Drops on an arbitrarily wetting substrate: a phase field description.

We propose a scheme for studying thin liquid films on a solid substrate using a phase field model. For a van der Waals fluid-far from criticality-the most natural phase field function is the fluid density. The theoretical description is based on the Navier-Stokes equation with extra phase field terms and the continuity equation. In this model free of interface conditions, the contact angle can be controlled through the boundary conditions for the density field at the solid walls [L. M. Pismen and Y. Pomeav, Phys. Rev. E 62, 2480 (2000)]. We investigate the stability of a thin liquid film on a flat homogeneous solid support with variable wettability. For almost hydrophobic surfaces, the liquid film breaks up and transitions from a flat film to drops occur. Finally, we report on two-dimensional numerical simulations for static liquid drops resting on a flat horizontal solid support and for drops sliding down on inclined substrates under gravity effects.