Modeling of Non-isothermal Film Blowing with Integral Constitutive Equations

Abstract

Non-isothermal, melt film-blowing is analysed by means of a nonlinear integral constitutive equation that incorporates shear history effects, spectrum of relaxation times, shear thinning and extension thinning or thickening. The temperature history, as predicted by the simultaneously solved energy equation, is introduced into the constitutive equation by means of the appropriate shift factor incorporated in the linear modulus of the constitutive equation. The resulting system of integrodifferential equations is solved by finite element discretization and Newton iteration. Bubble shape, velocity, temperature, stress and thickness profiles are predicted simultaneously. Predicted film thickness, temperature and stress profiles of blowing of polystyrene are compared with experimental data taken from the literature.

Numerical modelling and experimental verification of blown film processing

“…A comparison between the isothermal and non-isothermal bubble diameter profiles showed that the temperature is the most critical parameter for influencing the bubble shape, even more so than the rheological constitutive equation of state. This was also observed by other investigators of the blown film process [1,31,32]. Fig.…”

Numerical optimization of a multi-jet cooling system for the blown film extrusion

“…as differential descriptions, they take the upper convected Maxwell [3], the Phan-Thien and Tanner [4 -6] or the Pom-Pom [7] model, to obtain a realistic film contour prediction. Next to the differential models, there are integral constitutive ones [8,9] like the K-BKZ model. All these models show good simulation results of the blown film behavior compared to experimental data.…”

Application of variational principles in modeling of the film blowing process for high stalk bubbles

“…The height at which the solidification starts is referred to as the freezeline and the stresses frozen at this area are inextricably related to the final mechanical and optical properties of the film [1][2][3]. With the aim to understand more deeply the stability of the film blowing process and the relationship between machine design, processing parameters, materials and final film properties, intensive experimental as well as theoretical [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45] effort has been done in past 40 years. Probably the most popular way for the theoretical investigation of the film blowing process is based on the formulation proposed by Pearson and Petrie [27][28][29][30].…”