On the validity of the Poisson assumption in sampling nanometer-sized aerosols

For a constant aerosol concentration, it is traditionally assumed that a Poisson process describes the behavior of particle detections during sampling and consequently fluctuations in the measured concentration. Recent studies, however, have shown that sampling of micrometer-sized aerosols has non-Poissonian behavior with positive correlations. The validity of the Poisson assumption for nanometer-sized aerosols has not been established and thus was tested in this study. Its validity was tested for four particle sizes - 10 nm, 25 nm, 50 nm, and 100 nm - by sampling from indoor air with a differential mobility analyzer-condensation particle counter (DMA-CPC) setup to obtain a time series of particle counts. Five metrics were calculated from the data: pair-correlation function (PCF), scaled clustering index (SCI), coefficient of variation, probability of measuring a concentration at least 25% greater than average, and posterior distributions from Bayesian inference. To identify departures from Poissonian behavior, these metrics were also calculated for 1000 computer-generated Poisson time series with the same mean as the experimental data. For most comparisons, the experimental data fell within the range of 80% of the Poisson-simulation values. Essentially, the metrics for the experimental data were mostly indistinguishable from a simulated Poisson process. The greater influence of Brownian motion for nanometer-sized aerosols may explain the Poissonian behavior observed for smaller aerosols. Although the Poisson assumption was found to be reasonable in this study it must be carefully applied, as the results here do not definitively prove applicability in all sampling situations.