  he contact angle of a liquid droplet on a surface under partial wetting
conditions differs for a nanoscopically rough or periodically corrugated
surface from its value for a perfectly flat surface. Wenzel's relation
attributes this difference simply to the geometric magnification of the surface
area (by a factor $r_{\rm w}$), but the validity of this idea is controversial.
We elucidate this problem by model calculations for a sinusoidal corrugation of
the form $z_{\rm wall}(y) = \Delta\cos(2\pi y/\lambda)$ , for a potential of
short range $\sigma_{\rm w}$ acting from the wall on the fluid particles. When
the vapor phase is an ideal gas, the change of the wall-vapor surface tension
can be computed exactly, and corrections to Wenzel's equation are typically of
order $\sigma_{\rm w}\Delta/\lambda^2$. For fixed $r_{\rm w}$ and fixed
$\sigma_{\rm w}$ the approach to Wenzel's result with increasing $\lambda$ may
be nonmonotonic and this limit often is only reached for $\lambda/\sigma_{\rm
w}>30$. For a non-additive binary mixture, density functional theory is used to
work out the density profiles of both coexisting phases both for planar and
corrugated walls, as well as the corresponding surface tensions. Again,
deviations from Wenzel's results of similar magnitude as in the above ideal gas
case are predicted. Finally, a crudely simplified description based on the
interface Hamiltonian concept is used to interpret corresponding simulation
results along similar lines. Wenzel's approach is found to generally hold when
$\lambda/\sigma_{\rm w}\gg 1$, $\Delta/\lambda<1$, and conditions avoiding
proximity of wetting or filling transitions.
