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An analytical solution for the population balance equation using a moment method
Yu, Mingzhou1,2; Lin, Jianzhong1; Cao, Junji2; Seipenbusch, Martin3
Source PublicationPARTICUOLOGY

Brownian coagulation is the most important inter-particle mechanism affecting the size distribution of aerosols. Analytical solutions to the governing population balance equation (PBE) remain a challenging issue. In this work, we develop an analytical model to solve the PBE under Brownian coagulation based on the Taylor-expansion method of moments. The proposed model has a clear advantage over conventional asymptotic models in both precision and efficiency. We first analyze the geometric standard deviation (GSD) of aerosol size distribution. The new model is then implemented to determine two analytic solutions, one with a varying GSD and the other with a constant GSD. The varying solution traces the evolution of the size distribution, whereas the constant case admits a decoupled solution for the zero and second moments. Both solutions are confirmed to have the same precision as the highly reliable numerical model, implemented by the fourth-order Runge-Kutta algorithm, and the analytic model requires significantly less computational time than the numerical approach. Our results suggest that the proposed model has great potential to replace the existing numerical model, and is thus recommended for the study of physical aerosol characteristics, especially for rapid predictions of haze formation and evolution. (C) 2014 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.

KeywordSelf-preserving Aerosols Analytical Solution Taylor-expansion Method Of Moments Population Balance Equation
WOS HeadingsScience & Technology ; Technology
WOS KeywordLarge-eddy-simulation ; Brownian Coagulation ; Quadrature Method ; Size Distribution ; Asymptotic-behavior ; Expansion Method ; Temom Model ; Particles ; Regime ; Nanoparticles
Indexed BySCI
WOS Research AreaEngineering ; Materials Science
WOS SubjectEngineering, Chemical ; Materials Science, Multidisciplinary
WOS IDWOS:000349730200023
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Document Type期刊论文
Corresponding AuthorLin, Jianzhong
Affiliation1.China Jiliang Univ, Dept Phys, Hangzhou 310028, Peoples R China
2.Chinese Acad Sci, Inst Earth Environm, Xian 710075, Peoples R China
3.Karlsruhe Inst Technol, Inst Mech Proc Engn & Mech, D-76021 Karlsruhe, Germany
Recommended Citation
GB/T 7714
Yu, Mingzhou,Lin, Jianzhong,Cao, Junji,et al. An analytical solution for the population balance equation using a moment method[J]. PARTICUOLOGY,2015,18:194-200.
APA Yu, Mingzhou,Lin, Jianzhong,Cao, Junji,&Seipenbusch, Martin.(2015).An analytical solution for the population balance equation using a moment method.PARTICUOLOGY,18,194-200.
MLA Yu, Mingzhou,et al."An analytical solution for the population balance equation using a moment method".PARTICUOLOGY 18(2015):194-200.
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