  We study the forced displacement of a fluid-fluid interface in a
three-dimensional channel formed by two parallel solid plates. Using a
Lattice-Boltzmann method, we study situations in which a slip velocity arises
from diffusion effects near the contact line. The difference between the slip
and channel velocities determines whether the interface advances as a meniscus
or a thin film of fluid is left adhered to the plates. We find that this effect
is controlled by the capillary and Peclet numbers. We estimate the crossover
from a meniscus to a thin film and find good agreement with numerical results.
The penetration regime is examined in the steady state. We find that the
occupation fraction of the advancing finger relative to the channel thickness
is controlled by the capillary number and the viscosity contrast between the
fluids. For high viscosity contrast, Lattice-Boltzmann results agree with
previous results. For zero viscosity contrast, we observe remarkably narrow
fingers. The shape of the finger is found to be universal.
