Microscopic calculation of the sticking force for nanodrops on an inclined surface

A two-dimensional nanodrop on a vertical rough solid surface is examined using a nonlocal density functional theory in the presence of gravity. The roughness is modeled either as a chemical inhomogeneity of the solid or as a result of the decoration with pillars of a smooth homogeneous surface. From the obtained fluid density distribution, the sticking force, which opposes the drop motion along an inclined surface, and the contact angles on the lower and upper leading edges of the drop are calculated. On the basis of these results, it is shown that the macroscopically derived equation for a drop in equilibrium on an inclined surface is also applicable to nanodrops. The liquid-vapor surface tension involved in this equation was calculated for various specific cases, and the values obtained are of the same order of magnitude as those obtained in macroscopic experiments.