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

Abstract

Aerosol mobility size spectrometers are commonly used to measure size distributions of submicrometer aerosol particles. Commonly used data inversion algorithms for these instruments assume that the measured mobility distribution is broad relative to the DMA transfer function. This article theoretically examines errors that are incurred for input distributions of any width with an emphasis on those with mobility widths comparable to that of the DMA's transfer function. Our analysis is valid in the limit of slow scan rates, and is applicable to the interpretation of measurements such as those obtained with tandem differential mobility analyzers as well as broader distributions. The analysis leads to expressions that show the relationship between the inverted number concentration, mean size, and standard deviation and true values of those parameters. For narrow distributions (e.g., for a mobility distribution produced by a DMA with a 1:10 aerosol:sheath air flow ratio) under typical operating conditions, number concentrations and mean mobility obtained with inversion algorithms are accurate to within 0.5% and 1.0%, respectively. This corresponds to mean diameter retrieval errors of 1.0% for large particles and 0.5% for small (kinetic regime) particles. The widths (i.e., relative mobility variance) of the inverted distributions, however, significantly exceed the true values. EDITOR Jingkun JiangThe inversion algorithm described by Collins et al. (2002) eliminates this error by finely discretizing the mobility distribution function, thereby allowing variations within the DMA mobility window. The inversion technique described by Twomey (1975) is used to determine the size distribution; to our knowledge, this approach is not widely used by aerosol scientists. Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/uast.

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“…The first term on the left side of Equation (6) is the square of the relative mobility standard deviation of the SMPS recovered distribution. As demonstrated in Stolzenburg and McMurry (2018), this can be well approximated as…”

“…For the case of a narrow distribution such as the proposed mobility-classified challenge aerosol, this assumption is violated and the accuracy of the SMPS recovered size distribution may be compromised. Stolzenburg and McMurry (2018) have analyzed the accuracy of the recovered moments 1 of narrow size distributions with the following results:…”

A high resolution DMA covering the 1–67 nm size range

“…However, the anomalous increased peak width observed at 47 Lit/min is largely the result of having ignored diffusive broadening. We can estimate this effect by assuming the linear dependence obtained experimentally in Figure 4 (Stolzenburg 2018;Stolzenburg and McMurry 2018), FWHM for combined diffusion and intrinsic width would be (0.06 2 þ 0.043 2 ) 1/2 ¼ 7.4%. If we took FWHM ¼ 7.4% to be the effective intrinsic width of the IgG peak at that flow rate, the corresponding theoretical line would agree approximately with the experimental curve.…”