Here, ν stands for the three possible magnitudes of the c$_{i}$ set. Coefficient values are ω$_{0}$ = 2 / 9 , ω$_{1}$ = 1 / 9 and ω √$_{3}$ = 1 / 72; A f 0 = 9 / 2 − 7 / 2Tr P , A f 1 = A f √$_{3}$ = 1 /ρ Tr P and G f = 9 / (2 ρ ) P − 3 δ Tr P ; A g 0 = 9 / 2 − 21 / 2 ˆ Mµ, A g 1 = A g √$_{3}$ = 3 ˆ Mµ/ρ and G g = 9 / (2 ρ ) ˆ Mµ ( 1 − δ ) , where 1 is the unit matrix. It can be shown that equations (8) and (9) converge to the hydrodynamic equations (1), (2), and (3) by performing a Chapman-Enskog expansion. This procedure has been carried out elsewhere [31]. Boundary conditions in the lattice-Boltzmann scheme are implemented by fixing the distribution functions at the boundaries. To implement stick and no flow conditions at the solid, bounce back rules are implemented at the solid nodes [30]. Periodic boundary conditions are obtained as usual, e.g. , for the f$_{i}$ at y = W , f$_{i}$ ( x, y = W, z ) = f$_{i}$ ( x, y = 0 , z ) . Shear free and vanishing concentration gradient conditions are obtained in a similar way. The Cahn wetting boundary condition given by equation (5), is obtained by extrapolating the order parameter to the wall nodes in order to fix a prescribed gradient in the normal direction to the wall [28]. Throughout this paper, the diffuse interface model parameters are fixed to the following values (in lattice units): ρ = 1, 〈 η 〉 = 0 . 1, δη = 0 . 9, γ = 0 . 0023, ξ = 0 . 57, and M = 16. These values generally ensure numerical stability in the simulations. The interface thickness, ξ = 0 . 57, has been tested previously and proved not to give rise to important lattice artifacts [32, 33]. We will consider two equilibrium contact angles, θ$_{e}$ = 0 ◦ , and θ$_{e}$ = 90 ◦ , which correspond to C = 0 . 00167 and C = 0 respectively. A suitable value for the film thickness, which is small enough to keep reasonable computational costs and large enough to ensure the relaxation to the volume values of the order parameter needed for proper hydrodynamic resolution, is h$_{c}$ = 8. The mean velocity of the film is fixed to U = 0 . 005 by choosing the gravitational acceleration as g$_{x}$ = 3 η$_{+1}$U/ ( ρh 2 $_{c}$). Using these values, the capillary number is Ca = 0 . 41. The intrinsic time and lengthscales in forced thin films are set by the film growth rate, ˙ L ( θ$_{e}$ ), and by the most unstable wavelength of the linked to the contact line instability, Λ$_{max}$( θ$_{e}$ ), which depend on the wetting properties of the substrate, determined by the equi- III. HOMOGENEOUS SUBSTRATES 13