New approaches to calculate the transfer function of particle mass analyzers

This article provides an overview of methods to evaluate transfer functions for the Couette centrifugal particle mass analyzer (CPMA) and aerosol particle mass analyzer (APM). The work first considers finite difference approaches to solving the partial differential equation governing particle motion, which represents an accurate but computationally-demanding approach to evaluating the transfer function. This is used as a baseline to compare to particle tracking methods, which have been shown to yield closed form expressions for the transfer function. In this work, we extend on previous treatments by presenting a generalized framework that allows us to consider a range of representations of the particle migration velocity. As a result, we derive new closed form expressions for the exact representation of the particle migration velocity under APM conditions and provide significant improvements in the accuracy of the transfer function for CPMA conditions. In the latter case, for a CPMA, particle migration effects dominate, which makes the transfer function easier to approximate. We also show that Taylor series approximations to the particle migration velocity should be taken about the centerline radius rather than the equilibrium radius as was done previously. We end by extending the particle tracking approach and derive new closed form expressions for the transfer function that include diffusion. Copyright (c) 2019 American Association for Aerosol Research