Diffusion broadening of DMA transfer functions. Numerical validation of Stolzenburg model

This study investigates the validity of the assumptions inherent in the semianalytical expression derived by Stolzenburg [(1988). An ultrafine aerosol size distribution measuring system. Ph.D. thesis, Department of Mechanical Engineering, University of Minnesota, Minnesota] for the differential mobility analyzer (DMA) transfer function. For this purpose, a fourth-order finite-difference numerical method is employed to calculate the diffusion-broadened transfer function of two widely used DMA units: the “long” DMA (TSI Model 3081) and the “nano”-DMA (TSI Model 3085). Stolzenburg's results were in good agreement with the results of this study. Deviations were only observed near the boundaries of the transmitted mobility window. Under fully developed laminar flow, the area calculated with both methods agreed within 0.3%. Under plug-flow conditions, the same area was calculated 6.3% less than Stolzenburg's estimate for particles at the low detection limit of both DMAs. This corresponds to particle losses within the DMA classification region. The results confirm that Stolzenburg transfer functions can be used with good confidence in typical DMA applications and that two commercial DMA systems exhibit limited particle losses inside their classification region.