Thermocapillary flow and rupture in films of molten metal on a substrate

We consider fluid flow in thin films of molten metal resulting from irradiation by a Gaussian laser beam. Surface tension gradients due to nonuniform heating induce a flow of the molten liquid away from the center of the irradiated area, leading to formation of dry areas on the substrate. We develop a mathematical model of the flow under the assumption of the large ratio of laser beam radius to film thickness. The model extends the standard lubrication-type analysis to include the highly nonlinear dependence of evaporative flux on local interfacial temperature, unsteady heat conduction in the substrate, and positive disjoining pressure due to unbalanced contributions from the kinetic energy of free electrons in the metal. The latter is proportional to the inverse square of the film thickness. We identify thermocapillary stresses as the main mechanism of rapid removal of liquid metal from the irradiated area. Characteristic times of the process, as well as shapes of the molten region surface, agree with experimental observations. We investigate rupture of the molten film and find two different rupture scenarios. The melt surface can either touch the substrate at a point (point rupture) or along a line at a certain radial distance away from the center of the irradiated area (ring rupture). Nondimensional criteria for these two mechanisms are identified. In particular, we show that positive disjoining pressure promotes ring rupture. (C) 2003 American Institute of Physics.