(229c) Intriguing Nonlinear Dynamic and Stability Characteristics of Film Blowing Process

The successful simulation of the transient behavior of film in film blowing process has proved rather elusive, despite its modeling standards having been laid down more than 30 years ago by Pearson and Petrie in their seminal paper (1970) incorporating a moving material coordinate system. This is mainly because of the highly nonlinear nature of the partial differential equations involved and the difficulties in executing the numerical algorithms. It is thus only recent when Hyun et al. (2004) have successfully obtained for the first time the transient solutions of the dynamics using newly-devised mathematical/numerical schemes which employ a coordinate transformation converting a free-end-point problem to a more amenable fixed-end-point one and an orthogonal collocation on finite elements alleviating the dimensional burden in numerical computation. The transient solutions thus obtained have been found robust even during the severe oscillations of draw resonance instability also revealing a striking dynamic resemblance to experimental observations. In another seminal paper in 1988 by Cain and Denn the dynamics of the system like the multiplicity and stability of the steady states was first investigated systematically. Shin et al. (2007) have recently conducted an extended analysis both experimentally and theoretically with focus on the multiplicity, bifurcation, stability and hysteresis features and also provided physical explanations for the various dynamic features in the system. Quite recently, Lee et al. (2008) have included the flow-induced crystallization (FIC) into the non-isothermal, viscoelastic governing equations to obtain the robust, transient solutions for the whole distance coordinate from the die exit to the nip roll. These solutions are particularly significant in the sense that they have been obtained without assuming the boundary condition of the vanishing gradient of the bubble radius at the freeze-line height (FLH), which had been universally taken by all researchers in hitherto-published simulation models. The same vanishing gradient of the bubble radius at FLH has instead been obtained as part of the solution of the governing equations, not as an assumed boundary condition.