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

TL;DR

This paper provides an analytical model of the nucleation stage in supersaturated vapor, accounting for inhomogeneities caused by non-stationary diffusion onto growing droplets, revealing suppression effects in nucleation regions.

Contribution

It introduces a new analytical description that incorporates vapor concentration inhomogeneities due to non-stationary diffusion, extending nucleation theory beyond homogeneous assumptions.

Findings

Nucleation is suppressed in spherical diffusion regions around droplets.

The size of exclusion zones depends on vapor concentration profiles.

Comparison shows differences from mean-field vapor supersaturation theory.

Abstract

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).