Thermocapillary-assisted pulling of contact-free liquid films

We study the formation of a free liquid film that is pulled out of a bath at constant speed and stabilized by the action of thermocapillary stresses prescribed at the free surfaces. The basic concept was introduced recently by Scheid et al. ["Thermocapillary-assisted pulling of thin films: Application to molten metals," Appl. Phys. Lett.97, 171906 (2010)]10.1063/1.3505523. The theory suggests that very thin ribbons of molten material can be drawn out of a melt by adequately tuning the temperature gradient along the dynamic meniscus that connects the static meniscus at the melting bath to the region of the drawn flat film. In the present paper, we extend our original analysis by investigating the roles of inertia and gravity on the film thickness, and show how the results depend on heat transfer/conduction properties. Furthermore, we analyze the one-dimensional transverse stability of the free film with respect to the long-wave thermocapillary instability.