The onset of stationary Marangoni instability of an evaporating droplet

Evaporation at the surface of a liquid is an unsteady process involving heat and mass transport. The process of evaporation also leads to a local reduction in the temperature of the bulk liquid near the surface. Marangoni instability may then be induced by such a surface temperature reduction and the consequent variation in surface tension. The purpose of this study is to investigate theoretically the onset and physical mechanisms of Marangoni instability of an evaporating droplet. With the quasi-steady approximation, which means that the size change of the droplet is negligible, the surrounding gas motion is asymptotically steady and the temperature distribution of the droplet is temporarily frozen at each specified instant of interest, a lower limit of the onset condition for Marangoni instability is derived analytically through linear stability analysis. The following results are obtained from the analysis. As time proceeds, the temperature reduction and thermal boundary layer thickness near the free surface become larger and the droplet becomes more unstable. The critical wavenumber of small disturbances for the onset of Marangoni instability increases with the droplet initial temperature. The onset condition is a strong function of the droplet initial temperature with which the critical Marangoni number increases.