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A mathematical model for the wet-spinning process

Published online by Cambridge University Press:  26 September 2008

H. Ockendon  and
E. L. Terrill
H. Ockendon
Affiliation:
Mathematical Institute, 24–29 St Giles', Oxford, 0X1 3LB, UK
E. L. Terrill
Affiliation:
Mathematical Institute, 24–29 St Giles', Oxford, 0X1 3LB, UK
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Abstract

A mathematical model for the hydrodynamic flow and fibre deflections in a wet-spinning process is presented. The model is characterized by two parameters: α which is a characteristic ratio of the hydrodynamic force to the tension force acting on a fibre, and β which is a characteristic ratio of the fibre drag to the fluid inertia. The model is applied to three situations: (i) the spin bath of the process where α ≪ 1 and β ≫ 1, (ii) the preheat bath where α is order 1 and β ≫ 1, (iii) a fibre spreading process where α is order 1 and β is order 1 or smaller. In each case, analytical results are obtained for the fluid flow and fibre deflections and compared with experiment.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 4 , Issue 4 , December 1993 , pp. 341 - 360
Copyright
Copyright © Cambridge University Press 1993

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