Abstract
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 pointu, the relationship between asymptotic behavior and analytical solution, and the error of the high-order moment equations. All these analyses will contribute to the buildup of the theoretical system of the TEMOM model.
Highlights
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
Using a Taylor-series expansion at υ = u = M1/M0 for υk, the fractional moments can be approximated by the combination of integral moments as follows: υk = uk + uk−1k (υ − u) uk−2k
The results show that the relative errors are small, and the two sets of equations are equivalent approximately
Summary
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. Based on TEMOM model, the important information about the PSD, namely, the particle number density, particle mass, and geometric standard deviation, can be obtained for Brownian coagulation over the entire size regimes, and its results have a great agreement with other moment methods [3, 12,13,14,15,16] In these works, some fundamental problems are not clarified, for example, why the expansion point u is set to be M1/M0 instead of other formulas; why the Taylor-series are truncated just at the first three terms; and what about the errors estimation of the present TEMOM model. Mainly as a methodological introduction, we would like to demonstrate the theoretical analysis to answer these questions for Brownian coagulation in the continuum regime
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