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 ...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.展开更多
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...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.展开更多
基金Project (No. 10372090) supported by the National Natural Science Foundation of China
文摘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.
基金Project (No. 10632070) supported by the Major Program of theNational Natural Science Foundation of China
文摘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.
