Journal of Nanoparticle Research

, Volume 13, Issue 5, pp 2007–2020

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
Research Paper

DOI: 10.1007/s11051-010-9954-x

Cite this article as:
Yu, M., Lin, J., Jin, H. et al. J Nanopart Res (2011) 13: 2007. doi:10.1007/s11051-010-9954-x

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.

Keywords

Particle general dynamic equation Brownian coagulation Moment method Taylor-series expansion Entire regime Modeling and simulation 

List of Symbols

A

Constant (=1.591)

B1,B2

Collision constant in Eqs. (2a) and (2b)

\( \bar{c} \)

Mean thermal velocity (m s−1)

C

Cunningham correction factor

dp

Volume_averaged particle diameter

D

Particle diffusion coefficient (m2 s−1)

kB

Boltzmann constant (J K−1)

Kn

Particle Knudsen number

mk

kth moment of particle size distribution

Mk

Dimensionless kth moment of particle size distribution

NQ

Order of the quadrature formulation

n(v, t)

Particle number concentration density with size v at time t (particles/m3/m3)

N0

Total particle number concentration at initial time (particles/m3)

t

Time (s)

T

Temperature (K)

v, v1

Particle volume (m3)

vg

Geometric mean particle volume (m3)

\( \tilde{w} \)

Quadrature weight

Greek Variables

ν

Kinematic viscosity (m2 s−1)

ρ

Gas density (kg m−3)

ρp

Particle density (kg m−3)

β

Particle collision kernel

μ

Gas viscosity (kg m−1 s−1)

λ

Mean free path of the gas (m)

\( \sigma_{\text{g}} \)

Geometric standard deviation of particle size distribution

\( \tau \)

Dimensionless coagulation time, \( B_{2} N_{0} t \)

\( Q_{k} \)

Particle number in kth section

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Mingzhou Yu
    • 1
    • 2
  • Jianzhong Lin
    • 1
    • 2
  • Hanhui Jin
    • 2
  • Ying Jiang
    • 1
  1. 1.China Jiliang UniversityHangzhouPeople’s Republic of China
  2. 2.Department of MechanicsZhejiang UniversityHangzhouPeople’s Republic of China

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