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On the solution of fiber orientation in two‐dimensional homogeneous flows
Author(s) -
Akbar Sameer,
Altan M. Cengiz
Publication year - 1992
Publication title -
polymer engineering and science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.503
H-Index - 111
eISSN - 1548-2634
pISSN - 0032-3888
DOI - 10.1002/pen.760321208
Subject(s) - orientation (vector space) , distribution function , materials science , kinematics , fiber , rotation (mathematics) , flow (mathematics) , geometry , tensor (intrinsic definition) , distribution (mathematics) , mathematical analysis , mechanics , physics , mathematics , classical mechanics , composite material , thermodynamics
This work presents an analytical technique to describe the orientation behavior of short fibers in arbitrary two‐dimensional homogeneous flows. It is shown that the fiber orientation, specified by a unit vector, can be analytically calculated at any instant using any initial orientation and flow kinematics. The rotation of a fiber with the bulk fluid deformation is expressed in terms of orientation vector components by utilizing an equivalent strain tensor calculated from the fluid kinematics. This technique is then used to evaluate the orientation behavior of a large number of fibers starting from different initial orientations, representing an orientation state. The orientation distribution function is generated statistically by considering the frequency distribution curve of the orientation of the large number of fibers. It is shown that using a combination of analytical solutions and statistical methods provides a convenient description of fiber orientation behavior. The accuracy of the generated orientation distribution function is found to be dependent on the number of fibers used in the analytical solution. The statistical orientation distribution function is compared with the exact solutions for certain homogeneous flows and found to be in close agreement.