Effect of viscoelastic relaxation modes on stability of extrusion film casting process modeled using multi-mode Phan-Thien-Tanner constitutive equation

Extrusion film casting (EFC) is a commercially important process that is used to produce a significant quantity of polymer films, sheets and coatings for both industrial and household applications. Recently, we have demonstrated the influence of polymer chain architecture on the extent of necking under isothermal as well as non-isothermal film casting operation for commercially relevant polyolefin based materials [1-4]. In the present research, we focus on another instability that frequently occurs in high-speed EFC process called as draw resonance. Draw resonance manifests itself as an instability that causes periodic fluctuations in both the width as well as thickness of the extruded molten film above a critical draw ratio (DR). In this work, we have carried out a linear stability analysis of the isothermal EFC process using a multi-mode Phan-Thien-Tanner (PTT) constitutive equation to determine the onset of draw resonance. We show that as the number of relaxation modes is increased there is a dramatic change in the stability regions. In particular, there is a marked variation in the stability regions obtained by simulating the multi-mode model and those obtained by taking averaged relaxation time of the modes. Additionally, as the number of faster-relaxing modes in a multi-mode spectrum is progressively increased, the process becomes increasingly stable as the level of elasticity in the melt decreases. Finally, the addition of a long relaxation mode in a multi-mode spectrum is akin to adding a long chain branch to a linear polymer that leads to a reduction in film necking and in many cases to enhanced process stability.