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ZJUS-A
Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)  2005, Vol. 6 Issue ( 4): 2-    DOI: 10.1631/jzus.2005.A0257
    
Research on the behavior of fiber orientation probability distribution function in the planar flows
ZHOU Kun, LIN Jian-zhong
Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, China
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Abstract  The equation of two-dimensional fiber direction vector was solved theoretically to give the fiber orientation distri-bution in simple shear flow, flow with two direction shears, extensional flow and arbitrary planar incompressible flow. The Fok-ker-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 Mechanics Fluid Power Transmission and Control     
Received: 25 December 2003     
CLC:  O359  
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ZHOU Kun
LIN Jian-zhong
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ZHOU Kun, LIN Jian-zhong. Research on the behavior of fiber orientation probability distribution function in the planar flows. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2005, 6( 4): 2-.

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http://www.zjujournals.com/xueshu/zjus-a/10.1631/jzus.2005.A0257     OR     http://www.zjujournals.com/xueshu/zjus-a/Y2005/V6/I 4/2

[1] ZHOU Kun, LIN Jian-zhong. Research on 3D fiber orientation distribution in arbitrary planar flows[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2007, 8(7): 1021-1025.
[2] LIN Jian-zhong, ZHANG Ling-xin. On the structural features of fiber suspensions in converging channel flow[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2003, 4(4): 400-406.
[3] LIN Jian-zhong, ZHANG Wei-feng, WANG Ye-long. Research on the orientation distribution of fibers immersed in a pipe flow[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2002, 3(5): 501-506.