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Solution of the problem of the form and tension of a filament in its three-dimensional balloon during twisting

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Fibre Chemistry Aims and scope

Systems of differential equations in cartesian and cylindrical coordinates are obtained to describe a flexible filament rotating in a resisting medium. The concept of the unit aerodynamic drag coefficient of the filament is introduced in addition to the assumptions used in previous studies. The systems of differential equations that were obtained are solved in analytical form using the assumptions that were made. A value is found for the new concept of unit aerodynamic drag coefficient, and ways are described to study it and determine its value for different filaments in practical applications. Complete mathematical expressions are obtained to calculate parameters that are of practical importance in the twisting of a filament - its tension, the maximum radius (diameter) of the torsion balloon, and the conditions under which multiple balloons are formed. It is established that the problem of the form and tension of a filament during its twisting cannot be solved in final form without allowance for the resistance of the medium.

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Authors and Affiliations

  1. Scientific Research Institute of Synthetic Fibers, Tver, Russia

    Yu. S. Koval’

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  1. Yu. S. Koval’
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Translated from Khimichekie Volokna, No. 1, pp. 41–52, January-February, 2011.

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Koval’, Y.S. Solution of the problem of the form and tension of a filament in its three-dimensional balloon during twisting. Fibre Chem 43, 47–62 (2011). https://doi.org/10.1007/s10692-011-9307-2

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  • DOI: https://doi.org/10.1007/s10692-011-9307-2

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