  We study the dynamics of the interface between two immiscible fluids in
contact with a chemically homogeneous moving solid plate. We consider the
generic case of two fluids with any viscosity ratio and of a plate moving in
either directions (pulled or pushed in the bath). The problem is studied by a
combination of two models, namely an extension to finite viscosity ratio of the
lubrication theory and a Lattice Boltzmann method. Both methods allow to
resolve, in different ways, the viscous singularity at the triple contact
between the two fluids and the wall. We find a good agreement between the two
models particularly for small capillary numbers. When the solid plate moves
fast enough, the entrainment of one fluid into the other one can occur. The
extension of the lubrication model to the case of a non-zero air viscosity, as
developed here, allows us to study the dependence of the critical capillary
number for air entrainment on the other parameters in the problem (contact
angle and viscosity ratio).
