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The asymptotic stability of the Taylor-series expansion method of moment model for Brownian coagulation

Xie Mingliang (Huazhong University of Science and Technology, School of Energy and Power Engineering, State Key Laboratory of Coal Combustion, Wuhan, China)
Kong Tingting (Huazhong University of Science and Technology, School of Energy and Power Engineering, State Key Laboratory of Coal Combustion, Wuhan, China)
Li Jin (Huazhong University of Science and Technology, School of Energy and Power Engineering, State Key Laboratory of Coal Combustion, Wuhan, China)
Lin Jiang (Zhejiang University of Science and Technology, Hangzhou, China)

In the present study, the linear stability of population balance equation due to Brownian motion is analyzed with the Taylor-series expansion method of moment. Under certain conditions, the stability of the Taylor-series expansion method of moment model is reduced to a well-studied problem involving eigenvalues of matrices. Based on the principle of dimensional analysis, the perturbation equation is solved asymptotically. The results show that the Taylor-series expansion method of moment model is asymptotic stable, which implies that the asymptotic solution is uniqueness, and supports the self-preserving size distribution hypothesis theoretically.

Keywords: linear stability, moment method, population balance equation, Brownian motion, asymptotic solution