  We study the adsorption of a fluid in the grand canonical ensemble occurring
at a planar heterogeneous wall which is decorated with a chemical stripe of
width $L$. We suppose that the material of the stripe strongly preferentially
adsorbs the liquid in contrast to the outer material which is only partially
wet. This competition leads to the nucleation of a droplet of liquid on the
stripe, the height $h_m$ and shape of which (at bulk two-phase coexistence) has
been predicted previously using mesoscopic interfacial Hamiltonian theory. We
test these predictions using a microscopic Fundamental Measure Density
Functional Theory which incorporates short-ranged fluid-fluid and fully
long-ranged wall-fluid interactions. Our model functional accurately describes
packing effects not captured by the interfacial Hamiltonian but still we show
that there is excellent agreement with the predictions $h_m\approx L^{1/2}$ and
for the scaled circular shape of the drop even for $L$ as small as $50$
molecular diameters. For smaller stripes the droplet height is considerably
lower than that predicted by the mesoscopic interfacial theory. Phase
transitions for droplet configurations occurring on substrates with multiple
stripes are also discussed.
