Self-similar theory of nonisothermal vapor condensation on a droplet growing in a vapor-gas medium

Rigorous self-similar solutions to the joint problems of vapor diffusion toward a droplet growing in a vapor-gas medium and the removal of heat released during vapor condensation are found. An equation for the temperature of a droplet ensuring the existence of a self-similar solution is derived. This equation sets the constancy of the temperature of a droplet throughout the time of its growth and unambiguously determines this temperature. In the case of the strong heat effects, when the rate of droplet growth decreases substantially, the analytical solution to this equation is obtained. This temperature coincides precisely with the temperature, which is established in the droplet at the diffusion regime of its growth. At the found droplet temperature, interconnected fields of vapor concentration and temperature of vapor-gas medium around the droplet are expressed through the initial (prior to the droplet nucleation) parameters of a vapor-gas medium. These parameters are used to express the dependence of the radius of a droplet on the time at the diffusion regime of its growth and the time required to establish the diffusion regime of droplet growth. The case of weak heat effects is also studied.