Interpreting and reconciling classifier-order effects in effective density measurements

The effective density of an aerosol particle and the related mass-mobility exponent are useful for calculating the integrated particle mass and providing fundamental insights into particle morphology. Typically, the effective density is measured using two tandem aerosol classifiers, where each classifier selects particles of a specified mass, mobility diameter, or aerodynamic diameter. Since effective density conceptually represents a physical property of the sampled particles, it is expected to be independent of order of the classifiers. However, recent studies have reported different effective densities for different classifier arrangements, e.g. mobility-mass classification versus mass-mobility classification. In this study, we show that the root cause of the observed discrepancies lies in the fundamental properties of the underlying bivariate distribution and the calculation of effective density using a classifier setpoint and the mode of downstream distributions. The modes of conditional (i.e., classified) distributions differ depending on the conditioned property (i.e., which classifier setpoint is used in the calculation). It is only when the two properties are tightly correlated that the two fits become equal. We then provide analytical relationships that enable transformation between classifier arrangements and validate the proposed relations using soot aggregates across four classifier arrangements involving a particle mass analyzer (PMA), differential mobility analyzer (DMA), or aerodynamic aerosol classifier (AAC): PMA → DMA, DMA → PMA, AAC → DMA, and DMA → AAC. After applying the transformation, discrepancies reduce from 15% for the APM → DMA configuration and 30% for the AAC → DMA configuration effective density to 5%.