Finite difference solutions have been obtained for the flow of dilute suspensions of high aspect-ratio fibers in Newtonian fluids through a planar contraction using the constitutive equation developed by Lipscomb et al. and flows of fiber suspensions through a rectangular channel with an abrupt contraction have also been observed to study the effects of volume fraction and aspect ratio of fibers on the flow flelds. Furthermore, the flow patterns of fiber suspensions have been compared with those of polymer solutions.
The presence of fibers drastically changes the planar entry flow field : the salient corner vortex grows as the volume fraction and/or aspect ratio of fibers increase. However, even in large growth of the corner vortex, the vortex boundary and the streamlines in the main flow become rather straight in fiber suspension flows. The flow of rigid fiber suspensions presents striking contrast to the wine-glass shaped flow in flexible molecule systems with the vortex boundary being more convex with respect to the center of rotation.
Furthermore, the length of the salient corner vortex is almost independent of flow rate under the Reynolds number of order unity and it decreases as the Reynolds number is further increased in fiber suspension flows. On the other hand, the salient corner vortex increases in size rapidly with an increase in flow rate for flexible polymer systems. Thus, an introduction of the effects of the change of fiber configuration during flow is necessary to develop better and simplified model fluids of polymer liquids.
Numerical predictions of both the effects of volume fraction and aspect ratio of fibers on the flow fields and the relation between the vortex length and parameter φμ/n A for low volume fraction of fibers are in good agreement with the flow visualization experiments. Thus, the constitutive equation used here is valid to predict the flow of dilute suspensions of high aspect-ratio rigid fibers.
It has also been confirmed that the growth of the salient corner vortex suppresses the increase in the first normal stress difference on the centerline, i.e. the so-called stress relief phenomenon due to vortex enhancement can also be seen in planar entry flows of rigid fiber suspensions.
Lastly, flow patterns in the plane parallel to the side wall clearly reveal that the tendency of 3-dimensional flow appears in fiber suspension flow even through a large height-to-width ratio rectangular channel with an abrupt contraction. The tendency becomes more pronounced in low flow rates, high fiber content and large fiber length.

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Crinkling mechanism of crepe is investigated in this paper, assuming that the yarn is as elastic body. The elastic curve of elastic body under distortion and tension is theoretically analyzed, and the relationsip between torsional moment and tensile force, and buckling when it occurs, are figured. The the oretical result shows the coincidental consequence as rubber yarn is tested. It is shown that a textile woven with twisted rubber yarn has the similar crimping effect as an actual crepe with twisted yarn. Therfore, it is possible to deal with crimping mechanism on crepe as an application of the elastic curve regarding elastic body under distorsion and tention.

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