journal article·2011-05

The verification of the Taylor-expansion moment method for the nanoparticle coagulation in the entire size regime due to Brownian motion

Mingzhou Yu, Jianzhong Lin, Hanhui Jin, Ying Jiang

Journal of Nanoparticle Research· Volume 13· Issue 5
Publisher page

Abstract

The closure of moment equations for nanoparticle coagulation due to Brownian motion in the entire size regime is performed using a newly proposed method of moments. The equations in the free molecular size regime and the continuum plus near-continuum regime are derived separately in which the fractal moments are approximated by three-order Taylor-expansion series. The moment equations for coagulation in the entire size regime are achieved by the harmonic mean solution and the Dahneke’s solution. The results produced by the quadrature method of moments (QMOM), the Pratsinis’s log-normal moment method (PMM), the sectional method (SM), and the newly derived Taylor-expansion moment method (TEMOM) are presented and compared in accuracy and efficiency. The TEMOM method with Dahneke’s solution produces the most accurate results with a high efficiency than other existing moment models in the entire size regime, and thus it is recommended to be used in the following studies on nanoparticle dynamics due to Brownian motion.
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Research context

OpenAlex topics: Coagulation and Flocculation Studies · nanoparticles nucleation surface interactions · Surfactants and Colloidal Systems

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (24)

Show source-provided references
1. Barrett JC, Jheeta JS (1996) Improving the accuracy of the moments method for solving the aerosol general dynamic equation. J Aerosol Sci 27:1135–114210.1016/0021-8502(96)00059-6 ↗
2. Dahneke B (1983) Simple kinetic theory of Brownian diffusion in vapors and aerosols. In theory of dispersed multiphase flow. Academic Press, New York
3. Friedlander SK (2000) Smoke, dust and haze: fundamentals of aerosol behavior. Wiley Press, New York
4. Friedlander SK, Pui DYH (2004) Emerging issues in nanoparticle aerosol science and technology. J Nanopart Res 6:313–32010.1023/B:NANO.0000034725.89027.6b ↗
5. Friedlander SK, Wang CL (1966) The self-preserving particle size distribution for coagulation by Brownian motion. J Colloid Interface Sci 22:126–13210.1016/0021-9797(66)90073-7 ↗
6. Fuchs NA (1964) The mechanics of aerosols. Pergamon Press, New York
7. Gordon RG (1968) Error bounds in equilibrium statistical mechanics. J Math Phys 9:655–67210.1063/1.1664624 ↗
8. Landgrebe JD, Pratsinis SE (1990) A discrete-sectional model for powder production by gas phase chemical reaction and aerosol coagulation in the free-molecular regime. J Colloid Interface Sci 139:63–8610.1016/0021-9797(90)90445-T ↗
9. Lee KW, Chen H, Gieseke JA (1984) Log-normally preserving size distribution for Brownian coagulation in the free-molecule regime. Aerosol Sci Technol 3:53–6210.1080/02786828408958993 ↗
10. Lee KW, Lee YJ, Han DS (1997) The log-normal size distribution theory for Brownian coagulation in the low Knudsen number regime. J Colloid Interface Sci 188:486–49210.1006/jcis.1997.4773 ↗
11. Lehtinen KEJ, Zachariah MR (2001) Self-preserving theory for the volume distribution of particles undergoing Brownian coagulation. J Colloid Interface Sci 242:314–31810.1006/jcis.2001.7791 ↗
12. Lin JZ, Chan TL, Lin S, Zhou K, Zhou Y, Lee SC (2007) Effects of coherent structures on nanoparticle coagulation and dispersion in a round jet. Int J Nonlinear Sci Numer Simul 8:45–5410.1515/IJNSNS.2007.8.1.45 ↗
13. McGraw R (1997) Description of aerosol dynamics by the quadrature method of moments. Aerosol Sci Technol 27:255–26510.1080/02786829708965471 ↗
14. Müller H (1928) Zur allgemeinen theorie der raschen koagulation. Kolloideihefte 27:223–250
15. Otto E, Fissan H, Park SH, Lee KW (1999) The log-normal size distribution theory of Brownian aerosol coagulation for the entire particle size range: part II-analytical solution using dahneke’s coagulation kernel. J Aerosol Sci 30:17–3410.1016/S0021-8502(98)00038-X ↗
16. Park SH, Lee KW, Otto E, Fissan H (1999) The log-normal size distribution theory of Brownian aerosol coagulation for the entire particle size range: part I-analytical solution using the harmonic mean coagulation kernel. J Aerosol Sci 30:3–1610.1016/S0021-8502(98)00037-8 ↗
17. Pratsinis SE (1988) Simultaneous nucleation, condensation, and coagulation in aerosol reactor. J Colloid Interface Sci 124:416–41710.1016/0021-9797(88)90180-4 ↗
18. Seipenbusch M, Binder A, Kasper G (2008) Temporal evolution of nanoparticle aerosols in workplace exposure. Ann Occup Hyg 52:707–71610.1093/annhyg/men067 ↗
19. Smoluchowski V (1917) Versuch einer mathematischen theorie der Koagulationskinetik kollider losungen. Z Phys Chem 92:129–168
20. Wang G, Garrick SC (2005) Modeling and simulation of titania synthesis in two-dimensional methane-air flames. J Nanopart Res 7:621–63210.1007/s11051-005-4966-7 ↗
21. Wright PG (1960) On the discontinuity involved in diffusion across an interface (the delta of Fuchs). Disc Faraday Soc 30:100–11210.1039/df9603000100 ↗
22. Yu MZ, Lin JZ, Chan TL (2008a) Effect of precursor loading on non-spherical TiO2 nanoparticle synthesis in a diffusion flame reactor. Chem Eng Sci 63:2317–232910.1016/j.ces.2007.11.008 ↗
23. Yu MZ, Lin JZ, Chan TL (2008b) A new moment method for solving the coagulation equation for particles in Brownian motion. Aerosol Sci Tech 42:705–71310.1080/02786820802232972 ↗
24. Yu MZ, Lin JZ, Chan TL (2009) Numerical simulation for nucleated vehicle exhaust particulate matters via the TEMOM/LES method. Int J Mod Phys C20:399–421