10th International Aerosol Conference September 2 - September 7, 2018 America's Center Convention Complex St. Louis, Missouri, USA
Abstract View
Inversion of Scanning Electrical Mobility Spectrometer and SMPS Measurements
RICHARD FLAGAN, Yuanlong Huang, Amanda Grantz, California Institute of Technology
Abstract Number: 778 Working Group: Instrumentation
Abstract The Scanning Mobility Particle Sizer, (SMPS) enables rapid particle size distribution measurements, but the data obtained as the voltage is scanned are analyzed using the transfer function for a constant voltage DMA; that transfer function would be valid for plug flow (uniform velocity within the DMA), but boundary layers within the DMA cause particles to follow different trajectories through the classification region, altering the transfer function. Particles also experience a distribution of time delays between the times when they exit the DMA and are counted by the CPC. Convolution of a delay-time distribution function with the DMA transfer function has been used to invert SEMS/SMPS data, but the distortions caused by the DMA itself are not taken into account. Recent coupling of finite element simulations of the flows and fields within the scanned DMA with Brownian dynamics simulations of the advection, migration, and diffusion of particles during SEMS measurements have revealed additional deviations of the transfer function from that at constant voltage.
Prompted by these results, we have re-examined SEMS/SMPS data inversion, which requires: (i) a transfer function for the instrument; (ii) a model that will be used to represent the resultant particle size distribution function; and (iii) an algorithm that will be employed to solve the inverse problem to deduce the size distribution that best represents the collection of signals acquired during the measurement. At constant voltage, the physics-based, Stolzenburg model of the transport and diffusion of particles within the DMA accurately describes the instrument. The delay time distribution caused by can be approximated the residence time distribution from one or more so-called continuously-stirred tank reactors combined with a fixed delay. The new transfer function for the TSI long-column DMA reveals a delay-time distribution within the classification region, and a more complex downstream delay time distribution that the previous models suggest. Combined with empirical transmission and detection efficiency functions and theoretically predicted charge distributions, these refinements reproduce the time and size variation in particle transmission through and detection by the SEMS/SMPS measurement system and form the foundation for data inversion. The computational effort to obtain the real-instrument transfer function is, however, large. We have, therefore, undertaken the development of a theoretical transfer function for the scanned-voltage DMA analogous to the Stolzenburg transfer function for the static DMA, and that is more readily applied to other DMA operating conditions, and to different DMA designs.
The discretized form of the particle size distribution also strongly affects the data inversion. Multimodal lognormal distributions impose a potential shape bias on the size distribution. Representation as a set of discrete particle sizes (delta functions) or as a histogram representation are also commonly used. Linear splines are used in a number of algorithms. Higher order basis functions can also be used. The degree of approximation directly impacts the quality of the data fit obtained. The algorithms employed can also affect the quality of the inversion. In this study, we examine the sensitivity to different models for the same instrument, size distribution representations, and inversion algorithms in order to understand their effects on the recovered distributions. While the focus of this study has been on SEMS or SMPS data inversion, the results have implications for all methods used to determine aerosol particle size distributions.