The fundamental aspects of the Taylor-series expansion method of moment (TEMOM) model proposed to model the aerosol population balance equation due to Brownian coagulation in the continuum regime is shown in this study, such as the choice of the expansion point

The population balance equations (PBE) are used to describe the evolution process of aerosol particles in a wide range of physical, chemical, and environmental subjects, such as nucleation, coagulation, diffusion, convection, and so on. When the Brownian coagulation plays a dominant role in such cases where aerosol particles at a high concentration are concerned or where suspended particles have evolved for a long time [

Because of its strong nonlinear partial integral-differential structure, the direct solution is very complicated and only a limited number of analytical solutions exist for simple coagulation kernel [

By multiplying

It should be pointed out that the TEMOM has no prior assumption for the PSD using the Taylor-series expansion to achieve the closure and is considered as a promising approach to approximate the PBE for its relative simplicity of implementation and high accuracy [

At the initial time, the particle size maybe small in the free molecule regime. As time advances, the particle volume will grow due to coagulation between particles, and the particle size will transform to the near continuum regime via the transition regime and finally will tend to the continuum regime [

In the TEMOM model, the choice of the expansion point at

The comparison of numerical results among (

The accuracy of the TEMOM model largely depends on the truncation errors of Taylor-series expansion. One method to determine the truncated errors is comparing the results of different TEMOM models, for example, the first three-moment model, the first four-moment model, the first five-moment model, and so forth. Similar to the derivation of the first three moment equations,

Without a prior assumption for the shape of particle size distribution, the TEMOM has been considered as a promising method to model the aerosol population balance equation. In this study, the fundamental problems of the TEMOM model in the continuum regime due to Brownian coagulation are clarified, such as the choice of the expansion point

With the same process as Yu et al. [

The authors should appreciate the useful discussion and suggestion from Dr. Yu Mingzhou at China Jiliang University. This work is supported by the National Natural Science Foundation of China with Grant nos. 50806023 and 50721005, the Fundamental Research Funds for the Central Universities (Project no. 2013TS078), and the Program of Introducing Talents of Discipline to Universities (“111” Project no. B06019), China.

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