Theoretical analysis of Marangoni instability of an evaporating droplet by energy method

Evaporation of a droplet is a process of heat and mass transports. When the droplet evaporates, heat is removed from the surface and the surface temperature is reduced thereby, resulting in a temperature gradient normal to the free surface. Such a situation is similar to that with a liquid layer heated from below. Thus, Marangoni instability as described by Pearson [J. Fluid Mech. 4 (1958) 489] may probably exist in an evaporating droplet, which is a very important and interesting phenomenon both from the academic and application points of view. In the present work, the energy method, which is appropriate for unsteady flows, is applied to investigate the stability of an evaporating droplet against disturbances of any amplitude.