Density functional theory is used to analyze the stability and structural properties of droplets formed by the condensation of a volatile solvent on a soluble fluid particle composed of a fixed number of molecules of a second species with extremely low volatility. Interaction parameters between the species are chosen to ensure that the soluble particle is completely wetted by the solvent. We study the properties of miscible and partially miscible mixtures. Droplets with a partially soluble core may exhibit a solubility transition at a vapor pressure above the vapor pressure of the bulk saturated solution. This transition resembles deliquescence in water soluble salts, but exhibits distinctive features. The soluble particle dissolves spontaneously at a well defined value of the supersaturation and the relative change in the droplet's size at the transition is greater for the smaller particles. Comparisons of our results with the predictions of Kohler theory of activation show that the capillarity approximation overestimates the vapor pressure of the droplets, particularly in small systems. (C) 2003 American Institute of Physics.