A Data Inversion Routine for the Two-Dimensional Mass-Mobility Size Distribution Function with DMA-APM Tandem Measurements

摘要

In principle, the combination of a differential mobility analyzer (DMA) and aerosol particle mass analyzer (APM, Ehara et al, 1996)) not only enables determination of particle properties such as effective density and dynamic shape factor, but also the two-dimensional size distribution function dN/dd_pdm, where N is the number concentration of particles, d_p is the particle diameter, and m is the particle mass. Although use of the APM is increasing, to date, the DMA-APM combination has not been used for dN/dd_pdm determination in large part because a specific inversion routine needs to be developed to infer this function from measurements, accounting for both DMA and APM transfer functions, particle losses, charging efficiencies, and condensation particle counter (CPC) detection efficiencies. In this work, we develop such an inversion routine, which directly outputs dN/dd_pdm for input CPC measured concentrations (N) as functions of DMA settings (settings i) and APM settings (settings j). The Twomey-Markowski algorithm (Markowski, 1987) is shown to be applicable for this inversion procedure, but can require more than 1000 iterations proper convergence of 2-D size distributions. We additionally show that improved description of dN/dd_pdm is possible by increasing the number of N(i,j) measurements made, which minimizes the need for spline fitting for values between channels.