Draw Resonance in Viscous Sheets

The instability known as the ``draw resonance'' in literature is studied for a viscous sheet considering the visco-gravity balances (Stokes number) and the heating/cooling effects (Stanton number). The analysis considers lubrication approximation for continuity, momentum and energy equations and determines the critical draw ratio for a range of Stokes numbers and Stanton numbers. The critical draw ratio is~very sensitive to the~variation of Stokes and Stanton numbers. It is shown that the decrease in Stokes number and/or the increase in Stanton number results in a decrease in the critical draw ratio.