Inversion to obtain aerosol size distributions from measurements with a differential mobility analyzer

To measure size distributions of submicrometer aerosols with an electrical differential mobility analyzer (DMA) requires an inversion procedure. The Knutson (1976) and the Hoppel (1978) inversion procedures were numerically investigated for the case of log-normal aerosol size distributions. It was found that the Hoppel procedure converges to the same result as that given by the Knutson procedure. The computational range for geometric mean diameter (_g) was 0.025-0.25 μm, and for geometric standard deviation (σ_g) was 1.1–2.4. The inversion error was found to be greater than 10% in certain “forbidden zones” of _g and σ_g values. For the case of an ideal DMA having no lower mobility limit, only one forbidden zone exists, this consisting of small σ_g values. The boundary of this forbidden zone intercepts the computational range boundaries at σ_g = 1.25, and σ_g = 1.62, . These results also apply to an actual DMA when the size distribution of particles larger than the DMA singly charged mobility limit is available a priori. If such information is not available, the concentration of these larger particles is assumed to be zero in performing the inversion. This assumption adds a second forbidden zone, consisting of large σ_g values and having the intercepts σ_g = 2.44, and σ_g = 1.50, . The first forbidden zone remains nearly the same.