Dissipative Processes in Thin Film Flows

The study of thin film flows leads to the development of reduced hydrodynamic models derived from a Navier-Stokes free boundary problem. The key dissipation processes contributing to these models include viscous dissipation, Navier-slip, and contact line dissipation. In this talk, we first present a general approach to reformulating the metric of dissipative processes using saddle point structures. We then discuss the corresponding discretization of these free boundary problems that are based on a gradient flow structure. The impact of varying the scaling of the Navier-slip length on pattern formation in three-dimensional flows will be showcased. Finally, we explore the existence of a similar discussion and a hierarchy of models for different orders of contact line dissipation.