The multiple monodisperse outlet differential mobility analyzer: Derivation of its transfer function and resolution

Conventional differential mobility analyzers (DMAs) for classification of aerosol particles have one polydisperse-particle inlet and one monodisperse-particle outlet. As a result, when they are used as particle classifiers in aerosol mobility spectrometers, it is needed to scan through different operating conditions, thereby requiring a significant amount of time (i.e., of the order of a minute) for a single mobility distribution measurement. DMAs with multiple outlets can significantly reduce this scanning time because particles of different mobilities can be classified and detected simultaneously. In addition, depending on the relative location of the first and the last outlet from the inlet, one can increase the dynamic mobility range of the selected particles in a single particle mobility distribution measurement. In this article, we derive analytical expressions for estimating the transfer function and the resolution of DMAs with multiple monodisperse outlets. Starting with the simple consideration of nondiffusing particles, we extend our analysis for diffusing particles and provide expressions of different complexity and accuracy. The theoretical framework provided in this article can be employed to optimize the design of DMAs with more than one monodisperse-particle outlet, and to analyze the measurements when such DMAs are used in aerosol mobility spectrometers.