it is found that the extinction radius decreases with increase in ambient O₂ concentration, which is in qualitative agreement with the experimental results. The model is compared with the simple shrinking core model.     

Modeling of the monomer role and the coalescence limitation in primary particle growth

The general dynamic equation (GDE) has been numerically solved to simulate the growth of ultrafine particles (UFPs) in a tubular aerosol reactor, approximating the particle size distribution by a lognormal function. The GDE includes all the terms describing diffusion, thermophoresis, nucleation, condensation and coagulation. We have also considered the efficiency of liquid-like coagulation to primary particles. The data calculated from our model were compared with those from the previous model and also with some experimental results from a TiO₂ UFP generator. The condensation term, which we split from a single coagulation term in the previous model, well described the monomer contribution to the particle growth. Introduction of one adjustable parameter, the efficiency of coagulation, was successful in limiting the growth of primary particles and fit the experimental data.     

Simulation of nano-particle formation in a wall-heated aerosol reactor including coalescence

The initial stage of particle formation during gas phase synthesis is characterized by a high concentration of particles that undergo rapid coagulation. The surface area of the agglomerates is reduced by coalescence. In this study a model is presented that accounts, in addition to nucleation and coagulation, for the shape of the particles by tracing both the particle volume and the total surface area density of the agglomerates. A moment model, based on a unimodal lognormal size distribution gives the concentration, polydispersity, and average volume of the particles as a function of space and time. The total surface area density of the particles is determined by solving an additional transport equation, incorporating a linear decay law to describe the decrease in surface area of a coalescing structure. The aerosol dynamics are calculated in combination with the convective and diffusive particle transport in a spatially inhomogeneous aerosol reactor.     

A One-Dimensional Model for Coagulation,Sintering, and Surface Growth of Aerosol Agglomerates

The size of the primary particles in aerosol agglomerates is determined in part by the interplay of surface growth, coagulation, and sintering. These processes are modelled by a one-dimensional (1-D) discrete-sectional model, DISGLOM2, which predicts the evolution of agglomerate and primary particle size distributions. DISGLOM2 is an extended version of DISGLOM (Rogak 1997), in which particles smaller than the "melting diameter" were assumed to sinter instantly while bigger particles did not sinter at all. Gradual sintering, "condensational obliteration" (whereby primary particles are lost during heavy surface growth), and diffusional wall deposition have been incorporated into DISGLOM2. Results from DISGLOM2 were comparable with those from 2-D sectional models, but DISGLOM2 was much faster. In addition, DISGLOM2 includes the effects of "condensation" of small spherical particles on large agglomerates, which were not modelled previously. The effect of condensation was shown to be significant at low temperature. DISGLOM2 was used to predict the primary particle diameter of titania particles generated by precursor reaction. By adding gradual sintering, the growth rate of agglomerate particles by coagulation was slightly decreased and the primary particle size considerably increased compared with the results given by DISGLOM. Although DISGLOM2 is an efficient model of the relevant physical processes, the predictions are sensitive to the kinetics of precursor reactions and particle sintering, which can be difficult to characterize in real experimental systems.     

Analysis of iron particle growth in aerosol reactor by a discrete-sectional model

The growth of iron particles by thermal decomposition of Fe(CO)₅ in a tubular reactor was analyzed by using a one dimensional discrete-sectional model with the coalescence by sintering of neighboring particles incorporated in. A thermal decomposition of Fe(CO)₅ vapor to produce iron particles was carried out at reactor temperatures varying from 300 to 1,000°C, and the effect of reactor temperature on particle size was compared with model prediction. The prediction exhibited good agreement with experimental observation that the primary particle size of iron was the largest at an intermediate temperature of 800°C. Model prediction was also compared with Giesen et al.’s [1] experimental data on iron particle production from Fe(CO)₅. Good agreement was shown in primary particle size, but a considerable deviation was observed in primary particle size distribution. The deviation may be due to an inadequate understanding of the sintering mechanism for the particles within an agglomerate and to the assumption of an ideal plug flow in model reactor in contrast to the non-ideal dispersive flow in actual reactor.     

颗粒孔结构的积木分形模型

构造了立方和四面体两种积木分形体，得到一般积木分形体模型，导出关联表面积和体积增量的3个分形表达式，并分析了表面分数维的几何意义. 实验结果表明，利用该模型的表面积与体积增量分形表达式可以从压汞和BET的实验数据计算表面分数维，相关系数较高. 对同一种颗粒，两种实验方法可以得到相同的分数维. 讨论了体积增量的计算方法.     

Emulsion polymerization of styrene: Simulation the effects of mixed ionic and non-ionic surfactant system in the presence of coagulation

A detailed model was developed for emulsion polymerization of styrene in batch reactor to predict the evolution of the product particle size distribution. The effect of binary surfactant systems (ionic/non-ionic surfactants) with different compositions was studied. The zero–one kinetics was employed for the nucleation rate, with the model comprising a set of rigorously developed population balance equations. The modeling incorporated particle formation by both nucleation and coagulation phenomena. The partial differential equations describing the particle population were discretized using finite volume elements. Binary surfactant systems, comprising sodium dodecyl sulfate (SDS) as anionic, and a commercial polyether polyol (Brij35^®) as non-ionic surfactants, were examined with different mass ratios. Increasing non-ionic surfactant mass fraction in binary surfactant system showed the decrease of particle number due to intensifying the coagulation between particles. Broader particle size distributions with greater average particle size were obtained with non-ionic surfactant comparing those obtained with anionic one.     

Revisiting shrinking particle and product layer models for fluid-solid reactions - From ideal surfaces to real surfaces

A general model based on an arbitrary geometry was developed for reactive solid particles which have surface defects and porosity. The model equations comprising intrinsic kinetics as well as mass transfer effects through the product layer and the fluid film surrounding the solid particle were derived for shrinking particle and product layer models. From the model equations, the fluid (gas or liquid) concentrations at the reaction surface can be calculated and the change of the solid phase can be predicted. The approach was illustrated with monodisperse particle distributions in batch reactors. Complex kinetics as well as simpler special cases were treated. In general, the model predicts a higher reaction order with respect to the solid component than the previous ideal models, which assume slab, cylindrical or spherical geometries for solid particles.