Including thermal effects in computing dynamics of thin films on thermally conductive substrates

Thin film dynamics, particularly on nanoscale, is a topic of extensive interest. The process by which thin liquids evolve is far from trivial and can lead to dewetting and drop formation. Not only does it involve resolving fluid mechanical aspects of the problem, but also requires the coupling of other physical processes, including liquid-solid interactions and heat transfer. In this talk, we focus on multiscale aspects of the problem. Separation of length scales (in-plane length scales are larger than those in the out-of-plane direction) allows for formulation of asymptotic theory that reduces the complicated problem of Navier-Stokes equations in evolving domains to a fourth-order nonlinear partial differential equation for fluid thickness. To include thermal effects, in the form of surface tension gradients, the local temperature profile must be calculated on a temporally evolving domain, presenting numerical challenges. In this talk, we present a thermal transport model, based on asymptotic theory, which reduces the computational complexity and produces consistent results with that of a full heat conduction model.