  An analytical description of 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
non-stationary diffusion onto growing droplets. This description suggests 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 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
time-dependent diffusion equation with a convective term describing the flow of
the gas-vapor mixture caused by moving surface of 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).
