Diffusion of Vapor in the Presence of a Growing Droplet

Abstract

As is shown, the solution to the diffusion equation for the concentration of vapor in the presence of a droplet growing in it, derived for the usual initial condition and equilibrium boundary conditions at the droplet surface, fails to ensure an equality between the numbers of molecules that have left the vapor due to diffusion by the current moment and those that have been included in the growing droplet. The difference between the total numbers of vapor molecules at the initial moment (when the vapor had a given uniform concentration) and at the current moment (when the size of the growing droplet is much larger than its initial size) differs from the total number of molecules in the droplet by a factor of 3/2. By substituting the usual boundary condition at the droplet surface by a time-dependent boundary condition at the surface of a constant-radius sphere with the center in the center of the growing droplet, a solution to the diffusion problem for the vapor concentration is derived. This solution describes the evolution of the vapor concentration field, which agrees with the rate of the vapor absorption by the growing droplet and with the law of the conservation of matter.