The aim of the project if to develop a stable and accurate numerical technique based on the Lattice-Boltzmann scheme to quantitatively study the diffusion behaviour of multicomponent droplets under flow. The ability of simulating correctly the diffusive dynamics of multicomponent droplets in presence of advection is per se an challenging and fundamental issue, the final purpose of the project is to develop numerical techniques suitable for the study and understanding of the so-called surface nano-droplets. These droplets are softly pinned to a substrate and their height is of the order of nanometers. They show an extremely long lifetime whose order is set by the macroscopic size of the system and by the value of the diffusion constant. From a first theoretical approach the resulting model shows a rich variety of dynamics for their dissolution.