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

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.

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