Prediction of the transfer function for a centrifugal differential mobility analyzer by streamline functions

For complexly shaped aerosol particles a single equivalent diameter is often not sufficient for comprehensive characterization. The newly developed Centrifugal Differential Mobility Analyzer (CDMA) allows the simultaneous assessment of two equivalent sizes, e.g., mobility and aerodynamic diameter. However, determining the full two-dimensional particle size distribution using the CDMA requires precise knowledge of the transfer function. Thus, the derivation of the ideal transfer function <i>via</i> streamline functions, as proposed by Stolzenburg (2008), is adapted to the two-dimensional framework of the CDMA and compared to the calculation of the transfer function using particle trajectories. Both methods yield identical results for an idealized situation, which strongly indicates validity. Subsequently, the streamline method is extended to calculate the transfer function by applying different inlet boundary conditions, namely the common assumption of constant particle flux density versus the assumption of a given velocity profile and constant particle concentration. This appears to be a more realistic assumption in case of a laminar flow profile at the inlet. Furthermore, diffusion is considered, leading to realistic transfer functions down to ultrafine particle sizes. The results demonstrate that the inlet boundary condition significantly affects the transfer function and that diffusion has a considerable impact on the shape of the transfer function, particularly for smaller particles. Consequently, the assumption of a Gaussian transfer function can be deemed to be valid even for larger particles.