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The surface of a liquid near a moving contact line is highly curved owing todiverging viscous forces. Thus, microscopic physics must be invoked at thecontact line and matched to the hydrodynamic solution farther away. Thismatching has already been done for a variety of models, but always assuming thelimit of vanishing speed. This excludes phenomena of the greatest currentinterest, in particular the stability of contact lines. Here we extendperturbation theory to arbitrary order and compute finite speed corrections toexisting results. We also investigate the impact of the microscopic physics onthe large-scale shape of the interface

Toward a description of contact line motion at higher capillary numbers