Simultaneous establishing of stationary growth rate and composition of supercritical droplets at isothermal binary condensation in the diffusion-controlled regime

Abstract

General integral relations expressing the droplet radius and time of the droplet nonstationary growth as nonlinear functions of solution concentration in the droplet have been derived. These relations are valid for a supercritical droplet (i.e., sufficiently large droplet, for which the Laplace pressure effect on the concentration at saturation of vapors is negligible) isothermally growing via stationary diffusion in the mixture of two condensing vapors and an incondensable carrier gas. The initial composition in the droplet may be arbitrary and partial molecular volumes of components are not fixed. Explicit analytical relations have been found for droplet composition and the droplet size as functions of time at small deviations from the stationary concentration in the growing droplet. These relations show that the assumption of the steady droplet growth rate is not valid for non-small deviations from the stationary concentration. Some illustrations of the general nonlinear theory have been done in situation when solution in the droplet can be considered ideal.