  We study adsorption at periodically corrugated substrates formed by scoring
rectangular grooves into a planar solid wall which interacts with the fluid via
long-range (dispersion) forces. The grooves are assumed to be macroscopically
long but their depth, width and separations can all be molecularly small. We
show that the entire adsorption process can be divided into three parts
consisting of (i) \emph{filling} the grooves by a capillary liquid; (ii)
\emph{depinning} of the liquid-gas interface from the wall edges; and (iii)
\emph{unbinding} of the interface from the top of the wall, which is
accompanied by a rapid but continuous flattening of its shape. Using a nonlocal
density functional theory and mesoscopic interfacial models all the regimes are
discussed in some detail to reveal the complexity of the entire process and
subtle aspects that affect its behaviour. In particular, it is shown that the
nature of the depinning phenomenon is governed by the width of the wall pillars
(separating grooves), whilst the grooves width only controls the location of
the depinning first-order transition, if present.
