In this paper, a slender body is used as the simplest model of a single fiber. Influences of the density, diameter, initial angle of a slender body and water temperature on the falling behaviors in the still water have been investigated by the numerical calculation and experiments. Its falling behaviors in the air have also been investigated and the effects of the difference of the fluid density on the falling behaviors have been clarified by comparison of the results in the air and in the still water.
The obtained results are as follows :
(1) The density and diameter of the slender body and the water temperature influences the trajectory, the translational velocity and angular velocity. The larger the density and diameter and the higher the water temperature, are the greater the translational and angular velocity.
(2) The initial angle influences the motion of the slender body within the small region where the slender body rapidly accelerates immediately after the beginning of the fall. Thereafter, its motion is independent on the initial angle.
(3) When the slender body falls in the air, its attitude vibrates around the horizontal position. Therefore, the horiaintal speed vibrates around zero, the vertical speed fluctuates and approaches to a constant value.
(4) The influence of different factors on the falling behaviors obtained by a numerical calculation almost agree with experimental results.

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In a false-twist texturing process, yarns in a twisting zone are twisted just after the feed rollersat the room temperature. Yarns gradually increase their twists on a heater plate according to the rising temperature of yarns, thus reaching a saturated twist level. The migrating phenomena of filaments in the twisted yarn were analysed by measuring the yarn tension in the twisting zone from the thermal stress of the raw yarn and the structure of the twisted yarn.
The thermal stress of the raw yarn was represented by the following formula :
F (x, T) =C₃x^c₄exp (C₅T+C₆
)where, x is a feed ratio in a heat treating zone, T is a heat treating temperature and C₃-C₆ areconstants.
The filament migrating ratio k, defined as below, ranged from 0.6 to 0.9 in a conventional texturing process. It was found that migration phenomena were not complete but distinguishable. The value of k seems to decrease as decreasing of feed ratio, increasing of heating temperature or decreasing of number of false-twists.
k=x_fNθ-x_fθ/x_fNθ-x_fM
where, .x_fθ, x_fM and x_fNθ are feeding ratios of a filament laid at twist angle θ, laid with completemigration and laid at twist angle θ with complete non-migration in the twisted yarn respectively.
The thermal stress of a partially oriented yarn (POY) was not sensitively affected by the change of feed ratio or yarn temperature comparing to that of a drawn yarn (FDY). The yarn tension at the twisting zone in a simulataneous draw-texturing process was not affected by the migrating ratio k but determined by the number of false-twists inserted to the yarn. Consequently any information concerning migrating ratio of this process cannot be given by applying the same analytical method. But it became clear that variation of cross sectional areas of the filaments from draw-texturing process was larger than that of the filaments from the conventional process.

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