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ZHOU Kun, LIN Jian-zhong. Research on the behavior of fiber orientation probability distribution function in the planar flows[J]. Journal of Zhejiang University Science A, 2005, 6(4): 257~264.

@article{title="Research on the behavior of fiber orientation probability distribution function in the planar flows",

author="ZHOU Kun, LIN Jian-zhong",

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volume="6",

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pages="257~264",

year="2005",

publisher="Zhejiang University Press & Springer",

doi="10.1631/jzus.2005.A0257"

}

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%I Zhejiang University Press & Springer

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T1 - Research on the behavior of fiber orientation probability distribution function in the planar flows

A1 - ZHOU Kun

A1 - LIN Jian-zhong

J0 - Journal of Zhejiang University Science A

VL - 6

IS - 4

SP - 257

EP - 264

%@ 1673-565X

Y1 - 2005

PB - Zhejiang University Press & Springer

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DOI - 10.1631/jzus.2005.A0257

**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.

**
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[1] Advani, S.G., Tucker, C.L., 1987. The use of tensors to describe and predict fiber orientation in short fiber composites. *J Rheol*, **31**(8):751-784.

[2] Advani, S.G., Tucker, C.L., 1989. Closure approximations for three-dimensional structure tensors. *J Rheol*, **34**(3):367 -386.

[3] Altan, M.C., Advani, S.G., Guceri, S.I., Pipes, R.B., 1989. On the description of the orientation state for fiber suspensions in homogeneous flows. *J Rheol*, **33**(7):1129-1155.

[4] Batchelor, G.K., 1970. The stress system in a suspension of force-free particles. *J Fluid Mech*, **41**:545-570.

[5] Bird, R.B., Armstrong, R.C., Hassager, O., 1987. Dynamics of Polymeric Liquids. John Willey & Sons, New York.

[6] Bretherton, F.P., 1962. The motion of rigid particles in a shear flow at low Reynolds number. *J Fluid Mech*, **14**:284-304.

[7] Chiba, K., Nakamura, K., 1998. Numerical solution of fiber suspension flow through a complex channel. *J Non-Newt Fluid Mech*, **78**:167-185.

[8] Chinesta, F., Chaidron, G., Poitou, A., 2003. On the solution of Fokker-Planck equations in steady recirculating flows involving short fiber suspensions. *J Non-Newt Fluid Mech*, **113**:97-125.

[9] Dinh, S.M., Armstrong, R.C., 1984. Rheological equation of state for semiconcentrated fiber suspensions. *J Rheol*, **28**(3):207-227.

[10] Folgar, F., Tucker, C.L., 1984. Orientation Behavior of Fibers in Concentrated suspensions. *J Reinf Plast Compos*, **3**:98-119.

[11] Hinch, E.J., Leal, L.G., 1975a. Constitutive equations in suspension mechanics. Part 1. General formation. *J Fluid Mech*, **71**:481-495.

[12] Hinch, E.J., Leal, L.G., 1975b. Constitutive equations in suspension mechanics. Part 2. Approximate forms for a suspension of rigid particles affected by Brownian rotations. *J Fluid Mech*, **76**:187-208.

[13] Leal, L.G., Hinch, E.J., 1971. The effect of weak Brownian rotations on particles in shear flow. *J Fluid Mech*, **46**:685-703.

[14] Lin, J.Z., Zhang, L.X., 2003. On the structural features of fiber suspensions in converging channel flow. *J Zhejiang University SCIENCE*, **4**(4):400-406.

[15] Shaqfeh, E.S.G., Koch, D.L., 1990. Orientational dispersion of fibers in extensional flows. *Phys Fluids A*, **2**(7):1077-1093.

[16] Stover, C.A., Koch, D.L., Cohen, C., 1992. Observations of fibre orientation in simple shear flow of semi-dilute suspensions. *J Fluid Mech*, **238**:277-296.

[17] Szeri, A.J., Leal, L.G, 1992. A new computational method for the solution of flow problems of microstructured fluids. Part 1. Theory. *J Fluid Mech*, **242**:549-576.

[18] Szeri, A.J., Leal, L.G, 1994. A new computational method for the solution of flow problems of microstructured fluids. Part 2. Inhomogeneous shear flow of a suspension. *J Fluid Mech*, **262**:171-204.

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Open peer comments: Debate/Discuss/Question/Opinion

<1>aihua xiong@nanchang<aihuaok2004@163.com>2012-08-23 10:53:25

thank you