The log-normal size distribution theory of brownian aerosol coagulation for the entire particle size range

Park, S.H.; Lee, K.W.; Otto, E.; Fißan, H.

doi:10.1016/s0021-8502(98)00037-8

Cited by 111 publications

(52 citation statements)

References 17 publications

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“…[92] Among several interpolations proposed, the harmonic mean approach has been widely applied to modal aerosol modeling because it allows the integral form of the integrodifferential MDEs to be reduced to the simple forms of equations (A4) and (A11) [Pratsinis, 1988;Binkowski and Shankar, 1995;Park et al, 1999;Park and Lee, 2000;Kajino et al, 2012a]. In order to use the more accurate interpolations such as Fuchs and Fuchs-Sutugin approaches in the modal methods, highly accurate but expensive quadrature method [Giorgi, 1986], referred to collectively as FFS(Q), and the efficient harmonic mean method with lookup table correction factors [Whitby et al, 1991] were developed.…”

Section: Discussionmentioning

confidence: 99%

“…The Fuchs kernel equation (A5) is used with Method IV (DMS-LDM-FFS). Park et al [1999] compared the harmonic mean method with the Fuchs coagulation and concluded that the overall error is always less than 20% (see also Table B2). Whether this discrepancy is unacceptably high or negligible in 3-D chemical weather and climate modeling depends on which processes or parameters you focus on and how large the errors you can permit.…”

Section: A12 Coagulation Equation With Fuchs Approachmentioning

confidence: 99%

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Modal Bin Hybrid Model: A surface area consistent, triple‐moment sectional method for use in process‐oriented modeling of atmospheric aerosols

2013

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[1] A triple-moment sectional (TMS) aerosol dynamics model, Modal Bin Hybrid Model (MBHM), has been developed. In addition to number and mass (volume), surface area is predicted (and preserved), which is important for aerosol processes and properties such as gas-to-particle mass transfer, heterogeneous reaction, and light extinction cross section. The performance of MBHM was evaluated against double-moment sectional (DMS) models with coarse (BIN4) to very fine (BIN256) size resolutions for simulating evolution of particles under simultaneously occurring nucleation, condensation, and coagulation processes (BINx resolution uses x sections to cover the 1 nm to 1 μm size range). Because MBHM gives a physically consistent form of the intrasectional distributions, errors and biases of MBHM at BIN4-8 resolution were almost equivalent to those of DMS at BIN16-32 resolution for various important variables such as the moments M k (k: 0, 2, 3), dM k /dt, and the number and volume of particles larger than a certain diameter. Another important feature of MBHM is that only a single bin is adequate to simulate full aerosol dynamics for particles whose size distribution can be approximated by a single lognormal mode. This flexibility is useful for process-oriented (multicategory and/or mixing state) modeling: Primary aerosols whose size parameters would not differ substantially in time and space can be expressed by a single or a small number of modes, whereas secondary aerosols whose size changes drastically from 1 to several hundred nanometers can be expressed by a number of modes. Added dimensions can be applied to MBHM to represent mixing state or photochemical age for aerosol mixing state studies.Citation: Kajino, M., R. C. Easter, and S. J. Ghan (2013), Modal Bin Hybrid Model: A surface area consistent, triplemoment sectional method for use in process-oriented modeling of atmospheric aerosols,

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Section: Discussionmentioning

confidence: 99%

Section: A12 Coagulation Equation With Fuchs Approachmentioning

confidence: 99%

Modal Bin Hybrid Model: A surface area consistent, triple‐moment sectional method for use in process‐oriented modeling of atmospheric aerosols

2013

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“…3 and 4 and discovered that the proposed analytical solution is more precise in the continuum regime than in the near-continuum regime. The main reason is that the GSD always varies with the Kn in the near-continuum regime, whereas in the continuum regime, it is nearly constant [34] . Notably, the division between the continuum regime and the near-continuum regime is slightly different from that reported in [34] regarding the Kn number.…”

Section: Pseudo-self-preserving Aerosolsmentioning

confidence: 99%

“…The main reason is that the GSD always varies with the Kn in the near-continuum regime, whereas in the continuum regime, it is nearly constant [34] . Notably, the division between the continuum regime and the near-continuum regime is slightly different from that reported in [34] regarding the Kn number. In this paper, the Kn , 0.10 0 0, is defined as the division point for these two regimes following the work displayed in [24] , whereas in [34] , the Kn is lower than 0.10 0 0. a b …”

Section: Pseudo-self-preserving Aerosolsmentioning

confidence: 99%

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A new analytical solution for agglomerate growth undergoing Brownian coagulation

Liu

Jin

et al. 2016

Applied Mathematical Modelling

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a b s t r a c tWe proposed a new analytical solution for a population balance equation for fractal-like agglomerates. The new analytical solution applies to agglomerates with any mass fractal dimensions. Two well-known numerical methods, including the Taylor-series expansion method of moments and the quadrature method of moments, were selected as references. The reliability of the analytical solution with three mass fractal dimensions of 1.0, 2.0, and 3.0 in the continuum-slip regime was verified. The accuracy of the new analytical solution is affected by both the Knudsen number and the mass fractal dimension. The new analytical solution can be further improved in accuracy by introducing a correction factor to the originally derived mathematical formula. The new analytical solution was finally confirmed to possess potential for replacing the numerical solution in the continuum-slip regime.

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Experimental and Numerical Study of Aerosol Coagulation by Gravitation

Kwon

Lee

2002

Part. Part. Syst. Charact.

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The behaviors of aerosols having particle diameters of 1–5 μm were studied experimentally and the results were compared with numerical calculations. For the experimental study, a specially designed coagulation cylinder was developed and the moment method was used in the numerical predictions. The experimental results were characterized by the size parameters including the geometric mean diameter (GMD), the geometric standard deviation (GSD) and the particle number concentration (N). Particle distributions in the cylinder were measured at certain time intervals. In a closed cylinder, the mechanism governing aerosol behavior appeared to be gravitational coagulation. Separately, the numerical calculations were carried out using the moment method. The experimental results and the numerical predictions were in reasonable agreement. It is believed that the present work represents the first experimental study on gravitational coagulation.

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The log-normal size distribution theory of brownian aerosol coagulation for the entire particle size range

Cited by 111 publications

References 17 publications

Modal Bin Hybrid Model: A surface area consistent, triple‐moment sectional method for use in process‐oriented modeling of atmospheric aerosols

Modal Bin Hybrid Model: A surface area consistent, triple‐moment sectional method for use in process‐oriented modeling of atmospheric aerosols

A new analytical solution for agglomerate growth undergoing Brownian coagulation

Experimental and Numerical Study of Aerosol Coagulation by Gravitation

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