A New Mathematical Scheme for Approximating Overall Aerosol Extinction Coefficient during Brownian Coagulation

The approximation of the overall aerosol extinction coefficient is conventionally achieved through integrating the single particle extinction efficiency over the whole size distribution, which requires much computational time. In this work, a new approximation scheme with higher efficiency than the conventional scheme is proposed, in which the combination of polynomials for fitting Mie’s solution and the method of moments produces the overall extinction coefficient of evolving nanoparticles. The closure of arbitrary moments is achieved by implementing the Taylor-series expansion method of moments. The new approximation scheme was verified by comparing it to a more exact referenced scheme for two different typical aerosol modes, namely the nucleation mode and the accumulation mode. This study verifies that the new scheme is a reliable method for approximating the overall extinction coefficient during aerosol evolution with acceptable efficiency and accuracy; thus, it is suitable for use in some atmospheric aerosol models.