Stability Analysis of Film Casting for PET Resins Using a Multimode Phan-Thien-Tanner Constitutive Equation

Abstract

In film casting or extrusion coating of polyethylene terephthalate (PET) resins, thickness and film-width nonuniformities arise due to edge neck-in or to flow instabilities such as draw resonance. Flow modeling can identify the parameter range of stable operation but requires accurate knowledge of melt rheology/elasticity in both shear and extension. Rheological data of a linear PET published earlier was used to fit, by nonlinear optimization, the linear relaxation spectrum and nonlinear parameters of a multimode Phan-Thien and Tanner (PTT) constitutive relation. The fitted PTT relation was then used in a finite-element model of the stability of film casting flow based on the thin membrane approximation. At low Deborah numbers (De), the critical draw ratio (Dr) for the onset of the draw resonance instability was found to be in agreement with previous analyses; but at higher De it was found to depend significantly on the stress boundary condition imposed at the inflow boundary. For a certain boundary condition and beyond a certain De, a new mode of instability with half the temporal and spatial frequency of draw resonance was found at small draw ratios.

Keywords

film casting stability analysis multi-mode Phan-Thien-Tanner equation PET

Get full access to this article

View all access options for this article.

References

1. Pakula, T. and Fischer, E. W. , J. Polym. Sci. Polym. Phys. Ed., 19, 1705-1705 (1981).

2. Petrie, C. J. S. and Denn, M. M. , AIChE, 22, 209-209 (1976).

3. Hatzikiriakos, S. G. , Heffner, G. , Vlassopoulos, D. and Christodoulou, K. , Rheol. Acta., 36, 568-568 (1977).

4. Phan-Thien, N. and Tanner, R. I. , J. Non-Newtonian Fluid Mech., 2, 353-353 (1977).

5. Cogswell, F. N. , Polym. Eng. Sci., 12, 64-64 (1972).

6. Pearson, J. R. A. , Mechanics of Polymer Processing, Elsevier, New York (1985).

7. Fisher, R. J. and Denn, M. M. , Chem. Eng. Sci., 30, 1129-1129 (1975).

8. Fisher, R. J. and Denn, M. M. , AIChE J, 23, 23-23 (1977).

9. Denn, M. M. in Computational Analysis of Polymer Processing, J. R. A. Pearson and S. M. Richardson , eds. Applied Science Publishers Ltd., Essex, 179-179 (1983).

10.

10. Beris, A. N. and Liu, B. , J. Non-Newtonian Fluid Mech., 26, 341-341 (1988).

11.

11. Beris, A. N. and Liu, B. , J. Non-Newtonian Fluid Mech., 26, 362-362 (1988).

12.

12. Devereux, B. M. and Denn, M. M. , Ind. Eng. Chem. Res., 33, 2384-2384 (1994).

13.

13. Gagon, D. L. and Denn, M. M. Polym. Eng. Sci., 21, 844-844 (1981).

14.

14. Iyengar, V. R. and Co., A. , J. Non-Newtonian Fluid Mech., 48, 1-1 (1993).

15.

15. Iyengar, V. R. and Co, A. , Chem. Eng. Sci., 51, 1417-1417 (1996).

16.

16. Piz-Lopez, M. E. and Co, A. , J. Non-Newtonian Fluid Mech., 66, 71-71 (1996).

17.

17. Piz-Lopez, M. E. and Co, A. , J. Non-Newtonian Fluid Mech., 66, 95-95 (1996).

18.

18. Barq, P. , Haudin, J. M. , Agassant, J. F. , Roth, H. and Bourgin, P. , Int. Polym. Proc. V: 264–276 (1990).

19.

19. Silagy, D. , Demay, Y. and Agassant, J. -F. , Polym. Eng. Sci., 36, 2614-2614 (1996).

20.

20. Rajagopalan, D. , Armstrong, R. C. and Brown, R. A. , J. Non-Newtonian Fluid Mech., 36, 159-159 (1990).

21.

21. Christodoulou, K. N. and Scriven, L. E. , J. Comp. Phys., 99, 39-39 (1992).

22.

22. Christodoulou, K. N. and Scriven, L. E. , J. Sci. Comput., 3, 355-355 (1998).

23.

23. Ji, C-C. , Yang, J.-C. and Lee, W. -S. , Polym. Eng. Sci., 36, 2685-2685 (1996).

24.

24. Matsumoto, T. and Bogue, D. C. , Polym. Eng. Sci., 18, 564-564 (1978).