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In this paper, thermocapillary migration of a planar droplet at moderate andlarge Marangoni numbers is investigated analytically and numerically. By usingthe dimension-analysis method, the thermal diffusion time scale is determinedas the controlling one of the thermocapillary droplet migration system. Duringthis time, the whole thermocapillary migration process is fully developed. Byusing the front-tracking method, the steady/unsteady states as the terminalones at moderate/large Marangoni numbers are captured in a longer time scalethan the thermal diffusion time scale. In the terminal states, theinstantaneous velocity fields in the unsteady migration process at largeMarangoni numbers have the forms of the steady ones at moderate Marangoninumbers. However, in view of the former instantaneous temperature fields, thesurface tension of the top surface of the droplet gradually becomes the maincomponent of the driving force on the droplet after the inflection pointappears. It is different from that the surface tension of the bottom surface ofthe droplet is the main component of the driving force on the droplet for thelatter ones. The physical mechanism of thermocapillary droplet migration can bedescribed as the significance of the thermal convection around the droplet ishigher than/just as the thermal conduction across the droplet at large/moderateMarangoni numbers.

Terminal states of thermocapillary migration of a planar droplet at moderate and large Marangoni numbers