Asymptotic thermal modeling of droplet assembly in nanoscale molten metal films

We consider a thin metal film on a thermally conductive substrate exposed to an external heat source in a setup where the heat absorption depends on the local film thickness. Our focus is on modeling film evolution while the film is molten. The film geometry modifies local heat flow, which in turn may influence the film surface evolution through thermal variation of material properties. We use asymptotic analysis to develop a thermal model that is accurate, computationally efficient, and that accounts for the heat flow in both the in-plane and out-of-plane directions. We apply this model to describe metal films of nanoscale thickness exposed to heating and melting by laser pulses, a setup commonly used for self and directed assembly of various metal geometries via dewetting while the films are in the liquid phase. We find that thermal effects play an important role, and in particular that the inclusion of temperature dependence in the metal viscosity modifies the time scale of the evolution significantly. The thickness, thermal conductivity, and rate of heat loss of the underlying substrate are shown to be crucial in accurately modeling film temperatures and subsequent phase changes in the film. Since in many cases the substrate cools the film, modifications to the substrate temperature may induce different dewetting speeds via temperature dependent viscosity of the film. We show via 3D GPU simulations that this may result in various frozen film patterns since full dewetting may not occur while the film is in the liquid phase. This research was supported by NSF CBET-1604351, NSF-DMS-1815613 and by CNMS2020-A-00110.