This thesis presents a new numerical algorithm for 2D nonisothermal time-stepping simulations of a nonlinear viscoelastic cast film process. The most significant contribution of the algorithm is that an updated Lagrangian (UL) description of motion is employed, as opposed to the more conventional Eulerian (E) description generally used in polymer processing simulations. Furthermore, use is made of a constitutive equation unlike those generally employed for polymers. The constitutive equation accommodates viscoelasticity, extensional thinning/thickening, and strain-hardening. A comparison of the UL and E algorithms and constitutive equations shows that the UL algorithm in some respects represents a more natural and intuitive approach, which has the advantage of being "closer" to the physics of the film casting problem.

This new numerical algorithm can find the steady-state film properties, and it can predict the onset of instability by observing draw resonance as a response problem. By determining the critical draw ratio as a response problem, the mathematical complications of the more common linear stability analysis approach are avoided. In terms of the stability of the film, it was observed that stability is decreased by extensional thinning, strain-hardening, and higher relaxation times and stability is increased by extensional thickening, higher heat transfer and higher ratios of air-gap length to die width.

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