THE ROLE OF THERMOVISCOUS AND THERMOCAPILLARY EFFECTS IN THE COOLING OF A MOLTEN FREE LIQUID FILM DRAINING DUE TO GRAVITY

Abstract

We consider theoretically the two-dimensional flow in a vertically-aligned thick molten liquid film to investigate the competition between cooling and draining due to gravity, relevant in the formation of metallic foams. The molten liquid in the film cools as it drains, losing its heat to the surrounding colder air and substrate. We extend our previous model in Alahmadi et al. [1] to include non-isothermal effects resulting in coupled nonlinear evolution equations for the film’s thickness, extensional flow speed, and temperature. The coupling between the flow and cooling is via a constitutive relationship for the temperature-dependent viscosity and surface tension. This model is parameterized by the heat transfer coefficients at the film-air free surface and film-substrate interface, the Péclet number, the viscosity-temperature coupling parameter and the slope of the linear surface tension-temperature relationship. A systematic exploration of the parameter space reveal that at low Péclet numbers, increasing the heat transfer coefficient and a gradual reduction in viscosity with temperature is conducive for cooling and can slow down the draining and thinning of the film. The effect of increasing the slope of the surface tension-temperature relationship on the draining and thinning of the film is observed to be more effective at lower Péclet numbers where surface tension gradients in the lamella region oppose the gravity-driven flow. At higher Péclet numbers, though, the surface tension gradients tend to enhance the draining flow in the lamella region resulting in the dramatic thinning of the film at late times.