An iterative approach to the thermal Newtonian blown film model

Abstract

Film blowing, by which thin polymer film is manufactured, is an industrial process with products used in a wide range of applications. Modelling of this process requires solving the highly nonlinear differential equations necessary to describe the complex chemical and physical interactions involved. Earlier work applied a mixture of analytic and numerical techniques to this modelling when the polymer involved was a Newtonian fluid operating under isothermal conditions. Subsequent calculations extended this analysis to the non-isothermal Newtonian film. However, the numerical procedures used were found to be computationally expensive. We apply a more robust finite element approach to these computations, that avoids the difficulties of the earlier methods, and is an improvement on these previous efforts. References

• Ervin V. J., Non-uniqueness of the Newtonian film blowing model, in preparation.
• Bennett J. C., Interior Layer Structure in the Blown Newtonian Film, Honours Thesis, School of Mathematical and Geospatial Science, RMIT, 2004.
• Bennett J. C. and Shepherd J. J., Analysis of the non-isothermal Newtonian model in the blown film process, ANZIAM Journal (E), 47, pp. C325--C338, 2006. http://anziamj.austms.org.au/V47EMAC2005/Bennett
• Luo X.-L. and Tanner R. I., A computer study of film blowing, Polymer Engineering and Science Vol. 25, No. 10, 1985, pp. 620--629.
• Muke S., Connell H., Sbarski I. and Bhattacharya S. N., Numerical modelling and experimental verification of blown film processing, Journal of Non-Newtonian Fluid Mechanics Vol. 116, 2003, pp. 113--138. doi:10.1016/j.jnnfm.2003.09.002
• Pearson J. R. A., Mechanics of Polymer Processing, Elsevier Applied Science Publishers, 1985.
• Pearson J. R. A. and Petrie C. J. S., The flow of a tubular film. Part 1. Formal mathematical representation, Journal of Fluid Mechanics Vol. 40, 1970, pp. 1--19.
• Pearson J. R. A. and Petrie C. J. S., The flow of a tubular film. Part 2. Interpretation of the model and discussion of solutions, Journal of Fluid Mechanics Vol. 42, 1970, pp. 609--625.
• Shepherd J. J. and Bennett J. C., Interior layer structure in the Newtonian blown film, ANZIAM Journal 46(E), 2005, pp. C839--C853. http://anziamj.austms.org.au/V46/CTAC2004/Shep/
• Shepherd J. J., Connell H. J. and Tam D. C. H., 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.
• Tam D. C. H., Shepherd J. J. and Connell H. J., 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.