Film blowing modeling

An objective of this work was to check whether the simple Zatloukal-Vlcek film blowing model can adequately describe the experimentally observed bubble shapes for linear as well as branched mLLDPEs when produced under different processing conditions. In Eigure 5 it is clearly demonstrated that the model has extremely high fitting capability to describe the experimentally determined bubble shapes from the Bradford film blowing equipment. 

With the aim to determine the temperature profile along the measured film bubble shape, we have used the simple film blowing model [4] which is given by the following set of eqnations ... 

This generalized Newtonian model has been used together with the film blowing model in the same way as described in [5] for the Newtonian model. In this case, however, the iteration numerical scheme has been required. 

Figure 4 Theoretical investigation of the molecular weight (4a) and long chain branching (4b) on the high stalk bubble formation by the help of the Zatloukal-Vlcek film blowing model and generalized Newtonian model.

Andre, J. M. ct al., 1998. Numerical modelling of the polymer film blowing process. Int. J. Forming Processes 1, 187-210. 

Despite the non-isothermal nature of the film blowing process we will develop here an isothermal model to show general effects and interactions during the process. In the derivation we follow Pearson and Petrie s approach [20], [19] and [21]. Even this Newtonian isothermal model requires an iterative solution and numerical integration. Figure 6.21 presents the notation used when deriving the model. 

Figure 6.23 Predicted film blowing process using an isothermal Newtonian model for a...

The first milestone in modeling the process is credited to Pearson and Petrie (42—44). who laid the mathematical foundation of the thin-film, steady-state, isothermal Newtonian analysis presented below. Petrie (45) simulated the process using either a Newtonian fluid model or an elastic solid model in the Newtonian case, he inserted the temperature profile obtained experimentally by Ast (46), who was the first to deal with nonisothermal effects and solve the energy equation to account for the temperature-dependent viscosity. Petrie (47) and Pearson (48) provide reviews of these early stages of mathematical foundation for the analysis of film blowing. 

Randomly branched polymers are of enormous importance for certain polymer processing operations, such as blow moulding and film blowing. The molar mass distribution of all randomly branched polymers is described by percolation models. For commercial randbmly branched polymers, the critical percolation model applies only very close to the gel point. The branching chemistry used in commercial randomly branched polymers is usually stopped far short of the critical region. While critical percolation does not apply to these polymers, the mean-field percolation model does a superb job of describing the molar mass distribution of randomly branched commercial polymers. 

J. M. Andre et al., Numerical Modelling of the Film Blowing Process, in J. Huetink and F. P. T. Baaijens, eds.. Simulation of Materials Processing Theory, Methods and Applications, A. A. Balkema, Rotterdam, 1998. 

A film blowing application of the crystallization model first developed for spinning in the articles by Doufas and McHugh, cited above, with comparisons to spinUne data for low-density and linear low-density polyethylene, is in... 

The blown film process is known to be difficult to operate, and a variety of instabilities have been observed on experimental and production film lines. We showed in the previous chapter (Figure 10.10) that even a simple viscoelastic model of film blowing can lead to multiple steady states that have very different bubble shapes for the same operating parameters. The dynamical response, both experimental and from blown film models, is even richer. The dynamics of solidification are undoubtedly an important factor in the transient response of the process, but the operating space exhibits a variety of response modes even with the conventional approach of fixing the location of solidification and requiring that the rate of change of the bubble radius vanish at that point. 

In a number of polymer processing operations, such as blow molding, film blowing, and thermoforming, deformations are rapid and the polymer melt behaves more like a crosslinked rubber than a viscous liquid. Figure I.l showed typical deformation and recovery of a polymeric liquid. As the time scale of the experiment is shortened, the viscoelastic liquid looks more and more like the Hookean solid. In Chapters 3 and 4 we develop models for the full viscoelastic response, but in many cases of rapid deformations, the simplest and often most realistic model for the stress response of these polymeric liquids is in fact the elastic solid. 

The film-blowing process is used industrially to manufacture plastic films that are biaxially oriented. Many attempts have been made to predict and model this complex but important process, which continues to mystify rheologists and polymer processing engineers worldwide. A constitutive equation, able to predict well the polymer melt in all forms of deformation, is required to model the process, together with the standard conservation equations of continuity, momentum, and energy. Pearson and Petrie [125,126] were the first to predict the forces within the blown film by the use of the thin-shell approximation, force balances, and the Newtonian constitutive equation. The use of the thin-shell approximation and force balances is standard in any attempt to model the film-blowing process, and it has been used in the vast majority of subsequent studies. 

There have been numerous studies on the film-blowing process. Since the initial thin-shell approximation proposed by Pearson and Petrie [125, 126] with the Newtonian model assumed for deformation, various rheological models have been incorporated in simulations, such as the power-law model [127,128], a crystallization model [129], the Maxwell model [130-133], the Leonov model [133], a viscoplasti-c-elastic model [134], the K-BKZ/PSM model [135-137], and a nonisothermal viscosity model [138]. A complete set of experimental data was reported by Gupta [139] for the Styron 666 polystyrene and by Tas [140] for three different grades of LDPE. 

Alaie, S.M. and Papanastasiou, T.C. (1993) Modeling of non-isothermal film blowing with integral constitutive equations. Int. Polym. Proc., 8, 51—65. 

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