We explore two problems involving the flow of thin liquid films. The first examines the flow that develops in thin metal films melted by a laser pulse. The second investigates the flow of a thin viscous liquid down an inclined solid surface and the fingering instability that develops in the flow.

For the first project, we develop a mathematical model of liquid flow and phase change phenomena during laser-induced melting and evaporation of thin metal films deposited on glass substrates. The interaction of the laser beam with the metal film is a complicated process, characterized by high temperature gradients. We consider the regime in which a phenomenon called phase explosion takes place in a small region of the metal film surrounded by a pool of molten metal. In the melt region, both evaporation from the surface and viscous flow induced by thermocapillary stresses take place; all of these processes are incorporated into the model. Evolution of the surface of the molten film is examined, and the impact of phase explosion on the flow is discussed.

Regarding the second project, we investigate the flow of evaporating thin films of viscous liquid on inclined solid substrates under the influence of gravity. A lubrication-type approach is used to develop a three-dimensional model of the flow including physical effects such as capillarity, gravity, Marangoni stresses, disjoining pressure, and evaporation. Numerical simulations are then carried out based on the model. The effect of evaporation on the so-called fingering instability that develops along the contact line in the transverse direction of the flow is studied. It is found that evaporation acts to suppress the instability if the evaporation number, a nondimensional measure of the mass flow rate across the interface, is above a critical value. The critical value decreases as the inclination angle is decreased. For the values of evaporation number below the critical one, the fingers grow initially, but then saturate at a length which depends on the evaporation conditions. It is also shown that thermocapillarity acts to enhance the instability.