Analytic solution to low knudsen number brownian coagulation

Lee, K.W.; Lee, Y.J.; Han, Dae Suk

doi:10.1016/s0021-8502(97)85319-0

Journal of Aerosol Science

1997

DOI: 10.1016/s0021-8502(97)85319-0

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Analytic solution to low knudsen number brownian coagulation

K.W. Lee¹,

Y.J. Lee²,

Dae Suk Han³

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Cited by 2 publications

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Realization of Self-Preserving Size Distribution Theory for the Evolution of Tropospheric Atmospheric Aerosols Through an Inverse Gaussian Distribution

Shen

Koivisto

et al. 2021

Journal of the Atmospheric Sciences

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The inverse Gaussian distributed method of moments (IGDMOM; J. Atmospheric Sci. 77 (9): 3011-3031, 2020) was developed to analytically solve the kinetic collection equation (KCE) for the first time. Using the IGDMOM, we obtained both new analytical and asymptotic solutions to the KCE. This is shown for both the free molecular and continuum regime collision frequency functions. The new analytical solutions are highly suitable for demonstrating the self-preserving size distribution (SPSD) theory. The SPSD theory is considered one of the most elegant research works in atmospheric science for aerosols or small cloud droplets. It was initially discovered by Friedlander (J. Meteorology 17 (5): 479-483, 1960) and then developed by Lee (J. Colloid Interface Sci. 92 (2): 315-325, 1983) with an assumption of the time-dependent lognormal size distribution function. In this study, we demonstrate that the SPSD theory of coagulating atmospheric aerosols can be presented in a simpler and more rigorous theoretical way, which is realized through the introduction of the IGDMOM for describing aerosol size distributions. Using the IGDMOM, the new formulas for the SPSD, as well as the time required for aerosols to reach the SPSD, are analytically provided and verified. Furthermore, we discover that the SPSD of atmospheric aerosols undergoing coagulation is only determined using a shape factor variable, 𝛺, which is composed of the first three moments at an initial stage. This study has critical implications for developing tropospheric atmospheric aerosol or small cloud droplet dynamics models and further verifies the SPSD theory from the viewpoint of theoretical analysis.

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Realization of Self-Preserving Size Distribution Theory for the Evolution of Tropospheric Atmospheric Aerosols Through an Inverse Gaussian Distribution

Shen

Koivisto

et al. 2021

Journal of the Atmospheric Sciences

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Taylor series expansion scheme applied for solving population balance equation

Lin

2017

Reviews in Chemical Engineering

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Abstract Population balance equations (PBE) are widely applied to describe many physicochemical processes such as nanoparticle synthesis, chemical processes for particulates, colloid gel, aerosol dynamics, and disease progression. The numerical study for solving the PBE, i.e. population balance modeling, is undergoing rapid development. In this review, the application of the Taylor series expansion scheme in solving the PBE was discussed. The theories, implement criteria, and applications are presented here in a universal form for ease of use. The aforementioned method is mathematically economical and applicable to the combination of fine-particle physicochemical processes and can be used to numerically and pseudo-analytically describe the time evolution of statistical parameters governed by the PBE. This article summarizes the principal details of the method and discusses its application to engineering problems. Four key issues relevant to this method, namely, the optimization of type of moment sequence, selection of Taylor series expansion point, optimization of an order of Taylor series expansion, and selection of terms for Taylor series expansion, are emphasized. The possible direction for the development of this method and its advantages and shortcomings are also discussed.

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Analytic solution to low knudsen number brownian coagulation

Cited by 2 publications

References 4 publications

Realization of Self-Preserving Size Distribution Theory for the Evolution of Tropospheric Atmospheric Aerosols Through an Inverse Gaussian Distribution

Realization of Self-Preserving Size Distribution Theory for the Evolution of Tropospheric Atmospheric Aerosols Through an Inverse Gaussian Distribution

Taylor series expansion scheme applied for solving population balance equation

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