Scanning DMA Data Analysis I. Classification Transfer Function

The scanning electrical mobility spectrometer (SEMS; also known as the scanning mobility particle sizer, SMPS) enables rapid particle size distribution measurements with a differential mobility analyzer (DMA)/condensation particle counter (CPC) combination by ramping the classifier voltage, and continuously counting particles into time bins throughout the scan. Inversion of scanning measurements poses a challenge due to the finite time response of the CPC; the distorted data can be deconvoluted to improve the fidelity of size distributions obtained with the SEMS/SMPS. Idealized models of the classification region have shown that, for rapid voltage scans that approach the particle residence time in the DMA, the nondiffusive transfer function deviates from the symmetric one seen at constant voltage. Nonetheless, most SEMS/SMPS data analyses employ the constant voltage transfer function, a result that is valid only for plug flow in the classification region. This article develops the scanning-mode transfer function for the actual geometry of the TSI Model 3081 DMA. Finite element calculations are used to determine the flow and electric fields through the entire DMA. The instantaneous scanning-DMA transfer function for diffusive particles is determined using Brownian dynamics simulations. Comparisons of the results from this simulation of a real instrument to those from the idealized models reveal the shortcomings of prior models in describing the instantaneous scanning-DMA transfer function. A companion paper (Part II) combines this scanning-mode transfer function with response functions for the other components of a SEMS/SMPS measurement system in order to derive the response function for the integrated measurement system