  We present a systematic study of capillary filling for a binary fluid by
using a mesoscopic lattice Boltzmann model for immiscible fluids describing a
diffusive interface moving at a given contact angle with respect to the walls.
The phenomenological way to impose a given contact angle is analysed.
Particular attention is given to the case of complete wetting, that is contact
angle equal to zero. Numerical results yield quantitative agreement with the
theoretical Washburn law, provided that the correct ratio of the dynamic
viscosities between the two fluids is used. Finally, the presence of precursor
films is experienced and it is shown that these films advance in time with a
square-root law but with a different prefactor with respect to the bulk
interface.
