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We study the adsorption of a fluid in the grand canonical ensemble occurringat a planar heterogeneous wall which is decorated with a chemical stripe ofwidth $L$. We suppose that the material of the stripe strongly preferentiallyadsorbs the liquid in contrast to the outer material which is only partiallywet. This competition leads to the nucleation of a droplet of liquid on thestripe, the height $h_m$ and shape of which (at bulk two-phase coexistence) hasbeen predicted previously using mesoscopic interfacial Hamiltonian theory. Wetest these predictions using a microscopic Fundamental Measure DensityFunctional Theory which incorporates short-ranged fluid-fluid and fullylong-ranged wall-fluid interactions. Our model functional accurately describespacking effects not captured by the interfacial Hamiltonian but still we showthat there is excellent agreement with the predictions $h_m\approx L^{1/2}$ andfor the scaled circular shape of the drop even for $L$ as small as $50$molecular diameters. For smaller stripes the droplet height is considerablylower than that predicted by the mesoscopic interfacial theory. Phasetransitions for droplet configurations occurring on substrates with multiplestripes are also discussed.

Scaling behaviour of thin films on chemically heterogenous walls