We examine the stability of a highly viscous and thin Newtonian liquid sheet that is heated as it is drawn onto a moving substrate. In a previous paper, Ng and Weinstein “Enhanced suppression of draw resonance in sheet casting due to heating,” Phys. Fluids 37, 044107 (2025) reported a significant suppression of the draw resonance instability in this heating configuration; a representative viscosity/temperature dependence for glass was used in their theoretical model. 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—was increased by many orders of magnitude when a portion of the sheet experienced a Gaussian heating profile. Internal and external heat transfer resistances were also considered, and the parameter space of enhancement was quantified. The prior study, however, incorporated only viscous forces in the flow model. Here, we consider the effects of inertia, surface tension, and gravity on the significant stabilizing effects observed by Ng and Weinstein due to heating. We find that fluid inertia further stabilizes the heated liquid sheet at surprisingly small Reynolds numbers, while surface tension and gravitational effects have quantitative but relatively minor effects. For the typical glass viscosity/temperature model used here, however, inertial stabilization cannot be realized in practice, and the prior conclusions of Ng and Weinstein regarding the enhanced suppression of instability by heating are largely unchanged.
Ng et al. (Sun,) studied this question.