Abstract
A non-stretchable fiber rotation in planar flows has been solved. The fiber will rotate periodically or run to the asymptotical direction decided by a discriminant defined in the paper involving the fiber aspect ratio and the flow characteristics. Subsequently the fiber orientation distribution is derived directly without the bother of solving the Fokker-Planck equation. The research clearly indicates the overall configuration of a fiber rotation movement in planar flows.
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References
Batchelor, G.K., 1970a. The stress system in a suspension of force-free particles. J. Fluid Mech., 41(3):545–570. [doi:10.1017/S0022112070000745]
Batchelor, G.K., 1970b. Slender-body theory for particles of arbitrary cross-section in Stokes flow. J. Fluid Mech., 44(3):419–440. [doi:10.1017/S002211207000191X]
Batchelor, G.K., 1971. The stress generated in a non-dilute suspension of elongated particles by pure straining motion. J. Fluid Mech., 46(4):813–229. [doi:10.1017/S0022112071000879]
Bretherton, F.P., 1962. The motion of rigid particles in a shear flow at low Reynolds number. J. Fluid Mech., 14(2):284–304. [doi:10.1017/S002211206200124X]
Courant, R., Hilbert, D., 1966. Method of Mathematical Physics, Volume II: Partial Differential Equations. Interscience Publishers, New York.
Jeffery, G.B., 1922. The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. London A, 102:161–179.
Lin, J.Z., Zhang, W.F., Wang, Y.L., 2002. Research on the orientation distribution of fibers immersed in a pipe flow. J. Zhejiang Univ. Sci., 3(5):501–506.
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. [doi:10.1017/S0022112092002490]
Zhang, L.X., Lin, J.Z., 2003. On the structural features of fiber suspensions in converging channel flow. J. Zhejiang Univ. Sci., 4(4):400–406.
Zhang, L.X., Lin, J.Z., Chan, T.L., 2005. Orientation distribution of cylindrical particles suspended in a turbulent pipe flow. Phys. Fluids, 17(9):093105-1–093105-8. [doi:10. 1063/1.2046713]
Zhou, K., Lin, J.Z., 2005. Research on the behavior of fiber orientation probability distribution function in the planar flows. J. Zhejiang Univ. Sci., 6A(4):257–264. [doi:10.1631/jzus.2005.A0257]
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Project (No. 10632070) supported by the Major Program of the National Natural Science Foundation of China
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Zhou, K., Lin, Jz. Research on 3D fiber orientation distribution in arbitrary planar flows. J. Zhejiang Univ. - Sci. A 8, 1021–1025 (2007). https://doi.org/10.1631/jzus.2007.A1021
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DOI: https://doi.org/10.1631/jzus.2007.A1021