Nonisothermal two‐dimensional film casting of a viscous polymer

Abstract

A model is presented for simulating two‐dimensional, nonisothermal film casting of a viscous polymer. The model accommodates the effects of inertia and gravity, and allows the thickness of the film to vary across the width, but it excludes film sag and die swell. Based on the simulation results, three factors are shown to contribute to reducing neck‐in and promoting a uniform thickness: the self‐weight of the material, for low viscosity polymers; nonuniform thickness and/or velocity profiles at the die; and cooling of the film, especially when localized cooling jets are employed.

Edge behaviour in the glass sheet redraw process

“…provided the imposed non-uniformity is confined to the naturally occurring boundary layer. One can therefore conduct numerical experiments by solving the boundary-layer problem from § 3 with different preform thickness profiles imposed at x = 0 and discover the corresponding final thickness profiles produced at x = 1; an approach similar to this was adopted by Smith & Stolle (2000). Alternatively, one could impose the condition of a uniform final sheet thickness at x = 1 and then try to determine the required preform profile h(0, y).…”

“…In § 5 we compare the predictions of our model with numerical solutions to the full three-dimensional problem and with experimental data. In § 6 we extend the Smith & Stolle (2000) idea of modifying the preform shape with the aim of producing a perfectly rectangular final cross-section, by presenting and illustrating a simple method for calculating the exact preform required. In § 7 we discuss the validity of our main assumptions (namely that heat flow is decoupled from fluid flow and that surface tension is not important) and the extension of the model to include a fully coupled temperature equation and surface-tension effects.…”

“…Other studies (for example, Debbaut, Marchal & Crochet 1995;Beaulne & Mitsoulis 1999) included viscoelasticity to more accurately model polymer film casting. Smith & Stolle (2000) used numerical simulations to show that edge thickening can be reduced by the use of a non-rectangular extrusion die. The stability of fibre and sheet drawing has received a great deal of attention due to the restrictions that instabilities place on industrial operating regimes.…”

Transient solutions of the dynamics of film casting process using a 2-D viscoelastic model

“…Co's group studied the draw resonance instability of various viscoelastic fluids using linear stability analysis on time and spatial variations of state variables [4,9]. However, the transient [15] successfully solved the nonisothermal 2-D governing equations with the finite element method (FEM), concluding that the neck-in phenomenon can be suppressed by the self-weight of the film, nonisothermal conditions, or nonuniform boundary conditions at the die exit. Satoh et al [16] also solved 2-D equations using Galerkin FEM with streamline elements for continuity and momentum equations.…”

“…The above three instability modes in film casting have been studied by many researchers, most notably by Agassant' and Co' groups, using (a) 1-D models to illustrate draw resonance phenomenon with the simplifying assumption of the constant film width [4,9];(b) other improved 1-D models that can predict both draw resonance phenomenon and the neck-in [6,[10][11][12][13], and (c) 2-D or 3-D models which can describe the edge beads as well as the above two instabilities [5,[14][15][16].…”