The Stefan outflow in a multicomponent vapor-gas atmosphere around a   droplet and its role for cloud expansion
  A new comprehensive analysis of Stefan's flow caused by a free growing droplet in vapor-gas atmosphere with several condensing components is presented. This analysis, based on the nonstationary heat and material balance and diffusion transport equations, shows the appearance of the Stefan inflow in the vicinity of the growing droplet and the outflow at large distances from the droplet as a consequence of nonisothermal condensation. For an ensemble of droplets in the atmospheric cloud, this flow provides an increase of the total volume of the cloud, which can be treated as cloud thermal expansion and leads to floating the cloud as a whole due to buoyancy. We have formulated the self-similar solutions of the nonstationary diffusion and heat conduction equations for a growing multicomponent droplet and have derived analytical expressions for the nonstationary velocity profile of Stefan's flow and the expansion volume of the vapor-gas mixture around the growing droplet. To illustrate the approach, we computed these quantities in the case of droplet of stationary composition in air with several specific vapors (${\mathrm{C_2H_5OH/H_2O}}$; ${\mathrm{H_2SO_4/H_2O}}$; ${\mathrm{H_2O}}$). 
A. E. Kuchma, A. K. Shchekin, and D. S. Martyukova
physics.ao-ph cond-mat.soft physics.chem-ph