First integrals of equations of motion of a droplet in the presence of mass transfer to the carrier medium

Analysis is performed of first integrals in the limiting Stokes and Newtonian modes of motion of a droplet for two cases, namely, that of the droplet moving in its own vapor in the presence of phase transitions and that of the droplet moving in dusty gas without phase transformations but in view of the capture of dust particles. Expressions are found for the lengths over which the processes of condensation, complete evaporation of droplet, and deposition of particles occur. Comparison is made of the lengths and times of complete evaporation of droplet in the Stokes and Newtonian modes of droplet motion. Asymptotic formulas are obtained for these quantities, which correspond to low and high superheating of vapor, as well as formulas for the limiting diameters of droplet in the cases of condensation of vapor or capture of particles.