Nucleation stage in supersaturated vapor with inhomogeneities due to nonstationary diffusion onto growing droplets

An analytical description of the nucleation stage in a supersaturated vapor with instantly created supersaturation is given with taking into account the vapor concentration inhomogeneities arising as a result of depletion due to nonstationary diffusion onto growing droplets. This description is based on the fact, that the intensity of the nucleation of new droplets is suppressed in spherical diffusion regions of a certain size surrounding previously nucleated droplets, and remains at the initial level in the remaining volume of the vapor–gas medium. The value of the excluded volume (excluded from nucleation) depends on the explicit form of the vapor concentration profile in the space around the growing droplet, and we use for that the unsteady self-similar solution of the time-dependent diffusion equation with a convective term describing the flow of the gas–vapor mixture caused by the moving surface of the single growing droplet. The main characteristics of the phase transition at the end of the nucleation stage are found and compared with those in the theory of nucleation with homogeneous vapor consumption (the theory of mean-field vapor supersaturation). It is shown that applicability of the mean-field approach depends on smallness of the square root of the ratio of the densities of metastable and stable phases. With increasing the temperature of the supersaturated vapor or for liquid or solid solutions, this smallness weakens, and then it would be more correct to use the excluded volume approach.