  In this paper, thermocapillary migration of a planar droplet at moderate and
large Marangoni numbers is investigated analytically and numerically. By using
the dimension-analysis method, the thermal diffusion time scale is determined
as the controlling one of the thermocapillary droplet migration system. During
this time, the whole thermocapillary migration process is fully developed. By
using the front-tracking method, the steady/unsteady states as the terminal
ones at moderate/large Marangoni numbers are captured in a longer time scale
than the thermal diffusion time scale. In the terminal states, the
instantaneous velocity fields in the unsteady migration process at large
Marangoni numbers have the forms of the steady ones at moderate Marangoni
numbers. However, in view of the former instantaneous temperature fields, the
surface tension of the top surface of the droplet gradually becomes the main
component of the driving force on the droplet after the inflection point
appears. It is different from that the surface tension of the bottom surface of
the droplet is the main component of the driving force on the droplet for the
latter ones. The physical mechanism of thermocapillary droplet migration can be
described as the significance of the thermal convection around the droplet is
higher than/just as the thermal conduction across the droplet at large/moderate
Marangoni numbers.
