Diffusional transfer function for the scanning electrical mobility spectrometer (SEMS)

Abstract

The scanning electrical mobility spectrometer (SEMS), or scanning mobility particle sizer (SMPS), uses the differential mobility analyzer (DMA) operated in scanning mode to measure particle size distribution rapidly. To obtain the actual size distribution, the real-time transfer function (transmission efficiency of particles of different mobilities) is necessary, which has previously been investigated with numerical simulations or semi-analytical calculations. We present here a rigorous derivation of the diffusional DMA transfer function for an increasing-voltage scan based on analytically resolving particle trajectories between the instrument inlet and the outlet. This requires a 2D integration in the inlet and outlet space over the contour plot of the particle mobility distribution that can successfully transmit through the scanning DMA. For the first time, we show that the up-scan DMA transfer function for non-diffusive particles is trapezoidal (instead of triangular). The key parameter that determines the shape of the scanning DMA transfer function is the ratio of the characteristic scanning time to the average residence time, which yields the same transfer function as that for the static DMA when the ratio gets sufficiently large. The effect of particle diffusion is included via an extended outlet. The dimensionless equations for the trajectories and the method presented here can be generalized to the column DMA of any geometry.