Synopsis This work investigates the two-and three-dimensional description of fiber orientation in homogeneous flow fields. Motion of the fibers is described using the Dinh-Armstrong model which was developed for semiconcentrated fiber suspensions. The calculation of rheological properties for fiber suspensions requires the determination of fourth-order moments of orientation distribution function which is defined as the fourth-order orientation tensor. Solution of the distribution function is

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... tamed in terms of the velocity gradients and transient calculations are presented for simple shear, planar elongational, and uniaxial extensional flows. Second-and fourth-order tensors are calculated by using the distribution function and the components of the second-order tensor are utilized to define an orientation ellipsoid for the graphical representation of the orientation state. The fourth-order tensor is approximated from second-order tensors through quadratic and hybrid closure equations, and compared with the exact results. Despite the qualitative agreement between the exact and approximated results, considerable quantitative discrepancy is observed which may result in inaccurate prediction of suspension behavior.