Numerical modeling of the performance of differential mobility analyzers for nanometer aerosol measurements

Abstract

A numerical model was developed to predict the performance of differential mobility analyzers (DMAs) for nanometer aerosol measurements. The model consists of three parts: flow field, electric field, and aerosol transport formulations. In order for the model to be applicable for all the existing DMAs, the swirling flow effect due to tangential aerosol injection is included. The tangential inlet design was used in several recently designed DMAs, e.g. Hauke, SMEC and RDMA. The swirling is incorporated in the model by introducing the assumption of negligible variation of the circumferential flow component. Mixed Galerkin and SUPG finite-element formulations with a nine-node velocity, three-node pressure flow elements and bilinear element are proposed. For the electric field, the space charge effect is neglected and the equation is solved by Galerkin finite element method with the second-order isoparametric element. The aerosol transport is modeled by the convective aerosol transport equation with external electrical force. The equation is further simplified by using the same assumption made for the flow field in the circumferential flow component. A modified adaptive characteristic Petrov-Galerkin finite-element method is proposed to overcome the difficulty involved in numerically solving the simplified equation. The model was used to calculate the transfer functions of TSI-short DMA for particle sizes between 5 and 50 nm. They were then validated by comparing the numerical and experimental results for simulated scans from two DMAs operating in series. The numerical transfer functions are compared with the available experimental data from two sources, namely, Hummes et al. (1996) Part. Part. System Charact. 13, 327–332 and Kousaka et al. (1986) J. Chem. Engng Japan 19, 401–407. A good agreement between them is obtained.