Wetting at curved substrates: Non-analytic behavior of interfacial properties

We argue that for complete wetting at a curved substrate (wall) the wall-fluid surface tension is non-analytic in $R_{\ab{i}}^{-1}$, the curvature of the wall, and that the density profile of the fluid near the wall acquires a contribution proportional to the gas-liquid surface tension $\times R_{\ab{i}}^{-1}$ plus higher-order contributions which are non-analytic in $R_{\ab{i}}^{-1}$. These predictions are confirmed by results of density functional calculations for the square-well model of a liquid adsorbed on a hard sphere and on a hard cylinder where complete wetting by gas (drying) occurs. The implications of our results for the solvation of big solvophobic particles are discussed.