Modality of human expired aerosol size distributions

An essential starting point when investigating the potential role of human expired aerosols in the transmission of disease is to gain a comprehensive knowledge of the expired aerosol generation process, including the aerosol size distribution, the various droplet production mechanisms involved and the corresponding sites of production within the respiratory tract. In order to approach this level of understanding we have integrated the results of two different investigative techniques spanning 3 decades of particle size from 700 nm to 1 mm, presenting a single composite size distribution, and identifying the most prominent modes in that distribution. We link these modes to specific sites of origin and mechanisms of production. The data for this were obtained using the Aerodynamic Particle Sizer (APS) covering the range 0.7≤d≤20 μm and Droplet Deposition Analysis (DDA) covering the range d≥20 μm.In the case of speech three distinct droplet size distribution modes were identified with count median diameters at 1.6, 2.5 and 145 μm. In the case of voluntary coughing the modes were located at 1.6, 1.7 and 123 μm. The modes are associated with three distinct processes: one occurring deep in the lower respiratory tract, another in the region of the larynx and a third in the upper respiratory tract including the oral cavity. The first of these, the Bronchiolar Fluid Film Burst (BFFB or B) mode contains droplets produced during normal breathing. The second, the Laryngeal (L) mode is most active during voicing and coughing. The third, the Oral (O) cavity mode is active during speech and coughing. The number of droplets and the volume of aerosol material associated with each mode of aerosol production during speech and coughing is presented. The size distribution is modeled as a tri-modal lognormal distribution dubbed the Bronchiolar/Laryngeal/Oral (B.L.O.) tri-modal model.     

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。     

Modeling of the evolution with length of bubble size distributions in bubble columns

Many of the existing methods, for the determination of the specific interfacial area in bubble columns, consider the column in a dynamic equilibrium between bubble coalescence and breaking-up. The aim of this work is to study if this consideration can be considered true for low superficial gas velocities. Two existing models have been chosen from literature in order to predict the break-up [Wang, T., Wang, J., Jin, Y., 2003. A novel theoretical breakup kernel function for bubbles/droplets in a turbulent flow. Chemical Engineering Science 58, 4629-4637] and the coalescence [Lehr, F., Millies, M., Mewes, D., 2002. Bubble size distributions and flow fields in bubble columns. A.I.Ch.E. Journal 48, 2426] rates. In order to confirm the validity of the models, predictions were compared with experimental results obtained by image analysis. Several simulations were performed for different superficial gas velocities and initial bubble size distributions. The column length needed to reach dynamic equilibrium was calculated for each simulation. The results show that the necessary length to reach the dynamic equilibrium does not depend on the shape of the initial distribution, but essentially on its Sauter mean diameter. The necessary length to reach the dynamic equilibrium is very important for low superficial gas velocities. The assumption that the entire column is in dynamic equilibrium is in general not valid. Therefore, the initial Sauter mean diameter and the total column length are important parameters for the determination of the specific interfacial area.     

A mixed Weibull model for size reduction of particulate and fibrous materials

This paper describes a simple alternative to the classical population balance breakage model, which characterizes and controls the size distribution of particles submitted to a reduction process. The new approach is based on cumulative distribution functions of mixed random variables. Results indicate that a Weibull mixture distribution function adequately models the size of particles submitted to various breakage processes. The model was further applied to experimental reduction processes with apparently random breakage probability and yielded good estimates of the unbroken particle and fragment distributions. Use of these results for direct and indirect prediction of the size alteration under dimensional reduction processes is discussed.     

Estimate of confidence intervals for geometric mean diameter and geometric standard deviation of lognormal size distribution

Confidence of particle size distribution, which is the size distribution of sample particles selected from a large population with lognormal size distribution, has been studied theoretically. Theoretical equations were derived from the basic formulas commonly used in statistics to estimate confidence intervals for geometric mean diameter and geometric standard deviation. Computer simulation has provided size distribution of sample particles by random sampling in order to confirm the theoretical equations. For both geometric mean diameter and geometric standard deviation, the confidence intervals were calculated so that both values of population were placed approximately in the middle of the intervals. The tendencies for the intervals to decrease with an increase in sample particle number and/or significance level, and with a decrease in geometric standard deviation, were reasonable in statistics. The proposed theoretical equations should be useful for estimating confidence of lognormal size distribution.     

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.     

Comparative study of elemental mass size distributions in urban atmospheric aerosol

Elemental mass size distributions in aerosols collected at four different urban sites with gradually increasing overall aerosol mass concentration are presented, compared and discussed in the present paper. The aerosol samples were collected with cascade impactor and stacked filter unit samplers, and were analyzed by particle-induced X-ray emission spectrometry and instrumental neutron activation analysis. Typical coarse-mode elements, i.e., Na, Mg, Al, Si, P, Ca, Ti, Fe, Ga, Sr, Zr, Mo and Ba, exhibited unimodal size distributions at all four urban locations studied, and the mass median aerodynamic diameters were increased with aerosol pollution level. Elements typically related to high-temperature or anthropogenic sources, i.e., S, Cl, K, V, Cr, Mn, Ni, Cu, Zn, Ge, As, Se, Br, Rb and Pb, either had a unimodal size distribution with most or their mass in the fine size fraction or clearly showed a bimodal size distribution at the urban background site. However, significant differences between the size distributions of four sampling sites were noted. There was a clear tendency for the accumulation mode to decrease and for the coarse mode to increase with increasing total aerosol mass concentration. A pronounced resuspension of the soil and roadway dust associated with the fine aerosol particles that were deposited on the ground surface previously, and the condensation process of volatile precursor gases on the already existing aerosol particles can explain the observed tendencies. The elemental mass size distributions derived for the polluted urban environments differ from those typically observed for industrial, combustion or automotive sources. A consequence of the diversity in the size distributions on the PM_2.5 speciation concept is also presented.     

Evolution of atmospheric aerosol particle size distributions via Brownian coagulation numerical simulation

Current atmospheric observations tend to support the view that continental tropospheric aerosols, particularly urban aerosols, show multimodal mass distributions. One of the obvious mechanisms causing the multimodality is the mixing of different primary sources. Other modes involve dissimilar aerosol formation processes in the atmosphere. Fine aerosol particles are generated from secondary processes such as nucleation, condensation and chemical reaction, whereas coarse particles usually consist of dust, fly ash and mechanically generated aerosols. With the use of a newly developed computer code GROWTH in our laboratory, we report here the simulated results of Brownian coagulation dynamics involving multimodal mass density functions for long periods of time. In our model calculations we assume that the aerosol particles are well mixed in an atmospheric volume so that spatial variation in the distribution is negligible. Our accurate numerical simulation of the Brownian coagulation dynamics indicates that once formed, an atmospheric multimodal aerosol distribution in the range 0.1 to 100 μm will maintain its identity for a very long period of time (at least hours) unless “atmospheric perturbations” such as meteorological instabilities, rain-washout and gravitational settling occur. It is our belief that understanding the complex domain of atmospheric aerosols requires systematic investigation of each process. This paper is a continuation of such an investigation.     

Experimental investigation of the light extinction method for measuring aerosol size distributions

The independent and the dependent models of light extinction methods were two new methods for measuring the particle size distribution. Some experiments were carried out to confirm these methods. The experimental results of the measurement of latex particles ranged from 0.091 to 9.85 μm and some samples of TiO₂ powder were presented. Experimental results have shown that these methods have a larger measurable range from about 0.01 to 10 μm, high accuracy and a short measurement time. The optimum value of I/I₀ in the measurement should lie between 0.4 and 0.9. The independent model of light extinction method can even measure ‘multi-peaks’ polydisperse aerosols.     

Numerical methods for retrieving aerosol size distributions from optical measurements of solar radiation

Retrieving aerosol size distributions from ground measurements is an ill-posed problem. Several methods have been developed to “regularize” it, giving a stable approximation of its solution. The aim of this paper is to review the techniques usually adopted and present some new approaches. The case of solutions retrieved both in their parametric and non-parametric form is considered. For all the considered methods the problem of choosing an optimal level of regularization is also discussed. Finally, numerical results comparing some inversion techniques in a real case are presented.     

Particle size monitoring in a fluidized bed using pressure fluctuations

Starting from the premise that the standard deviation, σ_p, of the pressure fluctuations in a fluidized bed is linearly proportional to excess gas velocity, it follows that σ_p is a function of particle size. This relationship has previously been recognised as a potential route to the continuous monitoring of particle size in fluidized bed processing, and is attractive because of the relative ease with which pressure and pressure fluctuations can be measured. Simple expressions with no fitted parameters can be derived for the case where the constant of proportionality between σ_p and excess gas velocity is unaltered by changes in mean particle size. The results of experiments with mixtures of silica sand prepared by mixing two base batches, with a different mean size, in incrementally varying proportions provide good support for the general validity of the model.     

About bubble breakup models to predict bubble size distributions in homogeneous flows

We present results of a study of the equilibrium between coalescence and breakup of bubbles in homogeneous media with isotropic turbulence. The Boltzmann equation for the particle distribution function (pdf) was evaluated in steady state, using a multigroup approach. Binary bubble breakup was assumed. We used uniform function, delta function, and the model proposed by Luo and Svendsen (1996) for the bubble size distributions resulting from a breakup. The bubble breakup rate was calculated with Luo and Svendsen (1996) and Prince and Blanch (1990) models. Significant differences in bubble breakup rate, and therefore in bubble size distribution, are predicted by both models. The models were compared to the bubble size distributions measured by Boyd and Varley (1998) in air-water flow. The transient response of the bubble size distribution and interfacial area density was also analyzed. This work is of significance in the prediction of reaction rates when they are dependent on bubble size distribution.     

Recovery of molecular weight distributions from transformed domains. Part I. Application of pgf to mass balances describing reactions involving free radicals

We present a general framework for the application of a transform technique, probability generating functions (pgf), to mass balances that describe free radical reactions, in particular synthesis or modification of polyolefins. Contributions of specific reactions to the mass balances are identified and transformed separately, so that a modular approach is possible for the construction of the pgf balance equations for different free radical processes. This simplifies the transformation step hopefully making the method useful to more people. Three examples taken from the literature are transformed using this modular method showing its ease of use. In Part II of this work, the resulting transforms are inverted to recover the complete molecular weight distribution.     

Newtonian power curve and drop size distributions for vibromixers

Power input data are presented for a twin flat disk up-and-down moving (vibromixer) impeller operating in a small vessel with a range of Newtonian liquids. Vibromixer power number and Reynolds number are defined and are used to establish the Newtonian power curve for this type of mixer. Drop size distributions are presented for xylene-in-water dispersions under turbulent flow conditions in the vibromixer and are shown to vary with the maximum velocity of the disk (2πAf). The Sauter mean drop diameter of the distribution is related to the vibromixer Weber number, (We =ρ(2πAf)²D/σ), by an equation of the type d₃₂/D = C (We)^?3/5 with the coefficient C = 0.37.     

Modelling local bubble size distributions in agitated vessels

Photography and capillary suction probe were used to measure local bubble size distributions (BSDs) from Rushton turbine agitated (14/200 L) air-tap water and CO₂-n-butanol dispersions. A multiblock stirred tank model with population balances (PBs) for bubbles was created to describe local BSDs in agitated vessels. Unknown parameters in breakage and coalescence models were adjusted by comparing the predicted and measured local BSDs. The BSDs from both investigated systems and varying vessel-operating conditions were included simultaneously to the fitting. The adjusted models were incorporated to MUSIG PB model in CFX-5.7 and tested for the laboratory stirred tanks. The multiblock model showed to be an optimal trade-off between the accuracy and CPU time for the investigation of gas-liquid hydrodynamics and validation of closure models. As a result of fitting, the adjusted model seems to describe local BSDs more accurately in agitated vessels than the model of Lehr et al. [2002. Bubble-size distributions and flow fields in bubble columns. A.I.Ch.E. Journal 48, 2426-2443], which has been successful in bubble column studies. This shows that phenomenological breakage and coalescence closures need experimental validation for various flow environments.     

Molecular weight distributions and size fractionations of H-coal liquids

This Paper deals with a comparative study on the use of gel permeation chromatography (g.p.c.) and vapour pressure osmometry (v.p.o.) to obtain molecular weight data for the hexane-soluble fractions of three H-coal liquids. The use of two types of column packing materials, polyvinylacetate and styrene-divinylbenzene copolymer gels, is described. A successful, preparative use of the polyvinylacetate gel to fractionate the hexane-soluble fraction of H-coal liquid, atmospheric still overhead (ASO), has been established. Molecular weight data obtained by v.p.o. for the benzene-soluble fraction and the pyridine-soluble fraction of the three H-coal liquids are reported. Solvent extraction has been utilized also to find the amount of oil, asphaltenes and asphaltols in the three H-coal liquids.     

The effect of wetting liquid droplet size on the growth of agglomerates during wet drum granulation

Results of investigation of the effect of wetting liquid droplet size on the growth of agglomerates during wet drum granulation of dolomite flour of selected grain-size composition which guaranteed geometrical similarity were discussed.

The process of granulation was carried out batch-wise in a drum granulator 0.5 m in diameter and 0.4 m long at rotational speed 0.33 s⁻¹ and constant volumetric drum filling degree =0.1. On the bed tumbling in the drum, the wetting liquid (distilled water) was supplied at a constant flow rate Q_w=12×10⁻³ m³/h. The size of wetting droplets was changed using various air flow rates through pneumatic spray nozzles in the range Q_a=1.0 to 3.0 m³/h and applying a sprinkler which supplied (drop-wise) the liquid uniformly along the entire drum length. In the whole experimental cycle, constant mean saturation degree of the feed equal to S=0.293 was used. Relationships determining the effect of wetting droplet size and particle size distribution of the raw material on the rate of agglomerate growth during drum granulation were developed.     

间歇结晶过程中几种可能的粒度分布

对间歇溶液结晶过程,依据粒数衡算方程,在忽略二次过程如聚集、破碎和老化等且混合良好情况的假设下,采用分离变量方法对粒度相关生长或生长分散的粒度分布进行理论分析,推导出间歇结晶过程中的几个粒数密度与结晶时间和晶体粒度的关系式.这些关系式可以用于间歇结晶过程中,选择合适的晶体生长机理与测定线性晶体生长速率,预测粒度分布与优化结晶过程,以及回归粒度分布.结果表明,本方法在溶液结晶过程中具有良好的应用价值.