Non-Newtonian effects on draw resonance in film casting

Abstract

In this paper, the influence of non-Newtonian material properties on the draw resonance instability in film casting is investigated. Viscoelastic models of infinite width film casting are derived systematically following an asymptotic expansion and using two well-known constitutive equations: the Giesekus model and the simplified Phan–Thien/Tanner (PTT) model. Based on a steady state analysis, a numerical boundary condition for the inlet stresses is formulated, which suppresses the unknown deformation history of the die flow. The critical draw ratio in dependence of both the Deborah number and the nonlinear parameters is calculated by means of linear stability analysis. For both models, the most unstable instability mode may switch under variation of the control parameters, leading to a non-continuous change in the oscillation frequency at criticality. The effective elongational viscosity, which depends exclusively on the local Weissenberg number, is analyzed and identified as crucial quantity as long as the Deborah number is not too high. This is demonstrated by using a generalized Newtonian fluid model to approximate the PTT model. Based on such a generalized Newtonian fluid model, the effects of strain hardening and strain thinning are finally explored, revealing two opposing mechanisms underlying the non-Newtonian stability behavior.