Bubble and droplet motion in binary mixtures: Evaporation-condensation mechanism and Marangoni effect

Bubble and droplet motion in binary mixtures is studied in weak heat and diffusion fluxes and in gravity by solving the linearized hydrodynamic equations supplemented with appropriate surface boundary conditions. Without gravity, the velocity field is induced by evaporation and condensation at the interface and by the Marangoni effect due to a surface tension gradient. In pure fluids, the latter nearly vanishes since the interface temperature tends to the coexistence temperature $T_{\rm cx}(p)$ even in heat flow. In binary mixtures, the velocity field can be much enhanced by the Marangoni effect above a crossover concentration $c^*$ inversely proportional to the radius $R$ of the bubble or droplet. Here $c^*$ is usually very small for large $R$ for non-azeotropic mixtures. The temperature and concentration deviations are also calculated.