  We use a lattice Boltzmann algorithm for liquid-gas coexistence to
investigate the steady state interface profile of a droplet held between two
shearing walls. The algorithm solves the hydrodynamic equations of motion for
the system. Partial wetting at the walls is implemented to agree with Cahn
theory. This allows us to investigate the processes which lead to the motion of
the three-phase contact line. We confirm that the profiles are a function of
the capillary number and a finite size analysis shows the emergence of a
dynamic contact angle, which can be defined in a region where the interfacial
curvature tends to zero.
