Study of the stability of the film casting process

Abstract

A theoretical study of the film casting process has been carried out. In this industrial process, a molten polymer is extruded through a flat die, then stretched in air and cooled on a chill roll. This involves mainly an extensional flow. Between the die and the chill roll, thick edges are formed and a neck‐in phenomenon is observed. Above a critical take‐up speed, a drawing instability, known as draw resonance, may occur. In this paper, a one‐dimensional model adapted from the classical model of the fiber spinning is developed (for a Newtonian or a Maxwell fluid). The influence of the processing parameters (draw ratio, Deborah number, and aspect ratio) on geometry of the lateral free surface (the so‐called neck‐in phenomenon) is studied. An unattainable zone very similar to the one encountered in fiber spinning is predicted, which only slightly depends on the stretching geometry (initial film width and stretching distance). The onset of draw resonance is studied through the linear stability method. A stability zone, depending on the geometry of the process, the elasticity of the polymer, and the draw ratio, has been obtained. This instability is observed with simultaneous width and thickness film variations. It is proved that the aspect ratio (stretching distance divided by die width) has a strong influence on the onset of the draw resonance instability.

Lateral shaping and stability of a stretching viscous sheet

“…Note the model proposed here extends to non-zero lateral stresses (i.e. S n = 0 and/or S t = 0) the model proposed by Silagy et al [4] for stress-free condition (S n = S t = 0). …”

“…Stress-free: Sn = 0, St = 0 a → ε finite a 1D fiber [10] 2D sheet [4] a → ∞ 1D sheet [7] not possible 3.1…”

“…Consequently, replacing (23) in (19) shows that a decrease of the width due to the necking phenomenon is automatically accompanied by an increase of the thickness, as was mentioned in the Introduction. The system of equations used for the linear stability analysis, setting S n = S t = 0 as done in [4], is obtained by eliminating first w in (12b) from (21a), and by substituting then (16) into (12a), (12b), (21b) and (22). We then followed the steps for the instability analysis given in Section 2.3.…”

“…Silagy et al [4] extended the one-dimensional model in [2] to sheets of larger aspect ratios by considering the edges of the sheet to be free surfaces. Consequently, the stress in the transverse direction depends instead on the edge curvature.…”

Effect of viscoelastic stress state at die exit on extrusion film casting process: Theoretical study

“…This frequently used model was capable of predicting the dog-bone effect under the stationary conditions. Silagy et al [14] continued and enriched membrane model by a supplementary kinematic hypothesis, which was originally brought Narayanaswamy [15] in his paper on float glass stretching, and carried out the extent isothermal study on the process condition and stability of EFC [16,17]. There has also been done a considerable amount of work on EFC under the non-isothermal conditions by Lamberti et al [18][19][20], Lamberti and Titomanlio [21][22][23][24], and Titomanlio [25].…”