Differential Electrical Mobility Analysis: A Theoretical Study

The subject of this work is the theoretical investigation of slowly scanning differential mobility analyzers (DMAs) which are, e.g., utilized to determine DMA transfer functions and to measure particle mobility distributions. A model to describe such systems is introduced and applied to investigate three different regimes of input mobility distributions: 1) a mobility distribution much narrower than the DMA transfer function, 2) a mobility distribution of about the same width as the DMA transfer function, and 3) a mobility distribution much wider than the DMA transfer function. Cases 1) and 2) are relevant for DMA transfer function measurements utilizing tandem differential mobility analyzer (TDMA) systems. For either regime, it is not possible to determine DMA transfer functions directly from the concentration distributions measured at the outlet of a DMA. For these cases, a deconvolution procedure is needed. Therefore, an iterative deconvolution procedure was developed. Determining DMA transfer functions utilizing the developed deconvolution procedure, different shapes of transfer function (triangular, Gaussian) are discussed. Case 3) is relevant for particle size distribution measurements. Here, the mobility distribution upstream of the DMA can be obtained by dividing the concentration distribution measured downstream of a DMA by the DMA transfer function area. The DMA transfer function area is influenced by diffusional losses inside the DMA, and therefore is size-dependent. Neglecting this size dependence results in an underprediction of particle number concentrations in the ultrafine particle size range.