Asymptotic behavior of the Taylor-expansion method of moments for solving a coagulation equation for Brownian particles--颗粒学报PARTICUOLOGY

Chen, Z.L., Lin, J.Z., & Yu, M. Z. ChenAsymptotic behavior of the Taylor-expansion method of moments for solving a coagulation equation for Brownian particles. (2014). Particuology, 14, 124–129. https://doi.org/10.1016/j.partic.2013.04.012

Asymptotic behavior of the Taylor-expansion method of moments for solving a coagulation equation for Brownian particles

Zhongli Chen ^a, Jianzhong Lin ^{a b *}, Mingzhou Yu ^b

a Department of Mechanics, Zhejiang University, Hangzhou 310027, China
b China Jiliang University, Hangzhou 310018, China

10.1016/j.partic.2013.04.012

Volume 14, June 2014, Pages 124-129

Received 30 December 2012, Revised 18 March 2013, Accepted 12 April 2013, Available online 24 August 2013.

E-mail: mecjzlin@public.zju.edu.cn

Highlights

• A characteristic parameter was used to investigate self-preserving size distribution.

• Asymptotic values of the parameter were determined for different regimes.

• Relation between time to reach self-preservation and initial value of parameter was obtained.

• Equations derived can be used to predict evolution of corresponding moments.

Abstract

The evolution equations of moments for the Brownian coagulation of nanoparticles in both continuum and free molecule regimes are analytically studied. These equations are derived using a Taylor-expansion technique. The self-preserving size distribution is investigated using a newly defined dimensionless parameter, and the asymptotic values for this parameter are theoretically determined. The dimensionless time required for an initial size distribution to achieve self-preservation is also derived in both regimes. Once the size distribution becomes self-preserving, the time evolution of the zeroth and second moments can be theoretically obtained, and it is found that the second moment varies linearly with time in the continuum regime. Equivalent equations, rather than the original ones from which they are derived, can be employed to improve the accuracy of the results and reduce the computational cost for Brownian coagulation in the continuum regime as well as the free molecule regime.

Graphical abstract

Keywords

Brownian particles; Coagulation; Size distribution; Accuracy

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