  We investigate the solvation of a hard spherical cavity, of radius $R$,
immersed in a fluid for which the interparticle forces are short ranged. For
thermodynamic states lying close to the liquid binodal, where the chemical
potential deviation $\delta \mu\equiv \mu - \mu_{co}(T)$ is very small and
positive, complete wetting by gas (drying) occurs and two regimes of
interfacial behavior can be identified. These are characterized by the length
scale $R_c=2 \gamma_{gl}^\infty/(\Delta \rho \delta \mu)$, where
$\gamma_{gl}^\infty$ is the planar gas-liquid surface tension and $\Delta \rho$
is the difference in coexisting densities at temperature $T$. For $R>R_c$, the
interfacial free energy and the density profile of the fluid near the hard wall
can be expanded in powers of the curvature $R^{-1}$, in keeping with the
analysis of Stillinger and Cotter, J. Chem. Phys. {\bf 55}, 3449 (1971). In the
other regime, $R<R_c$, the interfacial free energy and its derivatives acquire
terms depending on $\ln R$. Since $R_c^{-1}$ can be made arbitrarily small this
implies non-analytic behavior, as $R^{-1}\to 0$, of the work of formation of a
hard spherical cavity and of the Gibbs adsorption and the fluid density at
contact with the wall. Our analysis, which is based on an effective interfacial
Hamiltonian combined with exact statistical mechanical sum rules, is confirmed
fully by the results of microscopic density functional calculations for a
square-well fluid.
