The objective of this study is to well understand the interaction between the configuration of flexible fibers and flow kinematics in fiber suspension flows. In this framework, the evolution of the flow kinematics and configuration of multiple flexible fibers in a simple shear flow at low Reynolds number was numerically analyzed using an 'immersed boundary method' developed by Peskin. In the computations fibers with force-free configuration of being straight were used, and stretching/compression and bending deformations in the plane of flow were simply assumed.
In Part 3 of the series of papers, we described the effects of the parameters such as number of fibers, initial distance between fibers, bending stiffness of fibers and fluid viscosity on the hydrodynamic interaction between fibers and evolution of the flow kinematics. It was confirmed that the behavior of fibers and the flow kinematics become more complex owing to significant hydrodynamic interactions as the number of fibers increases, e.g., a fiber moves toward and beyond a forward fiber or a fiber on the left hand side can only rotate in a strong vortex and almost never translates.

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Air drag force on a nylon monofilament yarn in a confined jet was measured as a basic study for operating yarn by airflow, for example; for weft-insertion, for holding the yarn end, for adjusting yarn tension and for drawing yarn into a hollow spindle. The relative velocity of airflow around a yarn was expanded up to 300 m/s. Previously, this had been investigated up to 100 m/s. Both the supplying air pressure and combinations of nozzles and pipes changed diffusion of the flow in a pipe. Air drag force increased extremely if the primary stream acted on the yarn directly when the jet from the nozzle was directed at very high speed (around sonic velocity). Yarn was often stuck inside the pipe by the airflow when very thin pipes were used. When this occurred, air drag force was reduced to half. The air drag coefficient Cf for monofilament yarn has been arranged using the radius Reynolds number, Rea, for suction flow with lower than 100 m/s. The formula, Cf = KRea^-n, has been applied for suction flow under 500 in Rea. Cf could be arranged in the same manner for annular jet or confined jet if airflow acted on a yarn in the pipe uniformly. This formula, then, is also available even for very high velocity over 100 m/s. According to these results, we were able to calculate air drag force on monofilament yam. We anticipate applying this to the other kinds of yarn, and expect air power savings and improvement in yarn operation.

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