This work investigates the two-dimensional fiber orientation in nonhomogeneous flow fields through a parallel plate channel as an elementary study on anisotropic channel flow. In this analysis fiber suspensions are considered as a continuum.
The fiber orientation in a developing flow is simulated by computing the evolution equation for the secondorder orientation tensor, which includes the fourth-order tensor, along the streamlines (continuum method). In the computation the fourth-order tensor is approximated in tems of the second-order tensor through a quadratic closure equation. The accuracy of the closure approximation is explored by comparing with the second-order tensor obtained by the statistical method : orientations of a large number of fibers, which are injected in the entrance with a random initial orientation, can be evaluated by computing the Jeffery's equation, then the orientation distribution function can be recovered statistically and the second-order orientation tensor can be also calculated.
Fluid velocity has a relatively large y-direction (width-direction) component near the channel wall within the entrance region, thus fibers firstly begin to align in the y-direction, then the alignment in the x-direction (direction parallel to the channel wall) gradually becomes prevailed. This trend appears remarkable as the channel wall is approached. On the other hand, the alignment in the x-direction becomes better within a region near the centerline owing to acceleration of fluid velocity in the x-direction.
Predictions of fiber orientation in both a fully developed flow reported in the previous paper and a developing flow through a parallel plate channel may clearly indicate that the much simpler quadratic closure approximation performs well when the fibers are highly aligned, but it is not so suitable for random orientation state or a rapid change in fiber orientation which is caused by a significant change in fluid velocity observed within the entrance region in a developing flow or flip-over phenomenon.
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