The stage of nucleation of supercritical droplets with thermal effects in the regime of nonstationary diffusion and heat transfer

Abstract

Abstract Previously the stage of nucleation of supercritical droplets in the vapor–gas medium at instantaneously generated vapor supersaturation had been described within the mean-field, excluded-volume and stochastic probability (nearest neighbor) approaches which are based on different physical assumptions. Here we have formulated an extended excluded-volume theory which reconciles these approaches. The theory takes into account the drop of the nucleation rate in vicinities of growing supercritical droplets and mean-field mixing of vapor concentration and temperature at outer boundaries of the nonstationary diffusion shells around the droplets due to stochastic overlapping of the shells. The theory gives the distribution of supercritical droplets in sizes and predicts the vapor concentration profiles at any moment of the nucleation stage as well as duration of the nucleation stage, the total number of nucleating supercritical droplets and the mean droplet size to the end of nucleation stage. These characteristics are compared with the estimates obtained within the stochastic probability (nearest neighbor) approach. A generalization of the isothermal excluded-volume theory with the overlapping diffusion shells has been done to include the thermal effects of nonisothermal nucleation and the nonstationary transfer of heat in the vapor–gas medium. It has been shown that the mean-field and excluded-volume approaches lead to identical results in the limit of small nonstationarity of vapor diffusion and thermal conductivity.