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Heterogeneous nucleation is studied by Monte Carlo simulations andphenomenological theory, using the two-dimensional lattice gas model withsuitable boundary fields. A chemical inhomogeneity of length b at one boundaryfavors the liquid phase, while elsewhere the vapor is favored. Switching on thebulk field favoring the liquid, nucleation and growth of the liquid phasestarting from the region of the chemical inhomogeneity is analyzed. Threeregimes occur: for small fields, the critical droplet radius is so large that acritical droplet having the contact angle required by Young's equation in theregion of the chemical inhomogeneity does not yet fit there, since the baselinelength of the circle-cut sphere droplet would exceed b. For an intermediumregime of bulk fields, such droplets fit inside the inhomogeneity, and areindeed found in simulations with large enough observation times, but thesedroplets remain pinned to the chemical inhomogeneity when their baseline hasgrown to the length b. On general grounds one can predict that the effectivecontact angle as well as the excess density of the droplets, scaled by b^2, arefunctions of the product b and the bulk field, but do not depend on bothvariables separately. For larger fields the droplets nucleated at the chemicalinhomogeneity grow to the full system size.

Heterogeneous Nucleation of a Droplet Pinned at a Chemically Inhomogeneous Substrate: A Simulation Study of the Two-dimensional Ising Case