Interplay Between Inertia and Elasticity in Film Casting

Abstract

The influence of inertia and boundary conditions on the steady state and stability of isothermal film casting of viscoelastic fluids is examined using a Phan-Thien–Tanner rheological model. The elongational flow between the die exit and the take-up point is investigated. In general, the steady-state film tends to contract for low-inertia flow; this contraction, however, is significantly diminished by inertia. The polymeric normal stresses and primary normal stress difference decrease in the most of the air gap as inertia increases. In contrast, the stress and stress difference increase considerably near the take-up point due to a dramatic increase in the elongation rate. The linear stability analysis for two-dimensional disturbances is carried out. For a polymer with no degradation, and in the absence of inertia (Re=0), the analysis predicts critical draw ratios that form an envelope to an unstable region. This region of unstable conditions reduces as inertia increases. Two branches of neutral stability curve are observed for higher-inertia flow as opposed to a single curve for Re=0. The unstable region expands as α increases, where α is a measure of polymer degradation. When α becomes sufficiently large, the elasticity tends to destabilize the flow. It is also found that boundary conditions have an important influence on the steady-state profiles and stability region, particularly for high-elasticity fluids.