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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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References

Batchelor, G. K. 1970 Slender-body theory for particles of arbitrary cross-section in Stokes flow. J. Fluid Mech. 44, 419–440.CrossRefGoogle Scholar
Bergelin, O. P., Brown, G. A., Hull, H. L. & Sullivan, F. W. 1950 Heat transfer and fluid friction during viscous flow across banks of tubes – III A study of tube spacing and tube size. Trans. ASME, August, 881–888.Google Scholar
Cox, R. G. 1970 The motion of long slender bodies in a viscous fluid, Part 1. General theory. J. Fluid Mech. 44, 791–810.CrossRefGoogle Scholar
Drummond, J. E. & Tahir, M. I. 1984 Laminar viscous flow through regular arrays of parallel solid cylinders. Int. J. Multiphase Flow 10, 515–540.CrossRefGoogle Scholar
Hasimoto, H. 1959 On the periodic fundamental solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres. J. Fluid Mech. 5, 317–328.CrossRefGoogle Scholar
Keller, J. B. & Rubinow, S. I. 1976 Slender-body theory for slow viscous flow. J. Fluid Mech. 75, 705–714.CrossRefGoogle Scholar
Lund, I. D. 1985 Hydrodynamics and mass transfer problems in wet spinning. DPhil. Thesis, Oxford University.Google Scholar
Sanchez-Palencia, E. 1980 Non-Homogeneous Media and Vibration Theory. Volume 127 of Lecture Notes in Physics. Springer-Verlag.Google Scholar
Sangani, A. S. & Acrivos, A. 1982a Slow flow past periodic arrays of cylinders with application to heat transfer. Int. J. Multiphase Flow 8, 193–206.CrossRefGoogle Scholar
Sangani, A. S. & Acrivos, A. 1982b Slow flow through a periodic array of spheres. Int. J. Multiphase Flow 8, 341–360.CrossRefGoogle Scholar
Sparrow, E. & Loeffler, A. L. 1959 Longitudinal laminar flow between cylinders arranged in a regular array. A.I.Ch.E. J. 5, 325–330.CrossRefGoogle Scholar
Szaniawski, A. 1976 Equations of steady flow through multifilament bundles. Bull. Acad. Pol. Sci. Ser. des Sci. Tech. 24, 881–890.Google Scholar
Szaniawski, A. 1977 Equations of steady flow through slightly curved filament bundles. Arch. Mech. 29, 519–525.Google Scholar
Szaniawski, A. & Zachara, A. 1974 Bath penetration into the solidification zone of a fibre bundle. Polimery. 20, 87–98.Google Scholar
Szaniawski, A. & Zachara, A. 1975 The influence of the pressure difference at both sides of a plane fibre bundle on the flow inside fibre bundles. Polimery. 19, 143–148.Google Scholar
Terrill, E. L. 1990 Mathematical modelling of some spinning processes. DPhil. Thesis, Oxford University.Google Scholar
Ziabicki, A. 1976 Fundamentals of Fibre Formation. Wiley.Google Scholar