Stability analysis of a polymer film casting problem

Abstract : The polymer cast film process consists of stretching a molten polymer film between a flat die and a drawing roll. Drawing instabilities are often encountered and represent a drastic limitation to the process. Newtonian fluid film stretching stability is investigated using two numerical strategies. The first one is a ‘tracking’ method, which consists of solving Stokes equations in the whole fluid area (extrusion die and stretching path) by finite elements. The interface is determined to satisfy a kinematic equation. A domain decomposition meshing technique is used in order to account for a flow singularity resulting from the change in the boundary conditions between the die flow region and the stretching path region. A linear stability method is then applied to this transient kinematic equation in order to investigate the stability of the stationary solution. The second method is a direct finite element simulation in an extended area including the fluid and the surrounding air. The time-dependent interface is captured by solving an appropriate level-set function. The agreement between the two methods is fair. The influence of the stretching parameters (Draw ratio and drawing length) is investigated. For a long stretching distance, a critical Draw ratio around 20 delimitating stable and unstable drawing conditions is obtained, and this agrees well with the standard membrane models, which have been developed 40 years ago. When decreasing the stretching distance, the membrane model is no longer valid. The 2D models presented here point out a significant increase of the critical Draw ratio, and this is consistent with experimental results.