Liquid films on a substrate can become unstable due to various effects that exist in many engineering processes. These include gravity, temperature gradients, and interfacial effects. Through many analytical and experimental studies, the initial development of the instabilities has been well understood. The main objective of the proposed research is to examine the flow behavior beyond the initial instabilities. To achieve this goal the conventional weakly-nonlinear analysis, such as the dynamical-system approach will be extended, and a finite-element method introduced. The secondary and, for the first time, the fully-nonlinear behavior of three-dimensional films through a careful interplay of nonlinear analysis and full-scale computation will be investigated. In particular, focus will be placed on the wave-breaking of isothermal films and the rupture of heated films. The new information on these critical flow behaviors obtained through the proposed research will provide substantial contributions to the development of modern materials-processing technology. The vectorized numerical code developed will solve the coupled hydrodynamic, thermal, and mass-transfer system with free boundaries, and will serve as a platform for further generation to non-Newtonian materials processing with phase changes.
