Instability of thermocapillary–buoyancy convection in droplet migration

Abstract

The instabilities of thermocapillary–buoyancy convection in droplet migration are examined by linear stability analysis. The droplet is flattened by gravity and placed on a unidirectional heated solid surface. The velocity and temperature distributions of basic flow are derived as a function of the migration velocity and the Bond number. The critical Marangoni number is obtained, which depends on the Prandtl number (Pr), the Bond number, and the migration velocity. The preferred modes at small and moderate Pr are oblique waves, which travel either upstream or downstream. For high Pr, the preferred modes include oblique and streamwise waves, while the amplitude of temperature on the surface is much smaller than that of the hot spot in the flow region. The instability mechanism is discussed and comparisons are made with liquid layers.