Sensitivity of the Stability of Isothermal Melt Spinning to Rheological Constitutive Assumptions
An instability in polymer melt spinning known as draw resonance is characterized by the onset of sustained oscillations in tension and drawn-filament diameter at a critical draw ratio (takeup velocity/initial velocity). The oscillations have a well-defined period and amplitude. Theory and experiment are reviewed by Petrie and Denn (1976) and Denn (1980). The most general theory is that of Fisher and Denn (1976,1977), which is based on a singlerelaxation-time Maxwell model with a deformation-dependent viscosity. Broadly, the critical draw ratio is predicted to decrease as the viscosity function becomes more shear thinning, and to increase with increasing elasticity (increasing relaxation time or, equivalently, decreasing modulus.) Absolute stabilization is predicted above a critical value of a dimensionless group λvo/L, where vo is the initial velocity, L is the length of the melt zone, and λ is the relaxation time evaluated at vo/L. Cooling is usually stabilizing.
KeywordsDraw Ratio Maxwell Model Absolute Stabilization Normal Stress Difference Extensional Flow
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