Yue Lai1, Yueyan Liu1, Mingzhou Yu 1,2, Lina Wang , Jing Liu4, Qing Li1

China Jiliang University, Hangzhou 310018, China
Key Laboratory of Aerosol Chemistry and Physics, Chinese Academy of Science, Xi’an 710061, China
Shanghai Key Laboratory of Atmospheric Particle Pollution and Prevention (LAP3), Department of Environmental Science and Engineering, Fudan University, Shanghai 200433, China
School of Municipal and Environmental Engineering, Harbin Institute of Technology (HIT), Harbin 150000, China

Received: January 25, 2018
Revised: June 13, 2018
Accepted: July 11, 2018
Download Citation: ||https://doi.org/10.4209/aaqr.2018.01.0021  

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Cite this article:
Lai, Y., Liu, Y., Yu, M., Wang, L., Liu, J. and Li, Q. (2018). A New Mathematical Scheme for Approximating Overall Aerosol Extinction Coefficient during Brownian Coagulation. Aerosol Air Qual. Res. 18: 2895-2905. https://doi.org/10.4209/aaqr.2018.01.0021


  • A new scheme for overall extinction coefficient was proposed.
  • The scheme is verified to be with acceptable accuracy and efficiency.
  • The new scheme has advantage over conventional method.


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.

Keywords: Overall extinction coefficient; Method of moments; Polynomial; Taylor-series expansion; Aerosol evolution.


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