THE ASYMPTOTIC STABILITY OF THE TAYLOR-SERIES EXPANSION METHOD OF MOMENT MODEL FOR BROWNIAN COAGULATION

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.