A review of transfer theory and characterization of measured performance for differential mobility analyzers

Abstract

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.

Characterization of a high-resolution supercritical differential mobility analyzer at reduced flow rates

“…The empirical transfer functions and the penetration efficiencies of the half-mini DMAs were analyzed using the data inversion routine presented in Jiang et al (2011c) and Cai et al (2017) with updates reported by Stolzenburg (2018). The corrected ratio of the aerosol concentrations recorded by the two FCEs, N 2/N1, is equal to the product of penetration efficiency and transfer function:…”

“…The DMA transfer function used in this study is a diffusing transfer function (Stolzenburg 1988;Stolzenburg and McMurry 2008;Stolzenburg 2018):…”

“…The multiplicative broadening factor, fσ, characterizes the errors due to the assumptions of the diffusing transfer theory better than σdistor. However, it is usually difficult to separate these two kinds of affects (Stolzenburg 2018). Thus, both broadening factors are used in this study.…”

“…Sub-5 nm molecular ions and particles were generated using an electrospray and a wire generator, respectively, to calibrate the penetration efficiencies and transfer functions of the half-mini DMAs. Their empirical transfer functions and sizing resolutions are evaluated in comparison to a theoretical diffusing transfer function (Stolzenburg 2018). The penetration efficiencies of the new halfmini DMA at various flow rates and particle diameters are inferred according to the measured transfer functions.…”

Accuracy of recovered moments for narrow mobility distributions obtained with commonly used inversion algorithms for mobility size spectrometers

“…In the evaluation of the M Ã i integrals, the diffusing form of the transfer function (Stolzenburg and McMurry 2008;Stolzenburg 2018;and Equation (S2) of the online supplementary information [SI]) is used, dependent on Z p , fixed flow ratios b and d, and the dimensionless diffusion parameter s. The lengthy derivation of these moments is set forth in the SI and results in…”