This paper deals with numerical simulations of some capillary-driven flows. The focus is on the wetting phenomenon in sintering-like flows and in the imbibition of liquids into a porous medium. The wetting phenomenon is modeled using the coupled Cahn-Hilliard/Navier-Stokes system. The Cahn-Hilliard equation is treated as a system where the chemical potential is solved first followed by the composition. The equations are discretised in space using piecewise linear functions. Adaptive finite element method is implemented with an ad hoc error criterion that ensures mesh resolution along the vicinity of the interface. In the 3D case we use parallel adaptive finite element method. First, a basic wetting of a liquid drop on a solid surface is shown and is established the independence of the dynamic contact angle on the interface width. In addition, the dependence of the dynamic contact angle on the Capillary number is matched with experimental data. Next, some generic sintering-like flows with a fixed matrix is presented. Different geometries in 2D and 3D are considered. We observed rapid wetting, precursor films, coalescence, breakup of melt drops as well as pore migration and elimination that are all microstructural characteristics of a liquid phase sintering. Finally, the effect of equilibrium contact angles on imbibition of liquid into a porous medium is studied. (c) 2006 Elsevier Ltd. All rights reserved.