Journal of Zhejiang University-SCIENCE A

, Volume 6, Issue 4, pp 257–264 | Cite as

Research on the behavior of fiber orientation probability distribution function in the planar flows

  • Zhou Kun
  • Lin Jian-zhong
Mechanical and Energy Engineering


The equation of two-dimensional fiber direction vector was solved theoretically to give the fiber orientation distribution in simple shear flow, flow with two direction shears, extensional flow and arbitrary planar incompressible flow. The Fokker-Planck equation was solved numerically to validify the theoretical solutions. The stable orientation and orientation period of fiber were obtained. The results showed that the fiber orientation distribution is dependent on the relative not absolute magnitude of the matrix rate-of-strain of flow. The effect of fiber aspect ratio on the orientation distribution of fiber is insignificant in most conditions except the simple shear case. It was proved that the results for a planar flow could be generalized to the case of 3-D fiber direction vector.

Key words

Fiber suspension flow Orientation distribution Probability distribution function 

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Copyright information

© Zhejiang University Press 2005

Authors and Affiliations

  • Zhou Kun
    • 1
  • Lin Jian-zhong
    • 1
  1. 1.Department of Mechanics, State Key Laboratory of Fluid Power Transmission and ControlZhejiang UniversityHangzhouChina

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