Toward a description of contact line motion at higher capillary numbers

The surface of a liquid near a moving contact line is highly curved owing to diverging viscous forces. Thus, microscopic physics must be invoked at the contact line and matched to the hydrodynamic solution farther away. This matching has already been done for a variety of models, but always assuming the limit of vanishing speed. This excludes phenomena of the greatest current interest, in particular the stability of contact lines. Here we extend perturbation theory to arbitrary order and compute finite speed corrections to existing results. We also investigate the impact of different contact line models on the large-scale shape of the interface.