Simplified analysis of the effect of brownian diffusion on the relationship between applied voltage and central mobility in the DMA

The experimentally observed mismatch between the classification voltages for two identical differential mobility analyzers connected in series (TDMA) can be explained as a sole consequence of the Brownian motion of the particles when the aerosol concentration is relatively low. For a polydisperse aerosol, the peak of the DMA transfer function does not correspond to the ideal expected voltage, but may shift toward larger or smaller voltages depending on whether the mobility of the classified particles is, respectively, smaller or larger than the population mean mobility. For a monodisperse aerosol, the second DMA peak voltage is a constant independent of the voltage applied to the first unit. A simple model is proposed to derive a practical relationship between the applied voltage and the central mobility of the classified particles.