A self-similar regime of droplet growth with allowance for the Stefan flux and dependence of diffusion coefficient on vapor-gas medium composition

Abstract

An analytical self-similar description is formulated for the problem of nonstationary diffusion droplet growth in a vapor-gas medium with allowance for the Stefan flux of the medium, themotion of the surface of a growing droplet, and an arbitrary concentration dependence of the diffusion coefficient of a condensing vapor in the medium. Analytical expressions are found for the diffusion profile of condensing vapor concentration and for the droplet growth rate at a constant diffusion coefficient of the vapor and at a coefficient linearly dependent on vapor concentration. The combined allowance for the Stefan flux of the medium, the motion of the surface of the growing droplet, and the dependence of the vapor diffusion coefficient in the medium on the vapor concentration is shown to result in renormalization of the rate of droplet growth related to the stationary diffusion regime. At small deviations from the stationarity, the Stefan flux, nonstationary diffusion, and dependence of the diffusion coefficient on the vapor-gas mixture composition lead to corrections of the same order of magnitude.