Extended log-normal method of moments for solving the population balance equation for Brownian coagulation

An extended log-normal method of moments (ELNMOM) is presented in this study for solving the population balance equation (PBE) for Brownian coagulation. The method is an extension of the log-normal method of moments (LNMOM) proposed by Lee in 1983. The ELNMOM uses the superposition of log-normal subdistributions to represent the size distribution. Unlike previous modal studies, the subdistributions are not independent modes but flexible components in this study and the closure of this method is achieved by introducing additional higher-order moment equations. Based on some simplifying assumptions, the ELNMOM is implemented with only four adjustable parameters for a preliminary exploration. The method is then validated by comparing the size distribution parameters predicted by this method with those predicted by the LNMOM and other numerical methods for Brownian coagulation in the continuum regime and the free-molecular regime. The results show that the ELNMOM more accurately predicts the total particle number concentration, the geometric standard deviation and the geometric mean particle volume than the LNMOM while not taking much more computation time.

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