A Moment Method of the Log-Normal Size Distribution with the Critical Size Limit in the Free-Molecular Regime

The present work proposes new formulations of the moment in the free-molecular size regime involving (1) boundary equations at the critical size for evaporation, condensation, and nucleation, and (2) b coefficient functions for coagulation that are improved by two parameters (standard deviation and nondimensional critical size). Using these formulations based on the error function, the critical particle size is readily introduced into the log-normal moment method for applications in general aerosol dynamics. In the situation that the particle size distribution is located near the critical size, the proposed moment method (which considers the critical size limit) improves predictions of total particle number and particle volume concentrations as compared with previously well-used log-normal moment methods for sizes ranging from 0 to ∞. However, as the size distribution approaches to the continuum size regime, the influence of the critical size becomes smaller. Thus, the new formulations are expected to improve microphysical parameterization in the free-molecular regime in aerosol-transport models.

Copyright 2014 American Association for Aerosol Research     

A Study of the Size Distribution and Stability of Colloidal Gas Aphrons Using a Particle Size Analyzer

Abstract

Application of colloidal gas aphrons (CGA) in decontaminating soils and aqueous solutions is one of the emerging innovative technologies. This paper addresses the size distribution and stability of CGAs as studied by using a particle size analyzer. Cationic, anionic, and nonionic surfactants were used to generate the CGAs. Size distribution spectrum and volume fraction of microbubbles in sample solutions were studied as functions of time. The effects of surfactant concentrations used to produce CGAs and the presence of an electrolyte, such as sodium chloride, on the characteristics of the suspension were also studied.     

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.     

Investigating particle emissions and aerosol dynamics from a consumer fused deposition modeling 3D printer with a lognormal moment aerosol model

ABSTRACT

Particle emissions from consumer-fused deposition modeling 3D printers have been reported previously; however, the complex processes leading to observed aerosols have not been investigated. We measured particle concentrations and size distributions between 7 nm and 25 μm emitted from a 3D printer under different conditions in an emission test chamber. The experimental data was combined with a moment lognormal aerosol dynamic model to better understand particle formation and subsequent evolution mechanisms. The model was based on particles being formed from nucleation of unknown semivolatile compounds emitted from the heated filament during printing, which evolve due to condensation of emitted vapors and coagulation, all within a small volume near the printer extruder nozzle. The model captured observed steady state particle number size distribution parameters (total number, geometric mean diameter and geometric standard deviation) with errors nominally within 20%. Model solutions provided a range of vapor generation rates, saturation vapor pressures and vapor condensation factors consistent with measured steady state particle concentrations and size distributions. Vapor generation rate was a crucial factor that was linked to printer extruder temperature and largely accounted for differences between filament material and brands. For the unknown condensing vapor species, saturation vapor pressures were in the range of 10^?3 to 10^?1 Pa. The model suggests particles could be removed by design of collection surfaces near the extruder tip.

Copyright © 2018 American Association for Aerosol Research     

An Evaluation of Mass-Weighted Size Distribution Measurements with the Model 3320 Aerodynamic Particle Sizer

The ability of the Model 3320 aerodynamic particle sizer (APS) to make accurate mass-weighted size distribution measurements was investigated. Significant errors were observed in APS size distribution measurements with measured mass median aerodynamic diameters (MMADs) as much as 17 times higher than from cascade impactor measurements. Analysis of APS correlated time-of-flight and light scattering data indicated that the MMAD distortions were due to a few anomalous large particle measurements (～0.1% of the total measurements) with surprisingly low scattered light. Computational fluid dynamics modeling indicated that these anomalous measurements were due to particles that deviated from the intended aerosol pathway and recirculated through the APS measurement volume at low velocities leading to erroneous large particle measurements. A technique for removing erroneous measurements based on correlated aerodynamic diameter and light scattering values is presented. When this technique was used, APS and cascade impactor size distribution measurements agreed well.     

Effect of Pore Size and Particle Size Distribution on Granular Bed Filtration and Microfiltration

Abstract

The paper reviews the effect of particle size distribution and pore size distribution on granular bed filter and crossflow microfiltration performance. The experimental results of the granular bed filter with pollen particles in suspension showed that the presence of large particles improved the filter efficiency of smaller particles in suspension. Microfiltration results with bi and tri‐modal latex suspensions showed that the permeate flux and the quality were significantly affected by the particle size and its distribution, especially when the particle size was smaller than the pore size of the membrane. The mathematical model simulation results of granular bed filtration show that media pore size distribution is an important parameter of filtration for the particle removal and pressure drop across the filter.     

Temporal Characteristics of Aerosol Optical Depths and Size Distribution at Visakhapatnam,India

Aerosol spectral optical depths and size distribution derived from the direct solar flux measurements at nine discrete wavelengths in the visible and near IR region for a period of about 10 years exhibit a gradual increase in the aerosol spectral optical depths from 1994-1997. There was a very large increase in the optical depths during 1991 after the volcanic eruption of Mt. Pinatubo and its effect persisted until 1993-94. The size distribution during 1988-1996 (excluding 1991, 1992, and 1993) remained bimodal in nature with an increase in the small particle number density with year. The aerosol optical depths and size distribu tions at Visakhapatnam also show some short period changes, characterizing the high sensitivity of the coastal urban aerosol system to the mesoscale weather. The observed features have been explained on the basis of the aerosol genesis based on local sources, sinks, and the prevailing weather.     

Improved Determination of Bimodal Size Distributions from Measurements with Diffusional Size Classification

The size distribution of the unattached fraction of the short-lived radon progeny is reported in the literature to have a bimodal structure. Due to the weak size resolution of diffusional size classification, a wide variety of bimodal size distributions yields similar measurement results, obstructing the reconstruction of size distribution parameters from measured data. For example, it could be shown that although 2 of the commonly used nonlinear approximation algorithms per formed well for the reconstruction of a monomodal size distribution, the reproduc tion of parameters of a bimodal size distribution was unsatisfactory. In conse quence, a "random walk" approach is presented. The basic idea for this approach consists of probing the complete parameter space as an ideal method for locating the best set of parameters. Additionally, 2 steps are introduced for the reduction of computation time to render the ideal approach to an applicable method. The range of geometric standard deviations for the calculation was restricted to values between 1 and 5. The range of median diameters was limited according to the penetration functions of the diffusional samplers. This restricted volume of param eter space was subdivided into 10⁴ cells. During the calculation, cells with exceptionally large values of the minimization functional were eliminated from further computation. Compared to the results of EM and Simplex algorithms, this ''random walk'' method was able to retrieve parameters of both monomodal and bimodal size distributions with improved accuracy.     

Analytical Expression on Characteristic Time Scale of Black Carbon Aging due to Condensation of Hygroscopic Species

In this study, the characteristic time scale of black carbon (BC) aging due to condensation of hygroscopic species was parameterized as a function of the condensing species concentration and the size distribution of BC particles. The aging time scale defined based on the BC mass concentration was shown to increase with BC particle size as well as with polydispersity of the size distribution. The effects of the BC particle size distribution on the aging time scale are shown to be considerable in the continuum regime, whereas the aging time scale tends to converge to a constant value in the free-molecule regime. The polydispersity effect was shown to be significant except for extraordinarily small particles. When the aging time scale was defined based on the BC number concentration, the dependency of the aging time scale on polydispersity is much smaller because the effect of slow aging of largest particles is compensated by fast aging of smallest particles. The aging time scale was also shown to be a strong function of the condensing species concentration. The result of this study implies that the aging time scale parameterizations suggested in the previous studies, which did not take into account the effects of condensing species concentration and particle size distribution, cannot be easily generalized for being applied to global model simulations.

Copyright 2012 American Association for Aerosol Research     

凝并和冷凝/蒸发对颗粒尺度分布的影响

利用多重Monte Carlo算法对13种典型工况进行数值模拟,考察不同类型的凝并核和冷凝/蒸发核对多分散性颗粒尺度分布时间演变的影响。发现常凝并核要比线性和二次方凝并核对小颗粒的影响大一些、对大颗粒的影响小一些,线性和二次方凝并核对颗粒尺度分布的时间演变影响则取决于具体情况;常冷凝核要比线性冷凝核对小颗粒的影响大一些、对大颗粒的影响小一些;连续区布朗凝并核类似于常凝并核;扩散冷凝核对颗粒尺度分布的影响界于常冷凝核和线性冷凝核之间。     

Size Distributions of Motor Vehicle Exhaust PM: A Comparison Between ELPI and SMPS Measurements

Particle size measurements using the electrical low pressure impactor (ELPI) and scanning mobility particle sizer (SMPS) are compared from the perspective of characterizing the particulate matter in motor vehicle exhaust. Both steady state vehicle operation and transient drive cycles are considered, and both gasoline and diesel fueled vehicle emissions are compared. Although the ELPI and SMPS measure different physical properties, respectively, the aerodynamic diameter and mobility diameter, the steady state particle size distributions are in close agreement, except for the 37 nm impactor stage of the ELPI which may overestimate particle number by up to a factor of two relative to the SMPS. This has little effect on the volume, or mass, weighted distribution. These, too, are generally in good agreement, though discrepancies appear at large particle size due to multiple charging effects in the SMPS and to electrometer offsets and the small particle loss correction in the ELPI. Selecting particles based on their electrical mobility with the SMPS, and then measuring their aerodynamic diameter with the ELPI, reveals that diesel particulate matter with well-specified mobility diameter exhibits a wide range in aerodynamic diameter and, therefore, also in effective density. Over transient drive cycles, the ELPI provides second by second particle distributions, whereas the SMPS must be run in a fixed particle size mode and size distributions constructed from repeated tests. The ELPI registers higher instantaneous PM emission rates during transients than the SMPS due to the faster time responses of the ELPI. The time integrated ELPI and SMPS size distributions, however, remain in good agreement. The relative merits of the two instruments for steady state and transient tests are discussed.     

Mathematical simulation of mass transfer processes under heterogeneous reactions in polydisperse porous media

Submitted is a theoretical study of mass transfer processes in polydisperse porous media in the presence of chemical reactions. Kinetic regime of methane pyrolysis in a porous carbon skeleton considering external and internal diffusion resistances for different initial distributions of particles forming the porous medium is investigated. Derived is a general analytical expression describing the influence of the inner reaction surface variation on the degree of the pore filling for an arbitrary initial particle size distribution. Expressions defining the time of pores filling by pyrocarbon based on approximate and exact solutions of the equation for the probability density function (PDF) of particle size distribution are received. Dependence of pore filling time on effective diffusion coefficient and initial particle size distribution using both solutions for PDF-equation is compared. It is shown, that the dominant factor influencing the pore filling time is the dispersion of particle size distribution.     

Image Analysis Method (IAM) for Measurement of Particle Size Distribution and Mass Availability on Carpet Fibers

Exposure to particles that have deposited on surfaces is common in occupational and residential environments. Lack of an accurate tool for assessing particle size distribution and loading (mass per unit area) on carpet fibers available for exposure contributes to the uncertainty associated with current risk assessment models. This research presents a new, direct image analysis method (IAM) for measuring particle size distribution and loading on carpet fibers. New and old carpet fibers loaded with Arizona Test Dust were used to test the method. Carpet fibers were removed from the bulk carpet, mounted on substrates, and scanning electron microscopy (SEM) images were collected. Particle size distribution and total mass were calculated from the processed images. The Arizona Test Dust (ATD) size distribution on fibers from two different carpets had mass median diameters of 3.6 ( ± 1.2) and 4.1 (±0.7) μm, similar to that for bulk ATD, 4.0 (± 0.5) μm. Total ATD mass available on new carpet fibers calculated by IAM were statistically correlated with the mass collected on micro-vacuum samples (R ² = 0.95). Direct comparison of the aerodynamic diameters measured by IAM with those measured automatically by the SEM showed a slight negative bias due to image resolution problems for the smallest particles.     

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.     

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.     

Condensational Growth of Polydisperse Aerosol for the Entire Particle Size Range

The condensation problem of polydisperse aerosols is investigated theoretically. The single particle growth rate suggested by Kulmala (1993) is approximated and simplified by neglecting the Kelvin effect and by adopting the harmonic mean method for the transition correction, which is a good approximation of the representative flux-matching theories. An analytical solution to the particle size distribution change by condensation is derived in an explicit form using the modified growth rate. This study represents the first analytical solution to the condensation problem of polydisperse aerosols for the entire particle size range. The derived solution is compared with results of the previous study of Kulmala (1993) and is shown to be reasonably accurate, except for very small particles for which the Kelvin effect cannot be neglected.     

Absolute Mass and Size Measurement of Monodisperse Particles Using a Modified Millikan's Method: Part I—Theoretical Framework of the Electro-Gravitational Aerosol Balance

A new method for accurate mass and size measurement of monodisperse particles is proposed. In this method, charged aerosol particles are introduced into parallel plate electrodes similar to the Millikan cell, and the number of particles left suspended after a certainty holding time has elapsed is measured. The particle survival rate as a function of the voltage applied to the electrodes is used to determine the particle mass. The particle size is deduced by using the particle density which is determined in a separate experiment. The expression of the particle survival function, which is defined as the survival rate as a function of the mass, for particles with and without Brownian diffusion is derived. The sensitivity of this method to the number average diameter, as well as other size distribution parameters, is analyzed on the basis of the survival function.     

A new method to synthesize high solid content waterborne polyurethanes by strict control of bimodal particle size distribution

A new method named two-step emulsification process was developed to synthesize high solid content waterborne polyurethanes by strict control of the bimodal particle size distribution. In the first step, a series of 40% solid content polyester-based (WPU-1) with low content of hydrophilic group and large particle size were firstly synthesized. In the second step, polyether-based prepolymers (WPU-2 prepolymers) with high content of hydrophilic group were firstly prepared and WPU-1 emulsions were used to emulsify WPU-2 prepolymers to obtain the final emulsions with high solid content (WPU-3). The particle size of WPU-3 present bimodal distribution and the diameter ratio and volume percentage of large particles to small particles in WPU-3 were able to be strictly controlled by this method. The viscosity of WPU-3 with 55% solid content was only 489.1 mPa s⁻¹ when the diameter ratio of large particles to small particles was 9.2 and the volume percentage of large particles was 74%.     

Size Resolution of Laser Optical Particle Counters

The size-resolving capabilities of laser optical particle counters have been explored. The ideal size resolution displays a singular behavior (i.e., the leading edge of the pulse height spectrum observed when calibrating with strict monodisperse aerosol increases, whereas the trailing edge falls off infinitely). When a real test aerosol is used the singularity is suppressed; as a consequence, it has become common practice to take the observed regular pulse height spectrum as “the” resolution.

The tendency to judge the alignment of laser optical particle counters from the symmetry of the observed pulse height spectrum results in definite alignment errors, with a serious deterioration in functioning. The ambient Junge size distribution will not be distorted when sizing it by means of a laser optical particle counter. Essentially, the particle size-dependent number concentration will be underestimated up to some 15% for large particles.

When interpreting measured size distributions using a commonly assumed Gaussian resolution, differences of up to some 25% could result, particularly in the large size regime.     

Floc Formation,Size Distribution,and its Transformation Detected by Online Laser Particle Counter

Abstract

Coagulation and flocculation are widely applied in water and wastewater treatment. Removal of suspended particles is essential in water treatment and greatly depends upon the performance of the coagulant and the production of flocs with suitable properties. For monitoring floc size, formation, and size transformation, no particle size method now can be considered ideal. In this work an on‐line laser particle counter was used to follow coagulation with aluminum sulfate. The experiments showed that the floc formation and floc size distribution could be well monitored. The results showed that it is feasible to use particle counting for dosage control and for monitoring changes in floc formation, transformation and size distribution.