  Various experiments have found a boundary slip in hydrophobic microchannel
flows, but a consistent understanding of the results is still lacking. While
Molecular Dynamics (MD) simulations cannot reach the low shear rates and large
system sizes of the experiments, it is often impossible to resolve the needed
details with macroscopic approaches. We model the interaction between
hydrophobic channel walls and a fluid by means of a multi-phase lattice
Boltzmann model. Our mesoscopic approach overcomes the limitations of MD
simulations and can reach the small flow velocities of known experiments. We
reproduce results from experiments at small Knudsen numbers and other
simulations, namely an increase of slip with increasing liquid-solid
interactions, the slip being independent of the flow velocity, and a decreasing
slip with increasing bulk pressure. Within our model we develop a semi-analytic
approximation of the dependence of the slip on the pressure.
