A Differential Mobility Analyzer (DMA) for Size Selection of Nanoparticles at High Flow Rates

This article demonstrates the feasibility of scaling-up the technique for particle size selection in the gas phase based on differential mobility analysis. Nano-DMAs used to select the particle size in processes for the synthesis of nanomaterials in the laboratory operate at aerosol flow rates of a few liters per minute. A new DMA capable of classifying nanoparticles of up to 30 nm in size at aerosol flow rates as high as 100 l· min ^?1 will be presented (HF-DMA). A major advantage of the HF-DMA over current nano-DMAs covering the same particle size is that its resolution is almost unaffected by Brownian diffusion for particles as small as 3 nm. Monodisperse nanoparticles in the 5 to 25 nm size range have been produced at flow rates of up to 90 l· min ^?1 . The spread in particle size and the particle number concentration were studied with respect to their dependency on the flow rates in the HF-DMA. The measurements reflect the behavior predicted by the theory. The HF-DMA makes it possible to deliver nanoparticles of a well-defined size at yields two orders of magnitude higher than with current nano-DMAs.     

Measurements of Particle Loss Functions in a Differential Mobility Analyzer (TSI,Model 3071) for Different Flow Rates

Particle losses in a differential mobility analyzer (TSI, Model 3071) caused by diffusive deposition and Brownian diffusion are measured for particles in the diameter size range between 3 and 100 nm. For small sampling and aerosol flow rates (0.3 liters/min) at 20 nm, nearly 50% of the primary particles are lost; and for 2 liters/min, the particle losses have to be considered in the diameter size range below 30 nm (50% at 7 nm). From the measured penetration values, an effective tube length is derived which is useful to calculate particle losses for other flow rates through the analyzer.     

Determination of Particle Size Distribution of Ultra-Fine Aerosols Using a Differential Mobility Analyzer

The size analysis of ultrafine aerosol particles using a differential mobility analyzer combined with a CNC is discussed from two standpoints: (1) particle loss caused by Brownian diffusion in the analyzer, and (2) data reduction procedure where Fuchs' charging theory is applied. As a result, it has been found that (1) particle loss becomes significant when particle size is smaller than about 15 nm, and (2) a simple and practical data reduction procedure may be used, where the stationary bipolar charge distribution given by Boltzmann's law is modified by using Fuchs' charge distribution in the smaller size range.     

Sintering Rates for Pristine and Doped Titanium Dioxide Determined Using a Tandem Differential Mobility Analyzer System

Sintering rates of pristine and V-doped TiO ₂ were obtained using a tandem DMA system. A range of experiments were conducted to first map out the variation of mobility size of a monodisperse (by mobility) agglomerate with time at three fixed temperatures. Using relationships of the surface area to the mobility size, the sintering equation was solved to determine the activation energy and pre-exponential factor. The value of the activation energy was 236 (± 46) kJ/mol for pristine TiO ₂ and 363 (± 1) kJ/mol for V-doped TiO ₂ . The corresponding pre-exponential factors were 7.22 × 10 ¹⁹ and 2.22 × 10 ¹² s/m ⁴ K, respectively. These values were then used to predict changes in mobility diameter at different temperatures, and good agreement was obtained with measurements. Possible reasons for faster sintering rates of V-TiO ₂ relative to pristine TiO ₂ were conjectured.     

Field-Flow Fractionation for Poiseuille Flow through a Cylindrical Tube

Abstract

We calculate the longitudinal dispersion coefficient K for field-flow fractionation in a cylindrical tube by using a variational principle.     

Determination of Arbitrary Moments of Aerosol Size Distributions from Measurements with a Differential Mobility Analyzer

A method to determine arbitrary moments of aerosol size distributions from differential mobility analyzer measurements has been proposed. The proposed method is based on a modification of the algorithm developed by Knutson and Whitby to calculate the moments of electrical mobility distributions. For this modification, the electrical mobility and the charge distribution have been approximately expressed by power functions of the particle diameter. To evaluate the validity of the approximation, we have carried out numerical simulations for typical size distributions. We have found that for typical narrowly distributed aerosols such as polystyrene latex particles and particles that arise in the tandem differential mobility analyzer configuration, the distribution parameters can be accurately determined by this method. For a log-normally distributed aerosol, the accuracy of the distribution parameters determined by this method has been evaluated as a function of the geometric standard deviation. We have also compared the accuracy of the proposed method with other existing methods in the case of the asymmetric Gaussian distribution.     

Size Measurement of Polystyrene Latex Particles Larger than 1 Micrometer using a Long Differential Mobility Analyzer

We describe a newly constructed annular-type differential mobility analyzer (DMA) with an effective electrode length of 60 cm, which is longer than that of our original DMA (40 cm length). This long DMA was developed to extend the classification size of particles measuring up to 1.5 μm. As an application of this DMA, the mean diameters and standard deviations were determined for six samples of monodisperse polystyrene latex (PSL) particles ranging from 0.94 to 1.27 μm in nominal diameter. These PSL particles suspended in double-distilled water were aerosolized by a glass nebulizer and then introduced into the DMA. The mean diameters and standard deviations of these PSL particles were calculated by Ehara's method and compared with the nominal diameters and uncertainties. There was good correlation between the nominal diameters of these samples—particularly for recently certified samples—and the measured diameters. Classification of aerosol particles more than 1 micrometer in diameter using this DMA will be useful for many purposes.     

Diffusion Distortions in a Differential Mobility Analyzer: The Shape of Apparent Mobility Spectrum

The effect of molecular and or small-scale turbulent diffusion in a differential mobility analyzer (DMA) is described in terms of apparent mobility spectrum. Without restricting generality, the normalized apparent spectrum, i.e., the apparent spectrum of unimobile particles with unity charge density is introduced. An approach based on the calculation of the probabilities of the random displacements of particles around their regular trajectories enables us to derive analytical expressions for the normalized apparent spectrum. A particular derivation is carried out for the case of a second-order DMA with one collecting electrode and variable electric field strength. Explicit analytical equations of various approximation degrees have been derived. The normalized apparent spectrum of the particular DMA shows a remarkable asymmetry; its mobility mode is shifted toward lower mobilities. The derived equations serve as a basis for the estimation of the spectral resolution of the DMA. The equations can also be used for a proper design of the DMA, reducing the effect of diffusion. Once the normalized apparent spectrum is known, a possibility appears to improve the resolution of the DMA by solving a relevant equation and eliminating the effect of diffusion in such a way.     

Single Charging of Nanoparticles by UV Photoionization at High Flow Rates

The feasibility of UV photoionization for single unipolar charging of nanoparticles at flow rates up to 100 l· min ^?1 is demonstrated. The charging level of the aerosol particles can be varied by adjusting the intensity of the UV radiation. The suitability of a UV photocharger followed by a DMA to deliver monodisperse nanoparticles at high aerosol flow rates has been assessed experimentally in comparison to a radioactive bipolar charger ( ⁸⁵ Kr, 10 mCi). Monodisperse aerosols with particle sizes in the range of 5 to 25 nm and number concentrations between 10 ⁴ and 10 ⁵ cm ^?3 have been obtained at flow rates up to 100 l· min ^?1 with the two aerosol chargers. In terms of output particle concentration, the UV photoionizer performs better than the radioactive ionizer with increasing aerosol flow rate. Aerosol charging in the UV photoionizer is described by means of a photoelectric charging model that relies on an empirical parameter and of a diffusion charging model based on the Fuchs theory. The UV photocharger behaved as a quasi-unipolar charger for polydisperse aerosols with particles sizes less than 30 nm and number concentrations ～10 ⁷ cm ^?3 . Much reduced diffusion charging was observed in the experiments, with respect to the calculations, likely due to ion losses onto the walls caused by unsteady electric fields in the irradiation region.     

Determination of Particle Effective Density in Urban Environments with a Differential Mobility Analyzer and Aerosol Particle Mass Analyzer

Effective densities of atmospheric aerosols in various locations of the Los Angeles Basin were determined by a DMA-APM technique. Effective density was calculated by comparing voltage distributions of sampled atmospheric aerosols with PSL particles of known density. The five sites chosen for field experiments were: (1) Interstate-710 Freeway, impacted by heavy-duty diesel vehicles; (2) State Route CA-110, open only to gasoline vehicles; (3) Riverside, a receptor site known for secondary particle formation; (4) University of Southern California, a typical urban and industrial environment; and (5) Coast for marine aerosol. The size range selected for this study was from 50 nm to 414 nm. While 50 nm particles exhibited a single effective density multiple effective densities were measured for each of the other particle sizes as significant fractions of these particles are transported from background sources. Regardless of location, 322–414 nm particle effective densities were considerably lower than unity. The lowest effective densities (～ 0.1 g cm ^{? 3} ) were reported for I-710, confirming that diesel combustion aerosols are rich in chain agglomerates with large void spaces. Riverside exhibited high effective densities (～ 1.2–1.5 g cm ^{? 3} ) for 50–202 nm particles, which we hypothesize is due to transformations that occur during advection from Los Angeles. Measurements of diurnal variation of effective density at Riverside support this hypothesis. Overall, our results suggest that effective density declines as the particle mobility diameter increases irrespective of location. Fractal dimensions calculated from average effective densities were lowest for I-710 ( D _f = 2.41) and CA-110 (D _f = 2.54) aerosols, presumably due to the influence of vehicular combustion emission on these sites. By contrast, average fractal dimensions at USC, Riverside and Coast were found to be 2.79, 2.83, and 2.92, respectively. High fractal dimensions at these sites may be the effects of aging, moisture absorption and/or organic vapor condensation on the particles, which fills void space and makes particles more spherical.     

Sizing of Aerosol in Gases Other Than Air Using a Differential Mobility Analyzer

The differential mobility analyzer (DMA) is a device that sizes aerosol particles based on their electrical mobility. The relationship between particle size and mobility depends, among other factors, on three gas specific parameters, namely, dynamic viscosity, mean free path, and Cunningham slip correction factor C c . Provided these parameters are known, DMA theory is expected to be valid independent of gas type. The present study demonstrates the sizing accuracy of DMAs for gases other than air using monodisperse polystyrene latex (PSL) spheres with nominal diameters of 60 nm, 149 nm, and 343 nm in He, Ar, H 2 , CO 2 , and N 2 O. Eliminating possible systematic errors due to uncertainties in DMA geometry and nominal PSL diameter by normalizing the measured PSL diameters to their respective diameters measured in air, the sheath flow rate Q sh and C c are expected to be the main sources for measurement errors. Since C c data are lacking for PSL spheres in gases other than air, an expression given by Allen and Raabe (1985b) was used to approximate C c . The experimental results of the present study are consistent with a 2% accuracy of this expression for C c , which is considerably better than the 5% accuracy estimated by Rader (1990) for a similar expression for oil drops. Finally, we discuss other aspects of operating a DMA with gases other than air, namely, flow meter calibration and dependence of electrical breakdown voltage on gas type. In the present study a thermal mass flow meter (MFM) was used to measure Q sh . Calibration of this MFM revealed that the gas specific MFM correction factors ( K factors) provided by the technical literature can be highly inaccurate (here between -12% and +31%). More accurate K factors are presented.     

Development of a Pulsed-Field Differential Mobility Analyzer: A Method for Measuring Shape Parameters for Nonspherical Particles

For a nonspherical particle, a standard differential mobility analyzer (DMA) measurement yields a mobility-equivalent spherical diameter, but provides no information about the degree of sphericity. However, given that the electrical mobility for nonspheres is orientation-dependent, and that orientation can be manipulated using electric fields of varying strength, one can, in principle, extract some type of shape information through a systematic measurement of mobility as a function of particle orientation. Here, we describe the development of a pulsed-field differential mobility analyzer (PFDMA) which enables one to change the peak E-field experienced by the particle to induce orientation, while still maintaining the same time-averaged field strength as a standard DMA experiment. The instrument is validated with polystyrene latex (PSL) spheres with accurately known size, and gold rods with dimensions accurately determined by transmission electron microscopy (TEM). We demonstrate how the instrument can be used for particle separation and extraction of shape information. In particular, we show how one can extract both length and diameter information for rod-like particles. This generic approach can be used to obtain dynamic shape factors or other multivariate dimensional information (e.g., length and diameter).

Copyright 2014 American Association for Aerosol Research     

Two Different Configurations of Flow Field-Flow Fractionation for Size Analysis of Colloids

Abstract

Flow field-flow fractionation (F.FFF) is a technique for measuring the size of species in the colloidal range (1 nm to 1 μm) which makes the use of the formation of a molecular or colloidal polarization layer at the surface of a filtering membrane. The species to be analyzed are introduced into a flow of liquid passing through a channel with porous walls (of pore size less than that of the colloids to be analyzed) which allow a certain controlled flow to pass through. The remaining fraction of the flow passes through the system, carrying the colloids to a nonspecific detector. The transit time of the colloids through the channel is found to be a function of their size and the permeation rate through the porous membrane. This chromatographic system can be calibrated by using known colloids, such as standard latex particles or fractionated polymer samples, and then used to determine the size of unknown colloids. Here we present results obtained in two different systems, an asymmetric module with a rectangular channel having a single flat membrane and a module based on a hollow ultrafiltration fiber with a radial symmetry. The common feature of the two systems is that there is only one fluid inlet. Measurements are reported for the mean size of various samples of real colloids, such as dextran macromolecules, emulsion paints, and milks, and a comparison is made with measurements using hydrodynamic chromatography (HDC), and photon correlation spectrometry (PCS).     

Measurement of Ambient Aerosols by the Differential Mobility Analyzer Method: Concepts and Realization Criteria for the Size Range Between 2 and 500 nm

Requirements for aerosol spectrometer based on the differential electrical mobility method are deduced from the principles of aerosol classification and concentration determination. Data reduction and method-inherent sources of errors are discussed in detail. Criteria for the components of the arrangement to be used for ambient aerosol size distribution measurements are given with respect to size range, concentration range and time resolution.     

Comparison Between the Theoretical and Experimental Performance of a Differential Mobility Analyzer with Three Monodisperse-Particle Outlets

Differential mobility analyzers (DMAs) with more than one monodisperse-particle outlet can offer a number of advantages compared to conventional single monodisperse-particle outlet designs. A generalized theoretical model and experimental measurements describing the performance of a DMA with 3 monodisperse-particle outlets have been independently reported in the literature. The objective of this article is to compare the theoretical predictions with the measurements. Resolutions determined by the theoretically predicted transfer functions for the three monodisperse-particle outlets are compared with measurements when the DMA was operated under different operating conditions. Predictions and measurements show good agreement when the DMA is operated at low sheath flow rates and for aerosol outlets relatively far from the aerosol inlet. For aerosol outlets relatively near the inlet there is evidence that the discrepancy between theoretical predictions and measurements may disappear at higher sheath flow rates, but the chances of flow disturbances in the classifier increase as well. The theory for multiple monodisperse-outlet DMAs is thus seen as successful in predicting the performance of this instrument, provided that disturbances in the flow field are avoided.

Copyright 2013 American Association for Aerosol Research     

Online Nanoparticle Mass Measurement by Combined Aerosol Particle Mass Analyzer and Differential Mobility Analyzer: Comparison of Theory and Measurements

A combination of a differential mobility analyzer (DMA) and aerosol particle mass analyzer (APM) is used to measure the mass of NIST Standard Reference Materials (SRM®) PSL spheres with 60 and 100 nm nominal diameter, and NIST traceable 300 nm PSL spheres. The calibration PSL spheres were previously characterized by modal diameter and spread in particle size. We used the DMA to separate the particles with modal diameter in a narrow mobility diameter range. The mass of the separated particles is measured using the APM. The measured mass is converted to diameter using a specific density of 1.05. We found that there was good agreement between our measurements and calibration modal diameter. The measured average modal diameters are 59.23 and 101.2 nm for nominal diameters of 60 and 100 nm (calibration modal diameter: 60.39 and 100.7 nm) PSL spheres, respectively. The repeatability uncertainty of these measurements is reported. For 300 nm, the measured diameter was 305.5 nm, which is an agreement with calibration diameter within 1.8%.

The effect of spread in particle size on the APM transfer function is investigated. Two sources of the spread in “mono-dispersed” particle size distributions are discussed: (a) spread due to the triangular DMA transfer function, and (b) spread in the calibration particle size. The APM response function is calculated numerically with parabolic flow through the APM and diffusion broadening. As expected from theory, the calculated APM response function and measured data followed a similar trend with respect to APM voltage. However, the theoretical APM transfer function is narrower than the measured APM response.     

Comparison and Combination of Aerosol Size Distributions Measured with a Low Pressure Impactor,Differential Mobility Particle Sizer,Electrical Aerosol Analyzer,and Aerodynamic Particle Sizer

Data from a different mobility particle sizer (DMPS) or an electrical aerosol analyzer (EAA) has been combined with data from an aerodynamic particle sizer (APS) and converted to obtain aerosol mass distribution parameters on a near real-time basis. A low pressure impactor (LPI), a direct and independent measure of this mass distribution, provided information for comparison.

The number distribution of particles within the electrical measurement range was obtained with the DMPS and EAA. Data from the APS for particles greater than that size were used to complete the number distribution. Two methods of obtaining mass distribution parameters from this number data were attempted. The first was to convert the number data, channel by channel, to mass data and then fit a log-normal function to this new mass distribution. The second method was to fit a log-normal function to the combined number distribution and then use the Hatch-Choate equations to obtain mass parameters.

Both the DMPS / APS and the EAA / APS systems were shown to successfully measure aerosol mass distribution as a function of aerodynamic diameter. Careful operation of the measurement equipment and proper data manipulation are necessary to achieve reliable results. A channel-by-channel conversion from number to mass distribution provided the best comparison to the LPI measurement. The DMPS / APS combination furnishes higher-size resolution and accuracy than the EAA / APS system. A small gap was observed in the EAA / APS combined data; however, this did not seem to adversely affect the determination of mass distribution parameters.     

Convective Heat Transfer Enhancement of a Rectangular Flat Plate by an Impinging Jet in Cross Flow

Experiments were carried out to study the heat transfer performance of an impinging jet in a cross flow. Several parameters including the jet-to-cross-flow mass ratio （X=2%-8%）, the Reynolds number （Red=1434-5735） and the jet diameter （d=2-4 mm） were explored. The heat transfer enhancement factor was found to increase with the jet-to-cross-flow mass ratio and the Reynolds number, but decrease with the jet diameter when other parameters maintain fixed. The presence of a cross flow was observed to degrade the heat transfer performance in respect to the effect of impinging jet to the target surface only. In addition, an impinging jet was confirmed to be capable of en-hancing the heat transfer process in considerable amplitude even though the jet was not designed to impinge on the target surface.     

The 1-by-3 Tandem Differential Mobility Analyzer for Measurement of the Irreversibility of the Hygroscopic Growth Factor

A new instrument, namely the 1 × 3 tandem differential mobility analyzer (1 × 3-TDMA), has been developed. Its primary measurement is the irreversibility of the hygroscopic growth factor of aerosol particles. The instrument uses the hysteresis of phase transitions to infer the solid or aqueous state of the particles. A first DMA passes particles of a selected electric mobility at relative humidity RH₀. Exiting this DMA, the particles are split into three separate flows. The first flow is exposed to RH ₀  → (RH ₀ +  δ ) → RH ₀ in a deliquescence test before passing through a second DMA that is set to the same electric mobility as the first DMA. The second flow passes directly to a third DMA without change in RH, thereby serving as a reference arm. This DMA is also set to the same electric mobility as the first DMA. The transmission ratio of the 1 × 3-TDMA is defined as the particle concentration passing the deliquescence test divided by that passing through the reference arm. The transmission ratio is unity in the absence of deliquescence and zero when a phase transition occurs, at least for ideal instrument performance in application to a test aerosol of fully deliquesceable particles. For the third flow passing out of the first DMA, an efflorescence test is run by using the RH profile of RH ₀  → (RH ₀ ? δ ) → RH ₀ before passing through a fourth DMA. A full data set for the 1 × 3-TDMA is obtained by scanning RH₀, typically from 20 to 85%. In the present paper, the 1 × 3-TDMA instrument is described, and laboratory data are presented for the phase transitions of externally mixed aerosols of aqueous and solid sodium chloride particles, aqueous and solid ammonium sulfate particles, and their mixtures, as well as a mixture of aqueous and solid sea salt particles. The observed transmission ratio is compared to a model analysis. The intent behind the development of this instrument is to deploy it for field measurements and use observations of the irreversibility of the growth factors of atmospheric particles as markers of their physical state.     

Accurate Determination of Aerosol Activity Coefficients at Relative Humidities up to 99% Using the Hygroscopicity Tandem Differential Mobility Analyzer Technique

Aerosol water content plays an important role in aqueous phase reactions, in controlling visibility, and in cloud formation processes. One way to quantify aerosol water content is to measure hygroscopic growth using the hygroscopicity tandem differential mobility analyzer (HTDMA) technique. However, the HTDMA technique becomes less reliable at relative humidity (RH) >90% due to the difficulty of controlling temperature and RH inside the second DMA. For this study, we have designed and implemented a new HTDMA system with improved temperature and RH control. Temperature stability in the second DMA was achieved to ±0.02°C tolerance by implementing active control using thermoelectric heat exchangers and PID control loops. The DMA size resolution was increased by operating high-flow DMA columns at a sheath:sample flow ratio of 15:0.5. This improved size resolution allowed for improving the accuracy of the RH sensors by interspersing ammonium sulfate reference scans at high frequency. We present growth factor data for pure compounds at RH up to 99% and compare the data to theoretical values and to available bulk water activity data. With this HTDMA instrument and method, the osmotic coefficients of spherical, nonvolatile aerosols of known composition between 30 and 200 nm in diameter can be determined within ±20%. We expect that data from this instrument will lead to an improvement of aerosol water content models by contributing to the understanding of aerosol water uptake at high RH.

Copyright 2013 American Association for Aerosol Research