The Spider DMA: A miniature radial differential mobility analyzer

Abstract

The Spider differential mobility analyzer (DMA) is a novel, miniaturized radial DMA developed to provide size classification in the 10–500 nm range for applications requiring high portability and time resolution. Its external dimensions are ∼12 cm in diameter by 6 cm in height (excluding tubing); it weighs ∼350 g, and is designed to operate at 0.6–1.5 L/min sheath and 0.3 L/min sample flowrates. It features a new sample inlet geometry that is designed to produce a uniform azimuthal particle distribution at the entrance of the classifier, optimized sample/sheath flow streams introduction in the classifier to minimize particle delays, and extension of the electric field interaction volume for ∼30% enhanced dynamic range. Based on three-dimensional finite element simulations of flows, electric fields, and particle trajectories, we demonstrate that the Spider DMA transfer functions can be predicted with high fidelity using a parameterized fit based on the Stolzenburg semi-analytical model. Experimental characterization of the instrument response with size-selected particles confirmed close agreement with model prediction; mobility size response is linear over three orders of magnitude in mobility span. Electrical ground shielding of the external surfaces of the DMA has been found to be necessary to avoid particle losses associated with field effects as the high voltage operating limit is approached. The mean deviation between the reference size of polystyrene latex spheres and the Spider DMA measurement is less than 2%, corroborating its high sizing precision and potential for high quality size distribution measurements.

Copyright © 2019 American Association for Aerosol Research

EDITOR:

• Jingkun Jiang

Acknowledgments

The authors would like to thank Dr. Huajun Mai for helpful discussions and assistance in preparation of the experimental data acquisition software.

Notes

1 In a balanced DMA flows condition, the aerosol inlet flow ($Q_a$) is equal to the classified sample flow ($Q_s$), and the sheath flow ($Q_{\mathit{sh}}$) is equal to the excess flow ($Q_e$).

2 For the Spider DMA geometry reported in this study, $Z_p^{*}$ is calculated based on $R_2=42.29$ mm, $R_1=2.41$ mm, and $b=5$ mm.

3 As formulated here, $f_{V }$is also equivalent to a correction factor to the theoretical voltage at which the peak transmission occurs according to Equation (2)(2) $$Z_{\mathrm{p}}^{\mathrm{*}}=\frac{\left(Q_{\mathrm{sh}}+Q_{\mathrm{e}}\right)\mathrm{ }b}{2\pi \left(R_2^2-R_1^2\right)V},$$(2) .

4 From Equations (6)(6) $${\widetilde{{\rm Z}}}_{\mathrm{p}}=\raisebox{1ex}{$Z_{\mathrm{p}}$}\!\left/ \!\raisebox{-1ex}{$Z_{\mathrm{p}}^{\mathrm{*}}$}\right.\mathrm{ }$$(6) and (17)(17) $$\zeta \left(\theta \right)=\frac{Q_{\mathrm{sh}}\left(\theta \right)}{Q_{\mathrm{sh},\mathrm{nom}}}=\frac{Z_{\mathrm{p}}^{\mathrm{*}}(\theta )}{Z_{\mathrm{p},\mathrm{nom}}^{\mathrm{*}}},$$(17) : $\zeta \left(\theta \right)= \frac{Z_p^{*}(\theta )}{Z_{p,\mathit{nom}}^{*}}=\frac{\raisebox{1ex}{$Z_p$}\!\left/ \!\raisebox{-1ex}{$Z_{p,\mathit{nom}}^{*}$}\right.}{\raisebox{1ex}{$Z_p$}\!\left/ \!\raisebox{-1ex}{$Z_p^{*}(\theta )$}\right. }=\frac{{\widetilde{{\rm Z}}}_p}{{\widetilde{{\rm Z}}}_p(\theta ) }\iff {\widetilde{{\rm Z}}}_p=\zeta (\theta ){ \widetilde{{\rm Z}}}_p(\theta )$

5 Lines in Figure 10 appear to be ascending because the mobility axis direction is reversed to correspond to increasing particle size.

Additional information

Funding

This research was supported by the Small Business Innovative Research and Small Business Technology Transfer Department of Energy Research Grant No. DE-SC0013152.