Practical mapping of the draw resonance instability in film casting of Newtonian fluids

• The draw resonance effect in film casting is quantitatively analysed.
• A Newtonian model including inertia and gravity effects is used.
• Using fluidity and inlet velocity as dimensionless control parameters reveals non-monotonic stability behaviour.
• Various stability regimes are identified, including a regime of unconditional stability.
• Correlations between the critical draw ratio and the control parameters are given.

The influence of viscosity and inlet velocity on the draw resonance instability of film casting processes is quantitatively analysed. By linear stability analysis of a Newtonian model including inertia and gravity effects, stability curves for different control parameter values are calculated numerically. For this purpose, we propose a scaling law which separates the fluidity, i.e. the reciprocal viscosity and the inlet velocity into two independent dimensionless parameters. This new scaling evidences a minimum of stability, separating two regimes of opposite behaviour: one for which increasing the inlet flow rate has a destabilizing effect due to viscosity and one for which increasing the inlet flow rate has a stabilizing effect due to gravity and inertia; increasing the fluidity has always a stabilizing effect. By fitting the stability curves with an appropriate postulated function, we are able to construct correlations between the critical draw ratio, the fluidity and the inlet velocity. For the first time regimes of negligible inertia or negligible gravity effects are revealed as well as a regime of unconditional stability. The proposed correlations for each of these regimes can further be used as an analytical solvable criterion for determining the onset of draw resonance in film casting.