Lattice Boltzmann simulations of contact line motion in a liquid-gas   system
  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. 
A. J. Briant, P. Papatzacos and J. M. Yeomans