Stability of fluid films of nanoscale thickness involving contact lines*

We discuss instabilities of fluid films of nanoscale thickness, with a particular focus on films where the destabilizing mechanism allows for linear instability, metastability, and absolute stability.  Our study is motivated by nematic liquid crystal films; however similar instability mechanisms, appear in other contexts, such as the well- studied problem of polymeric films on two-layered substrates.  Within the  long wave formulation, the nematic character of the film leads to an additional contribution to the disjoining pressure, changing its functional form. This effective disjoining pressure is characterized by the presence of a local maximum.
Such a form leads to complicated instability evolution that we study by analytical means, including the application of topological measures, and by extensive numerical simulations.  These simulations, carried out on GPUs, allow for considering large domains so that instability development is not influenced by the domain boundaries.  This combination of analytical and computational techniques allows us to reach novel understanding of relevant instability 
mechanisms, and of their influence on transient and fully developed fluid film morphologies.