Enhanced suppression of draw resonance in sheet casting due to heating

We consider the effect of heating on the stability of a highly viscous and thin Newtonian sheet of liquid drawn onto a moving substrate under conditions of negligible inertia and gravity. Whereas the stability of the drawing process has been well-studied under conditions where the liquid sheet is isothermal or cooled, the effect of heating has not. We impose a Gaussian temperature profile in the liquid to mimic a process in which film moves through a heating zone over a portion of the sheet; this is followed by a region of cooling. Here, we show a remarkable suppression of the draw resonance instability by heating the sheet as it flows. Compared with an isothermal configuration, the critical draw ratio—defined as the maximum ratio of the final to initial velocity in the sheet below which the sheet is stable—can be increased by many orders of magnitude depending on parameters of the imposed Gaussian heating profile. A cooling profile that follows the Gaussian has a quantitative but relatively small effect on the magnitude of the critical draw ratio. We find that a relatively narrow region of heating relative to the sheet length can dramatically increase the critical draw ratio. Although the results of this paper are provided predominantly in the limit of negligible heat transfer resistances, the effect of heat transfer on presented results is examined.