Description of aerosol dynamics by the quadrature method of moments
Open accessAbstract
The method of moments (MOM) may be used to determine the evolution of the lower-order moments of an unknown aerosol distribution. Previous applications of the method have been limited by the requirement that the equations governing the evolution of the lower-order moments be in closed form. Here a new approach, the quadrature method of moments (QMOM), is described. The dynamical equations for moment evolution are replaced by a quadrature-based approximate set that satisfies closure under a much broader range of conditions without requiring that the size distribution or growth law maintain any special mathematical form. The conventional MOM is recovered as a special case of the QMOM under those conditions, e.g., free-molecular growth, for which conventional closure is satisfied. The QMOM is illustrated for the growth of sulfuric acid-water aerosols and simulations of diffusion-controlled cloud droplet growth are presented.
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CQMOM numerical results show excellent agreement with the available analytical solution for particle growth with a linear growth law and with a diffusion-limited one.
“Numerical results show an excellent agreement with the available analytical solution [301,324] for the cases of particle growth with a linear growth law, and with a diffusion-limited one.”
From Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review (2022) · cites this paper as [301]
The Diffusion-Controlled Growth section says QMOM results agree excellently with calculations from the exact evolved distribution. The Calculations section says detailed calculations are limited to diffusion-controlled growth; it does not report numerical agreement for a linear growth law. The source discusses QMOM, not CQMOM. (LLM, conf=0.88)
Experimental — accuracy not yet measuredEQMOM numerical results compare favorably with available analytical ones for PBE considering aggregation, breakage, condensation, and evaporation.
“The EQMOM has been used to solve a PBE considering aggregation, breakage, condensation, and evaporation terms, and the numerical results compare favorably with the available analytical ones [288,293,301,318,322].”
From Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review (2022) · cites this paper as [301]
The Diffusion-Controlled Growth section reports that QMOM simulations agreed closely with numerical integrations of the exact evolved distribution. But this paper describes QMOM, not EQMOM, and its reported comparison concerns droplet growth—not a population balance equation combining aggregation, breakage, condensation, and evaporation. (LLM, conf=0.88)
Experimental — accuracy not yet measuredQMOM replaces growth law integrals with an n-point Gaussian quadrature so that abscissas and weights can be specified as a function of lower-order moments; the approximate equations are closed form and the size distribution or growth law does not require a special form.
“This is achieved by replacing the growth law integrals with an n-point Gaussian quadrature so that the abscissa and weights can be specified as a function of lower-order moments of an unknown distribution function. Thereby, the approximate set of equations results in closed form, and the size distribution or growth law does not require any special form.”
From Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review (2022) · cites this paper as [301]
McGraw [301] removed the deficiency of the MOM with QMOM, replacing the evolution equations of the moments by a quadrature-based approximate set of equations that can satisfy closure.
“The deficiency of the MOM is removed by the approach of McGraw [301] with the so-called Quadrature Method of Moments (QMOM). The evolution equations of the moments are replaced by a quadrature-based approximate set of equations that can satisfy closure.”
From Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review (2022) · cites this paper as [301]
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- Authors
- McGraw, R.
- Affiliations
- Brookhaven National Laboratory (US)
- Corresponding author
- McGraw, Robert
- ORCID
- McGraw, Robert
- Venue
- Aerosol Science and Technology
- Publisher
- Informa UK Limited
- Published
- 1997-01
- Volume
- 27
- Issue
- 2
- Pages
- 255-265
- ISSN
- 0278-6826 (ISSN-L)
- 1521-7388
- OpenAlex
- W2025376439
- Cited by
- 1,128
- References
- 15
- Citations by year
- 2026: 37 · 2025: 44 · 2024: 35 · 2023: 43 · 2022: 70 · 2021: 43 · 2020: 51 · 2019: 67 · 2018: 49 · 2017: 62 · 2016: 70 · 2015: 44 · 2014: 47 · 2013: 53 · 2012: 62
- FWCI
- 2.65
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Aerosol Science and Technology (publishedVersion)
- Topics
- Physical Sciences › Earth and Planetary Sciences › Atmospheric Science › Atmospheric chemistry and aerosols
- Physical Sciences › Environmental Science › Global and Planetary Change › Atmospheric aerosols and clouds
- Physical Sciences › Chemical Engineering › Fluid Flow and Transfer Processes › Advanced Combustion Engine Technologies
- Keywords
- quadrature method of moments, method of moments, aerosol size distribution, closure, cloud droplet growth, diffusion-controlled growth, aerosol dynamics
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