Journal of the Textile Machinery Society of Japan

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

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When fiber assemblies such as yarns and fabrics are washed, substances to be removed migrate through water and fibers. The coefficient of diffusion of the substance in water is remarkably different from that in fibers. In the previous papers[1, 2], treating the process of substance migration in fibers and water, an assumption was made that fibers can be regarded as columns and fiber assemblies as planes or columns. Theoretical equations had been derived on the basis of the diffusion theory and the validity of these equations had been confirmed by the washing experiment of polyvinylalcohol[10].
This paper deals with the washing of cotton and polyester fabrics, the properties of which are much different. Sodiumhydroxide and acidic dyestuff are selected as the substances to be removed. The experimental values are compared with the theoretical values. Results of washing in stirred water agree well with the values calculated by equations derived by regarding the fiber assembly as a column.

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