  We consider a nano-patterned planar wall consisting of a periodic array of
stripes of width $L$, which are completely wet by liquid (contact angle
$\theta=0$), separated by regions of width $D$ which are completely dry
(contact angle $\theta=\pi)$. Using microscopic Density Functional Theory we
show that in the presence of long-ranged dispersion forces, the wall-gas
interface undergoes a first-order wetting transition, at bulk coexistence, as
the separation $D$ is reduced to a value $D_w\propto\ln L$, induced by the
bridging between neighboring liquid droplets. Associated with this is a line of
pre-wetting transitions occurring off coexistence. By varying the stripe width
$L$ we show that the pre-wetting line shows universal scaling behaviour and
data collapse. This verifies predictions based on mesoscopic models for the
scaling properties associated with finite-size effects at complete wetting
including the logarithmic singular contribution to the surface free-energy.

Statistical Mechanics;Soft Condensed Matter