  Heterogeneous nucleation is studied by Monte Carlo simulations and
phenomenological theory, using the two-dimensional lattice gas model with
suitable boundary fields. A chemical inhomogeneity of length b at one boundary
favors the liquid phase, while elsewhere the vapor is favored. Switching on the
bulk field favoring the liquid, nucleation and growth of the liquid phase
starting from the region of the chemical inhomogeneity is analyzed. Three
regimes occur: for small fields, the critical droplet radius is so large that a
critical droplet having the contact angle required by Young's equation in the
region of the chemical inhomogeneity does not yet fit there, since the baseline
length of the circle-cut sphere droplet would exceed b. For an intermedium
regime of bulk fields, such droplets fit inside the inhomogeneity, and are
indeed found in simulations with large enough observation times, but these
droplets remain pinned to the chemical inhomogeneity when their baseline has
grown to the length b. On general grounds one can predict that the effective
contact angle as well as the excess density of the droplets, scaled by b^2, are
functions of the product b and the bulk field, but do not depend on both
variables separately. For larger fields the droplets nucleated at the chemical
inhomogeneity grow to the full system size.
