In this paper, the overall steady-state momentum and energy balances in the
thermocapillary migration of a droplet at small Reynolds numbers and large
Marangoni numbers are investigated to confirm the quasi-steady state assumption
of the system. The droplet is assumed to have a slight axisymmetric deformation
from a sphere shape. It is shown that under the quasi-steady state assumption,
the total momentum of the thermocapillary droplet migration system at small
Reynolds numbers is conservative. The general solution of the steady momentum
equations can be determined with its parameters depending on the temperature
fields. However, a nonconservative integral thermal flux across the interface
for the steady thermocapillary migration of the droplet at small Reynolds
numbers and large Marangoni numbers is identified. The nonconservative integral
thermal flux indicates that no solutions of the temperature fields exist for
the steady energy equations. The terminal thermocapillary migration of the
droplet at small Reynolds numbers and large Marangoni numbers cannot reach a
steady state and is thus in an unsteady process
