Particle transfer theory for steady-state differential mobility analyzers (DMAs) with and without diffusion is reviewed in detail with a particular focus on the assumptions and approximations made in ...the analysis. Impacts of the approximations are discussed and, where available, methods to reduce the errors of these approximations are suggested. The nondiffusing theory uses just one approximation, affecting the centroid calculation, which can be readily addressed via numerical modeling of the electric field. The diffusing theory makes numerous approximations to achieve an analytical expression. One of the most serious of these, neglecting secondary flows in the vicinities of the aerosol entrance and exit slits, could be improved upon using a numerical model of the flow field. Losses in the aerosol entrance plumbing can perturb the inlet profile to the classification region. The maximum effects on the transfer function are estimated to be a 1% increase in the mean mobility and a 14% reduction of the nondiffusing contribution to the variance. Methods of fitting transfer theory to measurements are also reviewed. Tandem differential mobility analyzer measurements generally do not have the resolving power to distinguish different shapes of the transfer function but newer measurements using truly monomobile ions have the potential to more rigorously test the diffusive transfer model. In adjusting the width of the theoretical transfer function to fit measurements from a real DMA demonstrating nonideal performance, it is physically more meaningful and accurate to use an additive adjustment to the variance as opposed to a multiplicative adjustment to the width.
Copyright (c) 2018 American Association for Aerosol Research
The basic equations governing the responses of single and tandem differential mobility analyzer (DMA) systems are summarized. Particle diffusion within the DMA resulting in broadening of the transfer ...function is included in this analysis. For tandem DMA (TDMA) work, a given particle diameter exiting the first DMA is modeled in the following conditioner as growing into a multi-modal lognormal distribution before entering the second DMA. Approximations and solution techniques for both single and tandem DMA systems are discussed. A new lognormal approximation to the DMA transfer function is introduced leading to a simple lognormal form for the TDMA response function. The maximum absolute error of the transfer function is 0.10 at 200 nm in the range plus or minus one and a half standard deviations of the lognormal fit. It is 0.035 at 3 nm in the range plus or minus two standard deviations of the lognormal fit. The maximum fractional error in the calculated TDMA response is no more than 0.08 at 200 nm and 3 nm in the range plus or minus one standard deviation of the lognormal fit.
The effect of working fluid on size-dependent activation efficiencies with the laminar flow ultrafine condensation particle counter described by
Stolzenburg and McMurry (1991)
was studied ...theoretically and experimentally. Criteria considered include tendency to avoid homogeneous nucleation within the condenser and toxicity. The working fluids that were identified have vapor pressures below that of butanol, so particles grow to smaller sizes and are more difficult to detect optically. Therefore we use a second, conventional CPC as a "booster" to grow particles to a detectable size. Experiments were performed to obtain the size- and material-dependent activation efficiencies for ethylene glycol, diethylene glycol, propylene glycol, oleic acid, and DOS. Using diethylene glycol and oleic acid, values of the 50% activation efficiency diameter, D
p50
, for negatively charged particles generated by evaporating sodium chloride, ammonium sulfate, and silver were < 1.2 (< 0.8) nm, 1.4-1.5 (1.0-1.2) nm, and 1.9-2.0 (1.5) nm as mobility (mass) diameter, respectively. The stability of the UCPC for long-term operation using ethylene glycol and propylene glycol as working fluids was tested by monitoring the instrument's response to silver particles having size near D
p50
in an air stream at 40-45% relative humidity. The performance was steady (±3%) for several days indicating the instrument performs stably during unattended operation for realistic atmospheric sampling conditions.
A new water-based condensation particle counter (WCPC) is presented. The WCPC is a thermally diffusive, laminar flow instrument. Condensational enlargement is achieved through the introduction of a ...saturated airflow into a "growth tube" with wetted walls held at a temperature higher than that of the entering flow. An unsheathed, 1 L/min instrument utilizing this principle has been evaluated with various aerosols. The particle size detected with an efficiency of 50% is at or below 4.8 nm for particles sampled from vehicular emissions or ambient air, and for various laboratory-generated inorganic salts. The cut point is higher for the organic materials tested, ranging from 8 nm to 30 nm depending on the compound and purity level. An empirically determined dead-time correction factor is applied to the coincidence correction, which allows extension of the single-count mode to higher concentrations. The counting efficiencies for 80 nm oil and salt aerosols are equal, and above 97% for concentrations approaching 10
5
cm
−3
. When subject to a step-fucntion change in input concentration the time required to attain 90% of the final value, including a 0.5 s lag, is 1.3 s. The corresponding exponential time constant is 0.35 s. The WCPC evaluated here is marketed as the TSI Model 3785.
During the Atlanta ANARChE Study of July and August 2002, atmospheric aerosol size distributions from 3 to 2000 nm were measured continuously with 5‐min resolution. Sulfuric acid vapor concentrations ...were also measured. During regional nucleation events these data showed the presence of a nucleation mode that grew at rates ranging from 3 to 20 nm h−1. In this paper we compare these measured modal growth rates with calculated rates that account for sulfuric acid condensation, intramodal coagulation of nucleation mode particles, and extramodal coagulation of nucleation mode particles with preexisting particles. Data collected during six time intervals were amenable to analysis. Calculated and measured growth rates were in reasonable agreement for the four events that involved growth below 40 nm (ratios of measured to calculated growth rates = 1.0, 2.1, 0.68, 0.60). Two of the three afternoon events involved growth above 40 nm, and in these cases, measured rates substantially exceeded calculated rates by factors of four to five, suggesting that our model did not account for all growth processes. We also compared observed rates of change in nucleation mode number concentration with calculated coagulation rates during these six time intervals. During the sub‐40 nm growth events, particle concentrations changed at rates that were significantly below calculated coagulation rates. In two of these cases, particle concentrations increased during the growth period, suggesting that a source of particles was present. Measured size distributions suggest that particle production by nucleation continued during these events and contributed to this discrepancy. Concentrations during the super‐40 nm events decreased at rates that exceeded calculated coagulation rates.
A method to estimate nanoparticle diameter growth rates (GR) during new particle formation (NPF) events from the measured dependence of charged fraction, f, on size, Dp, is introduced. The method is ...especially useful for observations during intense particle production rates, when the mode in the distribution of newly formed particles does not grow monotonically with time. This method assumes that the observed profile of f versus Dp during the nucleation and growth period is controlled by condensational growth, ion‐particle combination/recombination, scavenging by preexisting particles, and coagulation among growing nanoparticles. Values of growth rates obtained by this method (GRf) agree well with independently obtained particle growth rates due to gas‐to‐particle conversion processes (GRPSD) during regional NPF events. The method was then applied to characterize the NPF events observed at Tecamac, Mexico. These growth rates were found to range from 15–40 nm/h, which is significantly higher than values reported for other urban areas. The production rates for 1 nm particles calculated from the estimated growth rates and measured Fuchs surface area (J1nm = 1900–3000 particles/cm3 s) are comparable to those recently observed in New Delhi. Because critical nuclei are likely close to 1 nm in size, J1nm should provide a reasonable estimate for nucleation rates.
Bipolar diffusion charging is used routinely in aerosol electrical mobility size distribution measurements. In this study, aerosol charge fractions produced by six bipolar chargers (neutralizers) ...were measured using a tandem differential mobility analyzer system. Factors that were studied include the type of ion source (
210
Po,
85
Kr,
241
Am, and soft X-ray), source activity, charger design, and aerosol flowrate. It was found that all six types of neutralizers achieve stationary state charge distributions when the source activity is sufficiently high. For
210
Po neutralizers with an initial radioactivity of 18.5 MBq (0.5 mCi), stationary state charge distributions are achieved when the source is less than 3.25 years old (residual activity no less than 0.0527 MBq). Stationary state was achieved for
85
Kr neutralizers having residual radioactivity greater than 70 MBq. Source activities of
241
Am and soft X-ray neutralizers are discussed. Aerosol charge fractions for six neutralizers remain reasonably invariant over a wide range of flowrates. The positive charge fractions achieved by the soft X-ray neutralizer are higher than those by the other five neutralizers using radioactive sources while negative charge fractions for all neutralizers studied are all in a similar range. This study also raises questions about bipolar charging fractions used for data inversion in some scanning mobility particle spectrometer (SMPS) systems, and underscores the need to better understand bipolar charging to achieve more accurate measurements of particle size distributions.
Copyright 2014 American Association for Aerosol Research
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