Multiplicity, bifurcation, stability and hysteresis in dynamic solutions of film blowing process

The complicated nonlinear dynamics in film blowing process has been investigated focusing on the multiplicity, bifurcation, and stability in the dynamic solutions of the system using both the theoretical model simulation and experiments. A number of interesting findings have been revealed about the dynamics of the process including a fundamentally different behavior of the system with a maximum of three steady states for the nonisothermal operations in contrast to the isothermal approximation where only two steady states were predicted. These differences have been identified as stemming from the fact that multiple values of a bubble radius at the freezeline height can give the same value of the air pressure inside the bubble depending upon the process conditions and the values of the bifurcation parameters of the system. The stability of the three steady states also displays many different patterns dictated by the process conditions, including the hysteresis in the bifurcation diagrams. These stability results of the system are quite reminiscent of those in the well-known CSTR (continuous stirred tank reactor) cases found in the literature of chemical reaction engineering. The theoretical models of the film blowing system developed by this study produce quite accurate predictions of the bubble and film shape results both in the steady state and the transient solutions as compared with experiments. It is considered that the findings of this study can be readily utilized to enhance the stabilization and optimization of the film blowing operation.