Variational approach to dynamic contact angles for thin films

This paper investigates a modeling approach for viscous flows with dynamic contact angles based on variational energy-dissipation principles. A corresponding Stokes free boundary problem is reduced to a thin-film equation and its variational structure is constructed. The usefulness of this abstract modeling approach is demonstrated by providing numerical schemes for the Stokes flow and the thin-film model and by computing numerical solutions for the problem of gravity-driven thin droplets. Some implications of the contact angle model and properties of the numerical scheme are highlighted in this setting.