Geometry-induced interface pinning at completely wet walls

We study complete wetting of solid walls that are patterned by parallel nanogrooves of depth $D$ and width $L$ with a periodicity of $2L$. The wall is formed of a material which interacts with the fluid via a long-range potential and exhibits first-order wetting transition at temperature $T_w$, should the wall is planar. Using a non-local density functional theory we show that at a fixed temperature $T>T_w$ the process of complete wetting depends sensitively on two microscopic length-scales $L_c^+$ and $L_c^-$. If the corrugation parameter $L$ is greater than $L_c^+$, the process is continuous similar to complete wetting on a planar wall. For $L_c^-<L<L_c^+$, the complete wetting exhibits first-order \emph{depinning transition} corresponding to an abrupt unbinding of the liquid-gas interface from the wall. Finally, for $L<L_c^-$ the interface remains pinned at the wall even at bulk liquid-gas coexistence. This implies that nano-modification of substrate surfaces can always change their wetting character from hydrophilic into hydrophobic, in direct contrast to the macroscopic Wenzel law. The resulting surface phase diagram reveals close analogy between the depinning and prewetting transitions including the nature of their critical points.