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In the present study, the linear stability of population balance equation due to Brownian motion is analyzed with the Taylor-series expansion method of moment. Under certain conditions, the stability of the Taylor-series expansion method of moment model is reduced to a well-studied problem involving eigenvalues of matrices. Based on the principle of dimensional analysis, the perturbation equation is solved asymptotically. The results show that the Taylor-series expansion method of moment model is asymptotic stable, which implies that the asymptotic solution is uniqueness, and supports the self-preserving size distribution hypothesis theoretically.
PAPER REVISED: 2017-10-12
PAPER ACCEPTED: 2017-11-11
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THERMAL SCIENCE YEAR 2018, VOLUME 22, ISSUE Issue 4, PAGES [1651 - 1657]
  1. Friedlander, S. K., Smoke, Dust, and Haze: Fundamentals of Aerosol Dynamics, Oxford University Press, London, 2nd ed., 2000
  2. Pratsinis, S. E., Simultaneous Nucleation, Condensation, and Coagulation in Aerosol Reactor, Journal of Colloid and Interface Science, 124 (1988), 2, pp. 416-427
  3. McGraw, R., Description of Aerosol Dynamics by the Quadrature Method of Moment, Aerosol Science and Technology, 27 (1997), 2, pp. 255-265
  4. Marchisio, D. L., et al., Quadrature Method of Moments for Population Balance Equations, AICHE Journal, 49 (2003), 5, pp. 1266-1276
  5. Yu, M. Z., et al., A New Moment Method for Solving the Coagulation Equation for Particles in Browni-an Motion, Aerosol Science and Technology, 42 (2008), 9, pp. 705-713
  6. Yu, M. Z., et al., Generalized TEMOM Scheme for Solving the Population Balance Equation, Aerosol Science and Technology, 49 (2015), 11, pp. 1021-1036
  7. Xie, M. L., Wang, L. P., Asymptotic Solution of Population Balance Equation Based on TEMOM Mod-el, Chemical Engineering Science, 94 (2013), May, pp. 79-83
  8. Chen, Z. L., et al., Asymptotic Behavior of the Taylor-Expansion Method of Moments for Solving a Co-agulation Equation for Brownian Particles, Particuology, 14 (2014), June, pp. 124-129
  9. Yu, M. Z., et al., A New Analytical Solution for Solving the Smoluchowski Equation Due to Nanoparti-cle Brownian Coagulation for Non-Self-Preserving System, Aerosol and Air Quality Research, 14 (2014), 6, pp. 1726-1737
  10. Yu, M. Z., et al., A New Analytical Solution for Solving the Population Balance Equation in the Contin-uum-Slip Regime, Journal of Aerosol Science, 80 (2015), Feb., pp. 1-10
  11. Yu, M. Z., et al., An Analytical Solution for the Population Balance Equation Using a Moment Method, Particuology, 18 (2015), Feb., pp. 194-200
  12. Shen, X. T., Maa, J. P. Y., Numerical Simulations of Particle Size Distribution: Comparison with Ana-lytical Solutions and Kaolinite Flocculation Experiments, Marine Geology, 379 (2016), Sept., pp. 84-99
  13. Zhang, X. T., et al., Verification of Expansion Orders of the Taylor-Series Expansion Method of Mo-ment Model for Solving Population Balance Equations, Aerosol and Air Quality Research, 15 (2015), 6, pp. 2475-2484
  14. Xie, M. L., He, Q., Analytical Solution of TEMOM Model for Particle Population Balance Equation Due to Brownian Coagulation, Journal of Aerosol Science, 66 (2013), Dec., pp. 24-30

© 2022 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence