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Title: Solution of three-dimensional fiber orientation in two-dimensional fiber suspension flows
Authors: Zhou, K
Lin, JZ
Chan, TL 
Keywords: Fibres
Two-phase flow
Issue Date: Nov-2007
Publisher: American Institute of Physics
Source: Physics of fluids, Nov. 2007, v. 19, no. 11, 113309, p. 1-12 How to cite?
Journal: Physics of Fluids 
Abstract: The orientation of fibers in simple two-dimensional flows is investigated. According to different ranges of the Péclet number, Pe, defined as the ratio of a characteristic rotational speed of fibers and the orientational diffusivity, three methods are developed: characteristic method for Pe = ∞, regular perturbation method for Pe≫1, and spectral method for everything else. All the methods subtly utilize the evolving solution of the rotational dynamics of fibers, which is also given in this paper. Especially, the adoption of spherical harmonics in the spectral method eliminates the singularity of the Fokker–Planck equation in spherical coordinates, and provides high precision and efficiency. The evolving solution of orientation distribution with Pe = ∞ is obtained through the solution of rotational dynamics. Using a regular perturbation method, the solution of orientation distribution with Pe = ∞ is extended for the condition of Pe≫1. This paper provides systematical and high efficient techniques to deal with the fiber orientation.
ISSN: 1070-6631 (print)
1089-7666 (online)
DOI: 10.1063/1.2815718
Rights: © 2007 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in K. Zhou, J. Lin & T. L. Chan, Physics of Fluids 19, 113309 (2007) and may be found at
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