Efficacy of a portable, moderate-resolution, fast-scanning DMA for
ambient aerosol size distribution measurements

Abstract. Ambient aerosol size distributions obtained with a compact, scanning mobility analyzer, the Spider DMA, are compared to those obtained with a conventional mobility analyzer, with specific attention to the effect of mobility resolution on the measured size distribution parameters. The Spider is a 12-cm diameter radial differential mobility analyzer that spans the 10–500 nm size range with 30s mobility scans. It achieves its compact size by operating at a nominal mobility resolution R = 3 (sheath flow = 0.9 L/min, aerosol flow = 0.3 L/min), in place of the higher sheath-to-aerosol flow commonly used. The question addressed here is whether the lower resolution is sufficient to capture the dynamics and key characteristics of ambient aerosol size distributions. The Spider, operated at R = 3 with 30s up and down scans, was collocated with a TSI 3081 long-column mobility analyzer, operated at R = 10 with a 360s sampling duty cycle. Ambient aerosol data were collected over 26 consecutive days of continuous operation, in Pasadena, CA. Over the 20–500 nm size range, the two instruments exhibit excellent correlation in the total particle number concentrations and geometric mean diameters, with regression slopes of 1.13 and 1.00, respectively. Our results suggest that particle sizing at a lower resolution than typically employed is sufficient in obtaining the key properties of ambient size distributions.



Introduction
Mobility measurements of atmospheric aerosols in the 10-500 nm size range are important to atmospheric aerosol character-15 ization (McMurry, 2000). Measurements aloft are especially important to understand aerosols in remote regions (Creamean et al., 2020;Herenz et al., 2018), and to mapping three-dimensional profiles (Mamali et al., 2018;Ortega et al., 2019;Zheng et al., 2021). Traditional mobility analyzers that span this size range are large, and not suitable for most unmanned aerial vehicle (UAV) or tethered balloon payloads that increasingly serve as the platform for aerosol characterization aloft. Moreover, aircraft measurements also require a fast scan time resolution to enable a good spatial resolution, as time is proportional to 20 distance traveled in a moving platform.
To that end, Amanatidis et al. (2020) developed the "Spider DMA", a compact, lightweight, and fast differential mobility analyzer (DMA). The instrument was designed for 10-500 nm sizing, with an aerosol flowrate of 0.3 L/min to provide adequate 2.2 Transfer function determination by finite element modeling Amanatidis et al. (2020) evaluated the Spider DMA transfer function in static-mode based on the Stolzenburg (1988) transfer function model and its derivation for radial flow classifiers (Zhang et al., 1995;Zhang and Flagan, 1996). Here, we evaluate its transfer function at "scanning" mobility mode, wherein the electric field is varied continuously in an exponential voltage ramp (Wang and Flagan, 1990). The scanning transfer function was evaluated with 2D finite element simulations of flows, quasi-steady-state electric field, and particle trajectories, using COMSOL Multiphysics. Simulations were performed for 0.9 60 / 0.3 L/min sheath / aerosol flowrates, scanning voltage in the range 5 -5000V, and 30s exponential ramps for both up-and down-scans. Particles were modeled with the "Mathematical particle tracing" module, in which particle mass was assumed to be negligible since the electric field varies slowly, on a time scale that is long compared to the aerodynamic relaxation time of the particles being measured. Particle motion was calculated explicitly, by assigning particle velocity vector components equal to the steady-state fluid field solution, combined with the axial velocity acquired from interaction with the time-varying electrostatic field. Moreover, a Gaussian random-walk was employed in each time step of the solver to simulate particle Brownian motion, with a standard deviation proportional to particle diffusivity, i.e. dσ = √ 2 D dt. Monodisperse particles were injected in regular intervals over the scan, varying from 0.025s for large particles to 0.003s for those in the diffusing size range.
Modeling was repeated for 10 discrete particle sizes, spanning the dynamic range of the classifier.

70
The two sizing instruments, the Spider DMA and the LDMA system, were operated in parallel, sampling ambient air from a roof top at the Caltech campus in Pasadena, CA. Measurements were made between May 16 -June 11, 2020, and were done as part of a study of the impacts of the COVID-19 pandemic shut-down on air quality.
The experimental setup used is shown in Figure 1. Ambient aerosol samples passed through a soft X-ray charge conditioner, and were subsequently split between the two mobility sizing systems. Both systems were operated in scanning mode. Both used 75 a MAGIC water-based CPC as the detector. The size pre-cut stage in the inlet of both CPCs was removed to avoid additional smearing of the transfer functions. The Spider DMA was operated at 0.9 L/min sheath and 0.3 L/min aerosol flowrates. Its scanning program included a 30s upscan followed by a 30s downscan, during which the electrode voltage was exponentially varied between 5 -5,000V. The voltage was held steady for an additional 2s at each end of the voltage ramp to allow for incoming particles to transmit through the classifier. Particle counts over the scan were recorded with a 5 Hz rate. The LDMA 80 system was based on a TSI 3081 long-column DMA operated at 3.0 L/min sheath and 0.3 L/min aerosol flowrates, offering classification in the 17-989 nm size range. The scans consisted of an exponentially increasing (upscan) voltage ramp between 25-9,875V with a 330s duration. As with the Spider DMA, the LDMA voltage was held constant at the beginning and end of the ramp for 15s, bringing its duty cycle to 360s. Particle counts for the LDMA system were recorded with a 2 Hz sampling rate. Data acquisition and instrument control (flows, high voltage) was performed with custom LabVIEW software for both 85 systems. an ADI "MAGIC" CPC as the particle detector.

Data inversion & analysis
Particle size distributions were obtained by inverting the raw particle counts recorded over each voltage scan. Raw counts were smoothed prior the inversion by Locally Weighted Scatterplot Smoothing (LOWESS) regression (Cleveland, 1979) to minimize inversion artefacts for noisy scans. The smoothed data were then inverted by employing regularized non-negative 90 least squares minimization for both systems.
The inversion kernel for the Spider DMA system was based on the scanning transfer function of the Spider DMA obtained by finite element modeling. In order to generate a dense kernel required for the inversion, the modeled transfer function data were fitted in Gaussian distributions, whose parameters were subsequently fitted to analytical expressions that allowed generation of transfer functions at any instant (i.e., time bin) over the voltage scan. The Spider transfer functions were subsequently 95 convoluted with a continuous stirred-tank reactor (CSTR) model Collins et al., 2002;Mai et al., 2018) to take into account the time response of the MAGIC CPC. A 0.35s time-constant was used for the CSTR model in the Spider DMA system (Hering et al., 2017). The resulting transfer function was combined with a size-dependent transmission efficiency model described by Amanatidis et al. (2020) to take into account particle losses occurring at the Spider inlet, as those are not evaluated in the 2D finite element modeling. Raw counts were shifted to earlier time bins to account for the 1.50s plumbing 100 time delay between the Spider outlet and the MAGIC CPC detector. Because the simulation enabled a strictly monodisperse "calibration" aerosol, the ratio of the number exiting the DMA during a particular counting time interval over the upstream particle number is the instrument transfer function.
The kernel for the LDMA system was based on the scanning transfer function model derived recently by Huang et al. (2020).
A CSTR model with a characteristic time of 0.35s, and a plumbing delay time of 0.95s were used to incorporate the response of the MAGIC CPC used in the LDMA system. The particle charge probability in the data inversion for both systems was assumed to follow the Wiedensohler approximation of the Boltzmann charge distribution (Wiedensohler, 1988).
3 Results 115 maximum number ratio. Moreover, they are somewhat narrower than the upscan peaks. This difference is the result of the scanning voltage operating mode. It should be noted that the transmission efficiency through the classification zone of a DMA is proportional to the area under the peak, rather than its maximum value. Hence, particle transmission over downscans is not necessarily higher than upscans. Diffusional broadening of the transfer function becomes important in the low voltage region of each ramp, increasing the transfer function width as voltage decreases, though the broadening is less than would be seen 120 with a higher resolution DMA (Flagan, 1999).       Figure 7 compares the total number and geometric mean diameter measured by the two instruments over the entire testing period. Each data point corresponds to a 1-hour average of the size distribution measured by each instrument, calculated over the 17-500 nm size range where the two systems overlap. Overall, the comparison includes 550h of measurement data. In 155 order to identify outliers in the data, we employed the "RANSCAC" (random sample consensus) algorithm (Fischler and Bolles, 1981). In this, random samples of the data are selected, analyzed, and classified as inliers and outliers through an iterative routine. The outliers identified are shown in Figure 7 with open square symbols. 2020-05-28 Next, a linear regression model (no intercept) was fitted to the data (excluding outliers) to evaluate the correlation between the two instruments. Since both instruments include measurement errors, we employed Orthogonal Distance Regression (Boggs 160 et al., 1987), where errors on both the dependent and independent variable are taken into account in the least squares minimization. The resulting regression lines exhibit slopes of α = 1.13 and α = 1.00 for number concentration and GMD, respectively, suggesting an overall excellent agreement between the instruments. Moreover, Pearson correlation coefficients of ρ = 0.98 and ρ = 0.93 indicate a strong correlation for both metrics of the size distribution.

Operational observations 165
The prototype Spider DMA used in this study incorporated an electrostatic-dissipative plastic that failed after several months of continuous operation, causing arcing within the instrument at the highest voltages. The Spider DMA has been redesigned to eliminate this material, and is currently being tested. This new Spider DMA has relatively minor changes to the classification region of the prototype presented here, and employs the same moderate resolution approach to maintain a compact size. We evaluated the performance of the Spider DMA, a highly-portable particle sizer, in measuring ambient size distributions against a co-located particle sizer based on a TSI 3081 long-column DMA (LDMA). Comparison measurements were performed at the Caltech campus in Pasadena, CA over a period of 26 days, between May 16 -June 11, 2020, as part of a field campaign examining the effects of COVID-19 shut-down on air quality. The Spider DMA system was operated at a lower nominal sizing resolution (0.9 L/min sheath and 0.3 L/min aerosol flowrates, R = 3) than the LDMA (3.0 L/min sheath and 175 0.3 L/min aerosol flowrates, R = 10), and at a higher time resolution (30s vs 330s scans).
The transfer function of the Spider DMA was obtained by finite element modeling at the conditions employed in the experiment, which included both up-and downscan exponential voltage ramps with 30s duration. Modeling data were fitted to Gaussian distributions, and were combined with the experimentally-determined transmission efficiency of the Spider DMA and the MAGIC particle counter response function to generate the inversion kernel of the combined system. Data inversion of 180 the LDMA system was based on the semi-analytical model of the LDMA scanning transfer function derived by Huang et al. (2020).
Regression analysis of 550h of measurement data showed an overall excellent correlation between the two instruments, with slopes of α = 1.13 and α = 1.00, and Pearson correlation coefficients of ρ = 0.98 and ρ = 0.93 in the reported particle number and geometric mean diameter (GMD), respectively. The good agreement between the two instruments suggests that particle 185 sizers operated at moderate resolution (R = 3 in this study) can sufficiently capture the dynamics and key characteristics of ambient size distributions, at least in the 10-500 nm size range. Lowering the resolution enables a wider dynamic range, or a more compact particle sizer for a desired size range, which is essential in many field applications, such as for measurements aloft with small UAVs or tethered balloons that have limited payloads. Moreover, it enables better counting statistics, as the wider transfer function results in higher counts per size bin, which is an important factor at low concentration aerosol measurements.