Instabilities and multiplicities in non-isothermal blown film extrusion including the effects of crystallization

Stable operating regions for blown film extrusion are mapped using a dynamic model that includes the effect of crystallization on the rheological properties of the polymer. In the computations, the bubble air mass and take-up ratio were held constant, and the machine tension and bubble inflation pressure were treated as dependent variables. For a given bubble air mass, the take-up ratio was used as the continuation parameter for mapping steady-state solutions. The take-up ratio varies smoothly, but not necessarily monotonically, with the machine tension. Curves of either blow-up ratio or thickness reduction versus take-up ratio reveal that there are take-up ratios where no, one, or multiple solutions exist. The heat transfer coefficient from the polymer film to the external air and surroundings has a marked influence on the qualitative and quantitative features of the blow-up ratio versus thickness reduction curves. Generalized eigenvalue analysis of the linearized blown film equations indicates that increasing the heat transfer rate increases the stability of operations. A corresponding decline occurs, however, in the thickness reduction of the blown film for a given blow-up ratio.