A Generalized 2.5 D FEM Formulation for Steady Non-Newtonian Viscous Multilayer Flow: Part 1 : Formulation and Theoretical Verification

It is an important theme to predict the formation of multilayered film interface in an extrusion device, such as a coat hanger die or a spiral mandrel die. At present, the 3 D viscoelastic fluid analysis method is available to evaluate multilayer flow behaviors, but applications are limited due to large computational storage and complex operations concerning the modeling of the viscoelastic material and the mesh generation. On the other hand, the 2 D viscous fluid analysis method, which is easy to operate, cannot be applied to estimate variations of multilayer flow thickness in the transverse direction. In this paper, we propose a new formulation for developing viscous multilayer flow in the entrance region near the flow junction. We also propose an improved formulation for a fully developed viscous multilayer flow. The theoretical background of each formulation is described. A simple Newtonian viscous two-layer flow model with a flow junction is employed to theoretically verify the developing viscous multilayer flow formulation. 2.5 D FEM (Finite Element Method) based on the fully developed viscous multilayer flow formulation is applied to simulate non-Newtonian viscous three-layer flow in a coat hanger die. The results of this research are summarized as follows. (1) A new formulation for the developing viscous multilayer flow is useful for estimating complex behaviors in the entrance region near the flow junction and can represent theoretically correctly the fully developed state as its asymptotic solution. (2) An improved formulation for the fully developed viscous multilayer flow is easy to use and can be effectively applied to simulate the fully developed state in short computational time. It is expected that a practical numerical technology for estimation of the viscous multilayer flow in extrusion devices can be constructed by combining these formulations.