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We study the forced displacement of a fluid-fluid interface in athree-dimensional channel formed by two parallel solid plates. Using aLattice-Boltzmann method, we study situations in which a slip velocity arisesfrom diffusion effects near the contact line. The difference between the slipand channel velocities determines whether the interface advances as a meniscusor a thin film of fluid is left adhered to the plates. We find that this effectis controlled by the capillary and Peclet numbers. We estimate the crossoverfrom 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 theoccupation fraction of the advancing finger relative to the channel thicknessis controlled by the capillary number and the viscosity contrast between thefluids. For high viscosity contrast, Lattice-Boltzmann results agree withprevious results. For zero viscosity contrast, we observe remarkably narrowfingers. The shape of the finger is found to be universal.

Three-dimensional aspects of fluid flows in channels. I. Meniscus and Thin Film regimes