Newtonian fluids film blowing

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. 

Unlike shear viscosity, extensional viscosity has no meaning unless the type of deformation is specified. The three types of extensional viscosity identified aind measured are uniaxial or simple, biaxial, and pure shear. Uniaxial viscosity is the only one used to characterize fluids. It has been employed mainly in the study of polymer melts, but also for other fluids. For a Newtonian fluid, the uniaxial extensional viscosity is three times the shear viscosity ( fe)uni = 3/ . This is confirmed at very low shear rates in Figure 13, which provides a typical example of the extensional viscosity behavior of a polymer (129). The two other extensional viscosities are used to study elastomers in the form of films or sheets. Uniaxial and biaxial extensions are important in industry (118,125-128,130,132), the former for the spinning of textile fibers and roller spattering of paints, and the latter for blow molding, vacuum forming, film blowing, and foam processes. 

Yeow (1976) theoretically analyzed the instabilities due to axisymmetfic disturbances in an isothermal Newtonian fluid and presented neutral stability curves in the space Wf (= H(/Ro) and Br and for various values of the parameter X (X = Z/Ro, which is the dimensionless freeze line). Kanai and White (1984) experimentally studied the stability of nonisothermal film blowing of viscoelastic melts, such as LLDPE, LDPE, and HDPE, and their results are shown in Figures 9.27 and 9.28. LDPE is more stable than LLDPE and HDPE, which is in accord with LDPE s strain hardening... 

The effect of processing conditions, die design and material characteristics on the stability of the film blowing process has been investigated theoretically by the recently proposed Zatloukal-Vlcek model [Zatloukal M Vlcek J., J. Non-Newtonian Fluid Mech. 123, p. 201-213, 2004 Zatloukal M., Vlcek J. J. Non-Newtonian Fluid Mech. 133, p. 63-72, 2006] and the theoretical predictions were compared with the corresponding experimental data. It has been found that the model predictions are in good correspondence with the experimental reality. 

MODELING OF NON-ISOTHERMAL HIGH STALK FILM BLOWING PROCESS BY USING VARIATIONAL PRINCIPLES FOR NON-NEWTONIAN FLUIDS... 

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