Measurement of the centrifugal particle mass analyzer transfer function

Abstract

Particle mass analyzers, in particular the centrifugal particle mass analyzer (CPMA) and the aerosol particle mass analyzer (APM), have provided new possibilities for aerosol science through their ability to classify particles by their mass-to-charge ratio. The performance of the CPMA in classifying particles is characterized by a probability distribution known as a transfer function. This study shows the theoretical models of the CPMA’s transfer function that exist in the literature cannot accurately predict the CPMA’s actual performance. In this study, a tandem CPMA (TCPMA) measurement technique was used to experimentally evaluate the deviation of the actual CPMA transfer function from its idealized triangular transfer function. This deviation was measured by three factors: (i) the width factor ($\mu$), (ii) the height factor ($\eta$), and (iii) the mass set point agreement (i.e., the agreement between the set points of the two CPMAs, $m_{12}^{\ast }$); such that concurrent values of 1 for all three factors implied no deviation between the actual and theoretical triangular CPMA transfer functions. These factors were derived by adjusting them to fit TCPMA data with the convolution of two triangular transfer functions with identical widths. TCPMA data were collected for a wide range of CPMA resolutions, flow rates, and mass set points ranging from 2 to 15, 0.3 to 8 LPM, and 0.05 to 100 fg, respectively. The mass set point agreement remained relatively constant over a range of CPMA mass set points and increased slightly with decreasing CPMA resolutions. Neglecting outliers, the average mass set point agreement was $m_{12}^{\ast }=1.02\pm 0.03,$ suggesting good reproducibility among the CPMAs. The width factor showed a functional dependence on the mass set point, resolution, and flow rate. It was observed that the CPMA transfer function was generally narrower ($\mu >1$) than the idealized transfer function except at a low flow rate (0.3 LPM) and low mass set points ($m^{\ast }<1$ fg), and the width factor approached unity at higher mass set points ($m^{\ast }>1$ fg) and higher resolutions ($R_m>6$). As expected, the height factor depends on the mass set point, resolution, and flow rate: it decreases with lower mass set points, lower flow rates and higher resolutions. Both the width and height factors were fitted robustly using multivariate non-linear fitting models so that CPMA users can easily calculate its transfer function over a wide range of operating conditions.

Copyright © 2023 American Association for Aerosol Research

Editor:

• Pramod Kulkarni

Notes

1 This assumption holds true since the relaxation time of the particles is much shorter than their residence time in the classification region.

2 As shown later in Figure 8 a, the stationary height factor (i.e., transmission efficiency) is $\sim$ 0.3 for particles at $\sim$0.05 fg in a single CPMA at $Q=$0.3 LPM. These particle losses would then be approximately doubled when the two CPMAs are operated in the tandem arrangement.

Additional information

Funding

The authors gratefully acknowledge funding from Transport Canada (Clean Transportation System – Research and Development Program), Alberta Innovates, and the Natural Sciences and Engineering Research Council of Canada (NSERC) FlareNet Research Network. TJJ appreciates the support of the NSERC Postdoctoral Fellowship Program.