Accelerated measurements of aerosol size distributions by continuously scanning the aerodynamic aerosol classifier

Abstract

Using an Aerodynamic Aerosol Classifier (AAC) upstream of a particle detector is a relatively new method for measuring the aerodynamic size distribution of an aerosol. This approach overcomes limitations of previous methodologies by leveraging the high transmission efficiency, independence from particle charging, and adjustable classification range and resolution of the AAC. However, the AAC setpoint must be stepped and stabilized before each measurement, which forces tradeoffs between measurement time and step resolution. This study is the first to develop and validate theory which allows the speed of the AAC classifier to be continuously varied (following an exponential function), rather than stepped. This approach reduces measurement time, while increasing the resolution of the measured distribution. Assuming uniform axial flow, the transfer function of the scanning AAC and its inversion are determined. Limited trajectory theory is used to derive the idealized transfer function of the scanning AAC, while parameterized, particle streamline theory is used to develop the non-idealized transfer function, which accounts for non-idealized particle and flow behaviors within the classifier. This theory and the practical implementation of the scanning AAC are validated by the high agreement of its measurements of polystyrene latex (PSL) particles (within 8.7% for six sizes between 100 nm to 2.02 μm), and of size distributions of three aerosol sources (Bis(2-Ethylhexyl) sebacate, NaCl and soot) to those measured by the stepping AAC (within 2% or better if the source stability is considered). The validity of assuming uniform axial flow in the classifier and downstream plumbing/detector are also discussed.

Copyright © 2020 American Association for Aerosol Research

EDITOR:

• Kihong Park

Acknowledgments

This research would not have been possible without the support from Cambustion Ltd, The Rt. Hon. Sir Winston S. Churchill Society of Edmonton and C-FER Technologies.

Notes

1 Due to the APS operating outside the Stokes regime, where viscous forces dominate inertial forces (Kulkarni, Baron, and Willeke 2011).

2 The radial acceleration of the particle is neglected as the relaxation time of the particle is orders of magnitude smaller than the time over which the centrifugal force field changes. For example, the maximum particle relaxation time classified by the AAC is $140\times {10}^{-6}$ s (Cambustion 2018) and the time constant (${\tau }_{\text{sc}}$) of a typical AAC scan is tens of seconds.

3 This example assumes the aerosol is at standard conditions (P = 101.325 kPa and T = 296.15 K) and that the particles have an effective density of 1000 kg/m³. This density results in the mobility and aerodynamic diameters of the particles being equivalent.

4 The data inversion does not use assumptions, such as interpolation or averaging, to increase or decrease the CPD of the reported measurements.

5 These scan values correspond to the particle detector operating with a 1 s counting time ($t_{\mathrm{c}}$), and the acceleration and deceleration capacity measured for AAC 2, as shown in Figure S2.2 (SI).

6 This estimate assumes the AAC is not spinning at the start of the down scan, and it takes approximately 140 s to reach the starting speed of 700 rad/s.

7 This ratio accounts for the standard 15 s retrace time for each consecutive SMPS scan.

8 This statement of independence neglects that the non-idealized parameters (${\lambda }_{\Omega }$ and ${\mu }_{\Omega }$) change based on the average setpoint of the scanning AAC over $t_{\mathrm{c}}$ (i.e., ${\overline{\tau }}_{\text{sc}}^{\ast }$ as defined by Equation (46)).

9 The lognormal distribution was fitted to each measured size distributions using least-squares minimization.

10 This ratio is based on the average times ($t_{\text{ss}}$) to complete the up or down scan using the steady-state AAC. The down scan of the steady-state AAC was 1% to 8% faster than its up scan due to its higher capacity to decelerate than accelerate.

11 The CPD of the measurements collected using the scanning AAC also depend on the counting time ($t_{\mathrm{c}}$) of the detector as shown in Equation (47). For this data, the CPC was operated with a counting time of 1 s.

12 The repeatability was estimated assuming a 95% confidence interval and using a t-distribution.