Analytic Solutions to Diffusional Deposition of Polydisperse Aerosols in Fibrous Filters

Deposition of polydisperse aerosols by Brownian diffusion was studied analytically using the penetration efficiency of monodisperse aerosols combined with the correlations among the moments of lognormal distribution functions. The analytic solutions, so obtained were validated using the exact solutions, which were applied to recalculate the filtration efficiencies of the existing experimental data for various filtration conditions. It was found that the collection efficiency of a fibrous filter should be corrected with respect to the position in the filter, if the particles are polydisperse. By considering the effect of the polydispersity of particle size, the analytic solutions showed good agreement with existing experimental data. It is believed that the present work makes it possible to determine the filtration efficiency of polydisperse aerosols in fibrous filters and to estimate errors associated with the degree of polydispersity of the particles quickly and accurately for the diffusion dominant regime.     

Analytic solutions for filtration of polydisperse aerosols in fibrous filter

In this study, analytical solutions for penetration efficiency of a polydisperse aerosol in fibrous filter were derived employing Brownian diffusion and inertial impaction as removal mechanisms. Size distribution of aerosol particles was assumed to be represented by a log-normal function during the filtration. Derived solutions were compared with the exact solution, which is not based on the log-normal assumption, showing good agreement. Error resulting from the log-normal assumption was shown to be greater in the impaction-dominant regime than in the diffusion-dominant regime due to higher size dependency of collision kernel which destructed log-normal shape of size distribution. The penetration efficiency of the analytic solution initially decreases faster and then decreases slower than that of the exact solution in the diffusion-and intermediate dominant size regimes due to its polydispersity of particle distribution, while it overpredicted the particle removal in the impaction size range because of neglect of polidispersity effect. A new solution for the most penetrating particle diameter was also provided showing the dependence on filtration velocity, fiber volume fraction, and fiber size.     

四氢呋喃和一氟二氯乙烷水合物颗粒聚结特性

实验研究了四氢呋喃（THF）水合物和一氟二氯乙烷（HCFC-141b）水合物颗粒聚结特性,将实验得到的水合物颗粒聚结粒度分布（PSD）与正态分布、对数正态分布、伽马分布、威布尔分布拟合曲线对比,探讨了初始四氢呋喃溶液和一氟二氯乙烷溶液浓度以及搅拌速度对水合物颗粒聚结的影响,并对四氢呋喃水合物和一氟二氯乙烷水合物颗粒特性进行了对比。结果表明,四氢呋喃水合物和一氟二氯乙烷水合物颗粒聚结粒径符合对数正态分布;初始溶液浓度越低、搅拌速度越大,水合物颗粒聚结粒径越小,可以起到防治水合物颗粒聚结的作用;四氢呋喃水合物颗粒粒径是一氟二氯乙烷水合物颗粒粒径的1.3倍左右,从成浆输送的角度来说,一氟二氯乙烷水合物颗粒更易于在管道中输送。     

Applications of the four-parameter distribution to electrostatic charge and particle size distribution

A four-parameter model has been developed to describe the size and charge distribution of aerosols. In the limiting case the distribution reduces to a log-normal distribution for the particle size and a normal distribution for the particle charge.A procedure for systematically determining the distribution is presented. Finally, applications of the distribution to model the optical diameter of asbestos fibers, the bimodal charge distribution of NaCl aerosols, and atmospheric aerosol size distributions are presented.     

NUCLEAR REACTOR SAFETY AEROSOLS

The deposition rate constants of the different unattached decay products of radon (²²²Rn) are evaluated from the measured radon and decay product concentrations in a 1-m³ chamber as a function of the degree of turbulence. The turbulence is induced by ventilation and/or generating heat. The coefficient of eddy diffusivity, k_e, in the theoretical formula of Crump and Seinfeld for calculating the deposition rate is examined by fitting the Crump and Seinfeld formula to our experimental results. The expression for k_e thus obtained is proportional to λ³ _v (ventilation) and W ^3/2 (generated heat). The deposition rate constant of ²¹⁸Po is found to be about three times that of ²¹⁴Pb, which means that the associated diameter of the ²¹⁴Pb particle is about twice as large as the diameter of the ²¹⁸Po particle. This difference could be due to the physical and chemical properties of the two elements     

Wet scrubbing of polydisperse aerosols by freely falling droplets

In this study, analytical solutions for removal of a polydisperse aerosol by wet scrubbing were derived employing Brownian diffusion and inertial impaction as removal mechanisms. Size distribution of aerosol particles were assumed to be represented by a time-evolving log-normal function during the scrubbing process. Derived solutions were compared with the direct integration solution, which is not based on the log-normal assumption, showing good agreement. Error resulting from the log-normal assumption was shown to be greater in the impaction-dominant regime than in the diffusion-dominant regime due to higher size dependency of collision kernel which destructed log-normal shape of size distribution. The monodisperse model significantly overpredicted particle removal in the diffusion- and impaction-dominant size regimes due to its incapability of tracing average particle size change, while it underpredicted particle removal in the intermediate size range because of neglect of polydispersity effect. A new solution for the minimum collection efficiency particle diameter was also provided. The minimum efficiency diameter was shown not to be very sensitive to the scrubbing condition and to lie around for wide range of size and concentration of water drops.     

以环氧树脂E-12包合热变色复配物微胶囊的研究

对以环氧树脂Ｅ １２为囊壁材料包合热变色复配物的微胶囊化工艺进行了研究。对于影响微胶囊粒度及结构的影响因素进行了研究,在９５００～１００００ｒ／ｍｉｎ高速乳化２０ｍｉｎ可得稳定乳液。溶剂与包囊材料质量比为７７∶１,固化配比要等当量,乳液在８０℃反应１ｈ,在９０℃反应２ｈ,可以制得粒度均匀且小于５μｍ的性能良好的微胶囊产品。     

Technical Note: Particle Extinction Coefficient for Polydispersed Aerosol Using a Harmonic Mean Type General Approximated Solution

In the present study, an approximated expression for the single particle extinction efficiency (Q _ext ) has been obtained, which was valid for a wide range of particle sizes. The approximate single particle extinction efficiency was obtained using the harmonic mean type approximation between the particle extinction efficiencies from the Rayleigh scattering and geometric scattering regions. The results were compared with the numerically calculated Mie's results, which showed that both the approximated and original Mie's results were comparable.

The approximated polydispersity of the overall extinction coefficient (b _ext ) obtained using the moment method was then tested and compared with the numerically integrated results. The approximated solution obtained showed how the b _ext effectively varied with the size distribution and greatly reduced computational time.

Consequently, a simple and straightforward method for estimating the extinction coefficient for polydispersed aerosols, which can be widely applied in atmospheric aerosol models, has been developed in this study.     

汽-液-固循环流化床蒸发器颗粒磨损特性

在不同循环流量和固含率条件下,通过1～2个月的操作运行实验,得到了汽-液-固三相循环流化床蒸发器内聚乙烯颗粒的磨损产物,分析了三相流化床的固含率和循环流量等条件对颗粒磨损速率、磨损粉体的直径和多分散度的影响,并探讨了颗粒磨损的机理。结果表明：磨损产物的粒径呈现三峰对数-正态分布,具有混合磨损机理特征;颗粒的磨损速率随固含率的减小和循环流量的增加而增大;较低固含率条件下,循环流量对颗粒的磨损速率影响较大;磨损速率随着运行时间的延长而减小;磨损粉体的粒径随固含率、循环流量、磨损时间的增加而减小;磨损颗粒的多分散度随固含率和循环流量的增加而减小。     

Generation of TiO2 Aerosols from Liquid Suspensions: Influence of Colloid Characteristics

The influence of the colloidal characteristics of aqueous TiO₂ nanoparticle suspensions and of the operating conditions on the total particle concentration and the particle size distribution of aerosols generated by nebulization has been studied. A commercial nebulization unit coupled to a diffusion dryer was used to generate aerosols using two different sources of titanium dioxide nanoparticles. Stable, concentration-tunable aerosols could be obtained for both types of nanoparticle suspensions. The effect of operating conditions during nebulization (air flow rate, purity of water source, nanoparticle concentration, and pH of the precursor suspension) was studied. The results obtained indicate that the degree of agglomeration in the liquid phase previous to aerosol formation has a direct influence both on the total nanoparticle count and on the particle size distribution of the generated aerosols.

Copyright 2013 American Association for Aerosol Research     

Simultaneous Use of Polystyrene Latex Particles of Different Sizes to Evaluate Performance of a Cyclone and Impactor

Monodisperse and polydisperse aerosols were produced to evaluate the effect of particle size on cyclone and impactor performance. Monodisperse aerosols were generated from polystyrene latex and divinylbenzene particles. Polystyrene aerosols were also generated by mixing several monodisperse aerosols of different sizes. The mixture ratio of monodisperse aerosols was found by trial and error to generate polydisperse aerosols. Generated polydisperse aerosols had multimodal aerosol size distribution, which had the same peak point as shown in the size distribution of monodisperse particles. The results show the collection efficiency curves of a cyclone and impactor, when generating monodisperse particles were coherent with those for polydisperse ones. Our findings show that the size distribution and the size range of test aerosols can be easily determined by mixing monodisperse particles of known particle sizes, using a time saving procedure.     

Etude des caracteristiques du silicium et de l''aluminium atmospherique

We have studied two important characteristics of silicon and aluminium aerosols. Concentration by neutron activation analysis (N.A.A.); an average value of 10% for the A1 and Si content was found. Median size by use of diffusion battery; with assumption of log-normal distribution of diffusion coefficient we have obtained a in the region of 10⁻² μm for both total aerosol and Si and Al aerosol.     

Analytic solution for polydispersed aerosol dynamics by a wet removal process

An analytic solution for polydispersed aerosol dynamics by wet deposition of droplets was obtained. The collection efficiency used was based on the results of Jung and Lee (Aerosol Sci. Technol. 29 (1998) 389). The derived efficiency was compared with the existing formula of Slinn (Atmospheric Science and Power Production—1979, Division of Biomedical Environmental Research, U.S. Department of Energy, Washington DC, USA, 1983 (Chapter 11)) and showed good agreement. The particle size distribution was assumed to have a log-normal function, and the Cunningham slip correction factor was simplified to introduce the moment relationship. Both analytic and numerical solutions were obtained and compared with each other. The results show that the analytic solution can simulate the scavenging of polydispersed aerosol by wet deposition for the diffusion-dominant range well. The particle diameter of minimum collection efficiency was obtained analytically. It was found that the minimum collection efficiency diameter increases with decreasing velocity and decreasing packing density.     

褐煤氧化氨解动力学的研究

在高压搅拌反应釜中对褐煤氧化氨解气液固三相反应进行了反应动力学研究。分别从搅拌速率和颗粒粒径考察了内外扩散对该反应的影响。结果表明：在实验条件下,搅拌速率高于750r／min和粒径小于60目就可以消除内外扩散对反应的影响。用polymath对动力学数据进行非线性拟合．得到了褐煤氧化氨解的本征动力学方程。如下：-rHA=21.5exp（-8520/RT）CHA^0.8PO2^0.45CNH3^0.12     

Size distribution of polydispersed aerosols during condensation in the continuum regime: Analytic approach using the lognormal moment method

An analytic solution for polydispersed aerosol condensation was obtained in the continuum regime. In this new approach, lower order moments, as compared to a previous study, were used to the log-normal aerosol size distribution, in order to obtain an analytical solution. The resultant analytic solution based on the lognormal size distribution was compared with the exact solution and proved to be in good agreement. The obtained solution was also found to be consistent to a greater degree with the exact solution was the previous analytic moment solution for the polydispersed aerosol condensation process. This is particularly true for cases in which broad size distributions exist.     

Diffusional Particle Loss Upstream of Isokinetic Sampling Inlets

Isokinetic sampling, in which a subsample is extracted from the center of laminar aerosol flow, is routinely used to collect representative particles for analysis. Isokinetic sampling minimizes wall effects, including particle loss due to Brownian diffusion to the tube wall. This particle diffusion is analogous to the heat transfer problem originally posed by Graetz in 1883. Analytical solutions to the Graetz problem have been applied to calculate particle loss averaged over the entire main flow. However, these solutions overestimate diffusional particle loss near the center of the main flow. In the present solution, confluent hypergeometric functions are used to solve analytically for particle concentration as a function of radius. The solution is integrated near the center of the main flow to determine particle loss for isokinetically sampled aerosols. Sampling efficiencies valid down to nanometer-sized particles are presented in terms of dimensionless parameters. Diffusional particle loss for isokinetically sampled aerosol can be 1.8 times less than that from the main flow aerosol. The present results can be used to design isokinetic sampling systems and to assess particle loss in these systems. For 5 nm diameter particles sampled isokinetically from a laminar flow tube (0.318 cm tube radius, 10 m length) into an ultrafine condensation particle counter, sampling efficiency is strongly affected by main flow Reynolds number, Re; sampling efficiency increases from 4.9%at Re=100 to 99%at Re=1500.     

HYDROTHERMAL SYNTHESIS OF ULTRAFINE FERRITE PARTICLES

Ultralfine Ni-, Co- and Zn-ferrite particles were synthesized by hydrothermal treatment of the same gel-like precipitates formed at room temperature. Round ultrafine particles were formed, whose size ranged from 6 to 16 nm, depending on hydrothermal conditions. The size distribution could be described by a log-normal function, and the geometric standard deviation defined as 84.1%-size/50%-side in the size distribution was determined to be about 1.2 regardless of hydrothermal temperature and time. The effect of the reaction conditions on the mean particle size was investigated. As the hydrothermal temperature rises, the particle size increases and crystallization is promoted. The effects of stirring speed in the autoclave and initial loadings of raw materials on the mean size of ferrites are negligibly small.     

Quantitative Assessment of the Effect of Surface Deposition and Coagulation on the Dynamics of Submicrometer Particles Indoors

Exposure to airborne particles indoors depends on particle concentration, which is affected by air filtration, ventilation, and particle dynamics. The aim of this work was quantitative assessment of the effects of coagulation, surface deposition, and ventilation on the submicrometer particle concentration indoors. The assessment was obtained from measured particle loss rate and deposition velocity parameters. The experiments were conducted in an experimental chamber for three different types of aerosols: environmental tobacco smoke, petrol smoke, and ambient air aerosols. Particle number concentration and size distribution were measured in the size range between 0.017 and 0.898 w m by SMPS. The average values for the overall deposition loss rates varied from 4.3 2 10 m 5 s m 1 (0.16 h m 1 ) to 1.1 2 10 m 4 s m 1 (0.39 h m 1 ). The overall deposition velocities associated with surface deposition and coagulation ranged from 9.6 2 10 m 4 cm s m 1 to 2.4 2 10 m 3 cm s m 1 , and for surface deposition only from 2.8 2 10 m 4 cm s m 1 to 6.3 2 10 m 4 cm s m 1 . For indoor conditions with an air exchange rate above 1.3 h m 1 , (natural ventilation, no filters) only a reduction in particle number of about 20% is attributed to the surface deposition and coagulation.     

Deposition and coagulation of polydisperse nanoparticles by Brownian motion and turbulence

Turbulent and Brownian coagulation rates as well as deposition coefficients of polydisperse nanoparticles were measured experimentally. The coagulation rates were obtained from the change in the total number concentration of polydisperse sodium chloride aerosols, with geometric mean diameters ranging from 30 to 120 nm, in a closed chamber at atmospheric pressure. The geometric standard deviations of the experiments were in the range of 1.55–1.65. The experimental coagulation rates took deposition rates into account, because coagulation and deposition occur simultaneously in a closed chamber. As a result of deposition, it was shown that the experimental deposition coefficients of polydisperse aerosols were agreed well with the theoretical data of Park et al. [(2001). Wall loss rate of polydispersed aerosols. Aerosol Science and Technology, 35, 710–717]. It was shown that the effect of the coagulation was much greater than that of the deposition in the high particle number concentration. In addition, the results represented that bigger turbulent coefficients, caused by higher fan rotation speeds, make the turbulent coagulation process become stronger. In the small particle size range, however, the coagulation rates tend to converge though turbulent coefficients are different. In conclusion, it was shown that experimental coagulation rates followed the values of Lee and Chen [(1984). Coagulation rate of polydisperse particles. Aerosol Science and Technology, 3, 327–334], which were calculated for polydispere aerosols in the gas-slip regime and free-molecule regime.     

煤粉粒径对HNCERI气化炉碳转化率与固/液渣层分布的影响

以中国华能集团清洁能源技术研究院（Huaneng Clean Energy Research Institute,HNCERI）两段干粉加压气化炉为研究对象,采用考虑了焦炭颗粒表面气体组分扩散效应的随机孔模型计算焦炭气化反应速率以评估碳转化率。同时,耦合熔渣子模型计算气化炉一段壁面固液渣层分布特性和热损失,研究了煤粉粒径对HNCERI气化炉碳转化率和固液渣层分布特性的影响。结果表明所构建的模型可以准确预测气化炉出口主要气体组分组成、碳转化率和气化炉一段壁面热损失;气化炉一段碳转化率受固有气化速率和停留时间控制,二段主要受颗粒停留时间控制;因此,通过减小煤粉粒径可以减小气体在颗粒表面扩散阻力,有利于提高气化炉一段碳转化率,而适量增加煤粉粒径可以增加煤粉颗粒在气化炉二段的停留时间,有利于提高二段碳转化率。模拟结果显示煤粉颗粒粒径从20μm增加到200μm,一段碳转化率从99.68%降低到了95.06%,二段碳转化率从69.03%增加到了89%。煤粉粒径对气化炉上缩口和直段壁面液态渣层分布影响很小,但显著影响固态渣层厚度的发展。