An improved inversion method for determining two-dimensional mass distributions of non-refractory materials on refractory black carbon

Abstract

The present study describes an improved inversion method for determining the two-dimensional mass distribution of non-refractory materials on refractory black carbon using a centrifugal particle mass analyzer (CPMA) and single-particle soot photometer (SP2) system. The novel approach is tested with several well-established regularization methods to determine which method works best in the new method. Contrary to other two-dimensional inversion applications in the literature, in the CPMA-SP2 inversion, there is a physical constraint that the refractory black carbon mass (mrBC) cannot exceed the total particle mass (mP). This constraint has to be considered in the inversion to accommodate the sharp edge where mrBC equals mP which causes established regularization methods to underperform and potentially smooth the distribution over this boundary. This study introduces a novel deconvolution scheme which accommodates the physical constraint and can be solved with various inversion techniques including: least-squares, Twomey, Twomey–Markowski, multiplicative algebraic reconstruction technique (MART), Tikhonov, and exponential distance methods. The new method also accounts for the problem that the mobility of the black carbon particles is unknown but is required for kernel construction, by using an innovative approach based on constraining the inversion so that the marginal distribution from the CPMA-SP2 inversion matches the distribution of dN/dlog⁡mrBC measured directly by SP2 while the CPMA is bypassed. The inversion technique is tested with synthetic data or “phantoms” – representing uncoated soot, soot coated with non-refactory material, and a mixture of coated and uncoated soot. The results reveal that the exponential distance method outperforms the other regularization methods tested.Copyright © 2020 American Association for Aerosol Research