In this work a free-energy binary liquid lattice-Boltzmann scheme is used to simulate Taylor/Bretherton flow in a micro-channel where elongated gas bubbles move through a liquid with thin liquid films between the bubbles and the channel walls. The numerical scheme has a diffuse interface, and a main focus of our work is to assess resolution requirements for correctly resolving the liquid film and bubble motion. The simulations are two-dimensional and span a capillary number range of 0.05-1.0 where the capillary number is based on the liquid dynamic viscosity, the velocity of the bubble, and the interfacial tension. The flow is driven by a body force, and periodic boundary conditions apply in the streamwise direction. We obtain grid independent results as long as the liquid film thickness is at least twice the width of the diffuse interface, with film thicknesses in accordance to literature results. We also show that the results in terms of film thicknesses are largely insensitive to the liquid-gas viscosity ratio and wettability parameters. (C) 2011 Elsevier B.V. All rights reserved.