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**A new method of moments for the bimodal particle system in the Stokes regime.**
*(English)*
Zbl 1470.82024

Summary: The current paper studied the particle system in the Stokes regime with a bimodal distribution. In such a system, the particles tend to congregate around two major sizes. In order to investigate this system, the conventional method of moments (MOM) should be extended to include the interaction between different particle clusters. The closure problem for MOM arises and can be solved by a multipoint Taylor-expansion technique. The exact expression is deduced to include the size effect between different particle clusters. The collision effects between different modals could also be modeled. The new model was simply tested and proved to be effective to treat the bimodal system. The results showed that, for single-modal particle system, the results from new model were the same as those from TEMOM. However, for the bimodal particle system, there was a distinct difference between the two models, especially for the zero-order moment. The current model generated fewer particles than TEMOM. The maximum
deviation reached about 15% for \(m_0\) and 4% for \(m_2\). The detailed distribution of each submodal could also be investigated through current model.

### MSC:

82C22 | Interacting particle systems in time-dependent statistical mechanics |

82C40 | Kinetic theory of gases in time-dependent statistical mechanics |

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\textit{Y.-h. Liu} and \textit{Z.-q. Yin}, Abstr. Appl. Anal. 2013, Article ID 840218, 6 p. (2013; Zbl 1470.82024)

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### References:

[1] | Chan, T. L.; Ning, Z.; Wang, J. S.; Cheung, C. S.; Leung, C. W.; Hung, W. T., Gaseous and particle emission factors from the selected on-road petrol/gasoline, diesel, and liquefied petroleum gas vehicles, Energy and Fuels, 21, 5, 2710-2718 (2007) |

[2] | Diemer, R. B.; Olson, J. H., A moment methodology for coagulation and breakage problems, part 2: moment models and distribution reconstruction, Chemical Engineering Science, 57, 12, 2211-2228 (2002) |

[3] | Jeong, J. I.; Choi, M., A bimodal moment model for the simulation of particle growth, Journal of Aerosol Science, 35, 9, 1071-1090 (2004) |

[4] | Pugatshova, A.; Reinart, A.; Tamm, E., Features of the multimodal aerosol size distribution depending on the air mass origin in the Baltic region, Atmospheric Environment, 41, 21, 4408-4422 (2007) |

[5] | Lonati, G.; Crippa, M.; Gianelle, V.; van Dingenen, R., Daily patterns of the multi-modal structure of the particle number size distribution in Milan, Italy, Atmospheric Environment, 45, 14, 2434-2442 (2011) |

[6] | Tang, H.; Lin, J., Research on bimodal particle extinction coefficient during Brownian coagulation and condensation for the entire particle size regime, Journal of Nanoparticle Research, 13, 12, 7229-7245 (2011) |

[7] | Koziol, A. S.; Leighton, H. G., The moments method for multi-modal multi-component aerosols as applied to the coagulation-type equation, Quarterly Journal of the Royal Meteorological Society, 133, 625, 1057-1070 (2007) |

[8] | Barrett, J. C.; Jheeta, J. S., Improving the accuracy of the moments method for solving the aerosol general dynamic equation, Journal of Aerosol Science, 27, 8, 1135-1142 (1996) |

[9] | Jung, C. H.; Kim, Y. P., Numerical estimation of the effects of condensation and coagulation on visibility using the moment method, Journal of Aerosol Science, 37, 2, 143-161 (2006) |

[10] | McGraw, R., Description of aerosol dynamics by the quadrature method of moments, Aerosol Science and Technology, 27, 2, 255-265 (1997) |

[11] | Yu, M.; Lin, J.; Chan, T., A new moment method for solving the coagulation equation for particles in Brownian motion, Aerosol Science and Technology, 42, 9, 705-713 (2008) |

[12] | Yu, M.; Lin, J., Taylor-expansion moment method for agglomerate coagulation due to Brownian motion in the entire size regime, Journal of Aerosol Science, 40, 6, 549-562 (2009) |

[13] | Yu, M.; Lin, J., Binary homogeneous nucleation and growth of water-sulfuric acid nanoparticles using a TEMOM model, International Journal of Heat and Mass Transfer, 53, 4, 635-644 (2010) · Zbl 1187.82103 |

[14] | Yu, M.; Lin, J.; Chan, T., Numerical simulation for nucleated vehicle exhaust particulate matters via the temom/les method, International Journal of Modern Physics C, 20, 3, 399-421 (2009) · Zbl 1419.76389 |

[15] | Lin, J.; Lin, P.; Chen, H., Research on the transport and deposition of nanoparticles in a rotating curved pipe, Physics of Fluids, 21, 12, 1-11 (2009) · Zbl 1183.76315 |

[16] | Yu, M.; Lin, J.; Jin, H.; Jiang, Y., The verification of the Taylor-expansion moment method for the nanoparticle coagulation in the entire size regime due to Brownian motion, Journal of Nanoparticle Research, 13, 5, 2007-2020 (2011) |

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