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ANZIAM J. 46(E) pp.C839--C853, 2005.

Interior layer structure in the Newtonian blown film

J. J. Shepherd

J. C. Bennett

(Received 29 October 2004, revised 27 July 2005)

Abstract

The techniques and methodology of singular perturbation theory analyse the film blowing of an incompressible Newtonian film. An appropriate, physically relevant small parameter guides the method of matched asymptotic expansions to obtain straightforward closed form approximate expression for the film profile throughout the blown region. This then determines such related quantities as the film thickness variation, and the film speed. The results of applying this closed form expression are compared with numerical calculations using the package Maple. The two methods show encouraging consistency.

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Authors

J. J. Shepherd

School of Mathematical and Geospatial Sciences, Royal Melbourne Institute of Technology, Melbourne, Australia. mailto:jshep@rmit.edu.au

J. C. Bennett

School of Mathematical and Geospatial Sciences, Royal Melbourne Institute of Technology, Melbourne, Australia. mailto:s2111773@student.rmit.edu.au

Published September 1, 2005. ISSN 1446-8735

References

1. J. C. Bennett, Interior Layer Structure in the Blown Newtonian Film, Honours Thesis, School of Mathematical and Geospatial Science, RMIT, 2004.
2. X.-L. Luo, R. I. Tanner, A Computer Study of Film Blowing, Polymer Engineering and Science, Vol.25, no.10, 1985, pp.620--629.
3. A. H. Nayfeh, Perturbation Methods, John Wiley and Sons, 1973.
4. J. R. A. Pearson, Mechanics of Polymer Processing, Elsevier Applied Science Publishers, 1985.
5. J. J. Shepherd, H. J. Connell and D. C. H. Tam, An interior layer in a film-blowing problem, Proceedings of the Fifth Biennial Engineering Mathematics and Applications Conference (EMAC2002), M. Pemberton, I. Turner, P. Jacobs (eds), The Institution of Engineers Australia, Brisbane, Queensland (2002), pp.181--186
6. D. C. H. Tam, Mathematical Analysis of the Blown Newtonian Film, MAppSc Thesis, RMIT, 2003
7. D. C. H. Tam, J. Shepherd and H. Connell, Modelling the film blowing process, Proceedings of the Fourth Biennial Engineering Mathematics and Applications Conference (EMAC2000), R. L. May, G. F. Fitz-Gerald, I. H. Grundy (eds), The Institution of Engineers Australia, Melbourne (2000), pp.271--274.