Practical Scaling and Stability Maps
摘要
While the effects of gravity, inertia, neck-in, surface tension and viscoelasticity were treated isolated in Chaps. 4 – 8 , they mostly superimpose in practice. This chapter treats the application oriented analysis of models including up to four of these effects simultaneously. For this purpose an alternative scaling is used to introduce control parameters with strong correlation to typical practical quantities. Newtonian models for infinite and finite-width film casting including inertia and gravity effects are analyzed as well as a fiber drawing model, which covers additionally the influence of surface tension. Moreover, the infinite-width film model and the fiber model are extended to cover viscoelastic effects by employing the PTT constitutive equation. For each model, stability maps in the control parameter space are presented and discussed, and empirical formulas, which enable a simple and quick estimation of the critical draw ratio in dependence of the practical control parameters, are derived for particular scenarios.