The phenomenon of apparent slip in micro-channel flows is analyzed by means of a two-phase mesoscopic lattice Boltzmann model with non-ideal fluid-fluid and fluid-wall interactions. Analytical solutions of the weakly inhomogeneous hydrodynamic limit of this model are successfully compared with numerical simulations and show that the present mesoscopic approach is capable of filling the gap between the atomistic size of the interaction potential and the millimetric size of the slip length reported in microflow experiments. In the critical interplay between fluid-fluid and fluid-wall interactions, our approach indicates an exponential inflation of the slip length as a function of the ratio of potential to thermal energy. (c) 2006 IMACS. Published by Elsevier B.V. All rights reserved.