966
Views
13
CrossRef citations to date
0
Altmetric
Original Articles

Extended log-normal method of moments for solving the population balance equation for Brownian coagulation

, &
Pages 332-343 | Received 24 Aug 2018, Accepted 17 Dec 2018, Published online: 22 Jan 2019

References

  • Barrett, J. C., and J. S. Jheeta. 1996. Improving the accuracy of the moments method for solving the aerosol general dynamic equation. J. Aerosol Sci. 27 (8):1135–1142. doi: 10.1016/0021-8502(96)00059-6.
  • Barrett, J. C., and N. A. Webb. 1998. A comparison of some approximate methods for solving the aerosol general dynamic equation. J. Aerosol Sci. 29 (12):31–39. doi: 10.1016/S0021-8502(97)00455-2.
  • Diemer, R. B., and J. H. Olson. 2002. A moment methodology for coagulation and breakage problems: Part 2 – moment models and distribution reconstruction. Chem. Eng. Sci. 57 (12):2211–2228. doi: 10.1016/S0009-2509(02)00112-4.
  • Frenklach, M. 2002. Method of moments with interpolative closure. Chem. Eng. Sci. 57 (12):2229–2239. doi: 10.1016/S0009-2509(02)00113-6.
  • Frenklach, M., and S. J. Harris. 1987. Aerosol dynamics modeling using the method of moments. J. Colloid Interf. Sci. 118 (1):252–261. doi: 10.1016/0021-9797(87)90454-1.
  • Friedlander, S. K. 2000. Smoke, dust, and haze: Fundamentals of aerosol dynamics. New York; Oxford: Oxford University Press.
  • Gelbard, F., Y. Tambour, and J. H. Seinfeld. 1980. Sectional representations for simulating aerosol dynamics. J. Colloid Interf. Sci. 76 (2):541–556. doi: 10.1016/0021-9797(80)90394-X.
  • Jeong, J. I., and M. Choi. 2004. A bimodal moment model for the simulation of particle growth. J. Aerosol Sci. 35 (9):1071–1090. doi: 10.1016/j.jaerosci.2004.04.005.
  • John, V., I. Angelov, A. A. Oncul, and D. Thevenin. 2007. Techniques for the reconstruction of a distribution from a finite number of its moments. Chem. Eng. Sci. 62 (11):2890–2904. doi: 10.1016/j.ces.2007.02.041.
  • Kajino, M. 2011. MADMS: Modal aerosol dynamics model for multiple modes and fractal shapes in the free-molecular and near-continuum regimes. J. Aerosol Sci. 42 (4):224–248. doi: 10.1016/j.jaerosci.2011.01.005.
  • Kruis, F. E., A. Maisels, and H. Fissan. 2000. Direct simulation Monte Carlo method for particle coagulation and aggregation. AIChE J. 46 (9):1735–1742. doi: 10.1002/aic.690460905.
  • Kumar, J., M. Peglow, G. Warnecke, S. Heinrich, and L. Morl. 2006. Improved accuracy and convergence of discretized population balance for aggregation: The cell average technique. Chem. Eng. Sci. 61 (10):3327–3342. doi: 10.1016/j.ces.2005.12.014.
  • Landgrebe, J. D., and S. E. Pratsinis. 1990. A discrete-sectional model for particulate production by gas-phase chemical-reaction and aerosol coagulation in the free-molecular regime. J. Colloid Interf. Sci. 139 (1):63–86. doi: 10.1016/0021-9797(90)90445-T.
  • Lee, K. W. 1983. Change of particle-size distribution during Brownian coagulation. J. Colloid Interf. Sci. 92 (2):315–325. doi: 10.1016/0021-9797(83)90153-4.
  • Lee, K. W., H. Chen, and J. A. Gieseke. 1984. Log-normally preserving size distribution for Brownian coagulation in the free-molecule regime. Aerosol Sci. Technol. 3 (1):53–62. doi: 10.1080/02786828408958993.
  • Lee, K. W., and J. Hwang. 1997. Erratum to “log-normally preserving size distribution for Brownian coagulation in the free molecule regime” by Lee et al. and “coagulation rate of polydisperse particles” by Lee and Chen. Aerosol Sci. Technol. 26 (5):469–470. doi: 10.1080/02786829708965446.
  • Mann, G. W., K. S. Carslaw, D. V. Spracklen, D. A. Ridley, P. T. Manktelow, M. P. Chipperfield, S. J. Pickering, and C. E. Johnson. 2010. Description and evaluation of GLOMAP-mode: A modal global aerosol microphysics model for the UKCA composition-climate model. Geosci. Model Dev. 3 (2):519–551. doi: 10.5194/gmd-3-519-2010.
  • Marchisio, D. L., and R. O. Fox. 2005. Solution of population balance equations using the direct quadrature method of moments. J. Aerosol Sci. 36 (1):43–73. doi: 10.1016/j.jaerosci.2004.07.009.
  • McGraw, R. 1997. Description of aerosol dynamics by the quadrature method of moments. Aerosol Sci. Technol. 27 (2):255–265. doi: 10.1080/02786829708965471.
  • Megaridis, C. M., and R. A. Dobbins. 1990. A bimodal integral solution of the dynamic equation for an aerosol undergoing simultaneous particle inception and coagulation. Aerosol Sci. Technol. 12 (2):240–255. doi: 10.1080/02786829008959343.
  • Müller, H. 1928. Zur allgemeinen theorie ser raschen koagulation. Fortschrittsber. Kolloide Polym. 27:223–250. doi: 10.1007/BF02558510.
  • Otto, E., H. Fissan, S. H. Park, and K. W. Lee. 1997. Brownian coagulation in the transition regime using the moments of a lognormal distribution. J. Aerosol Sci. 28:S629–S630. doi: 10.1016/S0021-8502(97)85314-1.
  • Otto, E., H. Fissan, S. H. Park, and K. W. Lee. 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 (1):17–34. doi: 10.1016/S0021-8502(98)00038-X.
  • Palaniswaamy, G., and S. K. Loyalka. 2008. Direct simulation, Monte Carlo, aerosol dynamics: Coagulation and condensation. Ann. Nucl. Energ. 35 (3):485–494. doi: 10.1016/j.anucene.2007.06.024.
  • Park, S. H., and K. W. Lee. 2002. Change in particle size distribution of fractal agglomerates during Brownian coagulation in the free-molecule regime. J. Colloid Interf. Sci. 246 (1):85–91. doi: 10.1006/jcis.2001.7946.
  • Park, S. H., R. Xiang, and K. W. Lee. 2000. Brownian coagulation of fractal agglomerates: Analytical solution using the log-normal size distribution assumption. J. Colloid Interf. Sci. 231 (1):129–135. doi: 10.1006/jcis.2000.7102.
  • Pratsinis, S. E. 1988. Simultaneous nucleation, condensation, and coagulation in aerosol reactors. J. Colloid Interf. Sci. 124 (2):416–427. doi: 10.1016/0021-9797(88)90180-4.
  • Ramkrishna, D., and M. R. Singh. 2014. Population balance modeling: Current status and future prospects. Ann. Rev. Chem. Biomol. 5 (1):123–146. doi: 10.1146/annurev-chembioeng-060713-040241.
  • Seo, Y., and J. R. Brock. 1990. Distributions for moment simulation of aerosol evaporation. J. Aerosol Sci. 21 (4):511–514. doi: 10.1016/0021-8502(90)90127-J.
  • Shekar, S., A. J. Smith, W. J. Menz, M. Sander, and M. Kraft. 2012. A multidimensional population balance model to describe the aerosol synthesis of silica nanoparticles. J. Aerosol Sci. 44:83–98. doi: 10.1016/j.jaerosci.2011.09.004.
  • Smoluchowski, M. V. 1918. Versuch einer mathematischen theorie der koagulationskinetik kolloider lösungen. Z. Phys. Chem. 92:129–168.
  • Vemury, S., and S. E. Pratsinis. 1995. Self-preserving size distributions of agglomerates. J. Aerosol Sci. 26 (2):175–185. doi: 10.1016/0021-8502(94)00103-6.
  • Wang, K., W. Peng, and S. Yu. 2019. A new approximation approach for analytically solving the population balance equation due to thermophoretic coagulation. J. Aerosol Sci. 128:125–137. doi: 10.1016/j.jaerosci.2018.11.010.
  • Whitby, E. R., and P. H. McMurry. 1997. Modal aerosol dynamics modeling. Aerosol Sci. Technol. 27 (6):673–688. doi: 10.1080/02786829708965504.
  • Xie, M. L., and Q. He. 2013. Analytical solution of temom model for particle population balance equation due to Brownian coagulation. J. Aerosol Sci. 66:24–30. doi: 10.1016/j.jaerosci.2013.08.006.
  • Yamamoto, M. 2004. A moment method of an extended log-normal size distribution application to Brownian aerosol coagulation. J. Aerosol Res. 19:41–49.
  • Yu, M. Z., and J. Z. Lin. 2009. Solution of the agglomerate Brownian coagulation using Taylor-expansion moment method. J. Colloid Interf. Sci. 336 (1):142–149. doi: 10.1016/j.jcis.2009.03.030.
  • Yu, M. Z., J. Z. Lin, and T. L. Chan. 2008. A new moment method for solving the coagulation equation for particles in Brownian motion. Aerosol Sci. Technol. 42 (9):705–713. doi: 10.1080/02786820802232972.
  • Yu, M. Z., and T. L. Chan. 2015. A bimodal moment method model for submicron fractal-like agglomerates undergoing Brownian coagulation. J. Aerosol Sci. 88:19–34. doi: 10.1016/j.jaerosci.2015.05.011.
  • Yu, M. Z., X. T. Zhang, G. D. Jin, J. Z. Lin, and M. Seipenbusch. 2015. A new analytical solution for solving the population balance equation in the continuum-slip regime. J. Aerosol Sci. 80:1–10. doi: 10.1016/j.jaerosci.2014.10.007.
  • Zhao, H. B., and C. G. Zheng. 2013. A population balance-Monte Carlo method for particle coagulation in spatially inhomogeneous systems. Comput. Fluids 71:196–207. doi: 10.1016/j.compfluid.2012.09.025.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.