Transient solutions of nonlinear dynamics in film blowing process accompanied by on-line crystallization

The nonlinear dynamics in film blowing process is investigated in this study solving the governing equations of the system, which include the dynamics of crystallization occurring on the film, defined over the entire distance from the die exit to the nip roll in a single region for transient (and steady-state) solutions. The present study does not assume a priori the bubble radius at freezeline height to have the zero slope with respect to the axial coordinate as the boundary condition of the governing equations of the system. Instead, the governing equations yield this result as part of the transient solution of the partial differential equations. Aside from this, the transient solutions reported in this study also reveal some fundamental breakthroughs over previous results even during the severe periodic oscillation of instability called draw resonance: For example, the oscillatory temporal curves of the bubble radius produced by simulation during the draw resonance instability accurately exhibit the skewed characteristics, and the inflection points in the curves, and also agree well with the minima points as observed in experimental data. Additionally, there is a notable improvement on the stability diagrams by the new model, eliminating the fictitious stability region predicted by the previous simulation model.