Numerical modeling and design of a nanometer aerosol differential mobility analyzer

This paper describes a numerical model we have developed to calculate transport of charged nanometer particles in a laminar flow and under an electric field. The model incorporates the flow field, electric field, and aerosol transport calculations inside a differential mobility analyzer (DMA). The DMA consists of two concentric cylinders through which charged particles are deflected in a laminar flow in the annular space between the cylinders maintained at different electric potentials. The continuity and the Navier-Stokes equations in the cylindrical coordinate system with the assumptions of laminar flow and negligible variation in the θ-direction were used to model the flow fields in the DMAs. The equations were solved by the mixed Galerkin and Streamline Upwind/Petrov-Galerkin (SUPG) finite element method with Lagrangian element for high Reynold number flows. For the electric field modeling in the DMAs, the Galerkin finite element formulation with the second order isoparametric element was used to solve the Laplace equation for the electric potential. Then the electric field was derived from the calculated electric potentials. Finally, aerosol transport in the DMAs was modeled by the convective transport equation including the electric force effect on particles. The equation was solved by an adaptive characteristic Petrov-Galerkin finite element method. This numerical model was then used to design a nano-DMA which was optimized for the nanometer particle size range.