  This paper investigates a variational approach to viscous flows with contact
line dynamics based on energy-dissipation modeling. The corresponding model is
reduced to a thin-film equation and its variational structure is also
constructed and discussed. Feasibility of this modeling approach is shown by
constructing a numerical scheme in 1D and by computing numerical solutions for
the problem of gravity driven droplets. Some implications of the contact line
model are highlighted in this setting.
