Study of Marangoni instability of an evaporating liquid layer

Abstract The onset of Marangoni instability of an evaporating liquid layer is studied theoretically. By assuming the surface regression of the liquid layer is negligibly small and the surrounding gas phase is asymptotically steady, similarity solutions are obtained prior to the onset of instability. Linear stability analysis is then applied to obtain the critical Marangoni number for the onset of instability. The results indicate that : (1) The onset condition is a strong function of the initial temperature of the liquid layer with which the critical Marangoni number decreases. (2) As time proceeds, the thermal boundary layer thickness near the free surface becomes larger, and the liquid layer becomes more unstable. (3) For a liquid layer with a higher initial temperature (closer to the boiling point) the most unstable mode of the disturbance shifts from a lower wave number to a higher wave number.