  A novel way to handle surface tension gradient driven flows is developed in
the volume-of-fluid (VoF) framework. Using an open source Navier-Stokes solver,
{\it Basilisk}, and the present formulation, we investigate thermocapillary
migration of drops/bubbles in a surrounding medium. Several validation
exercises have been performed, which demonstrate that the present solver is a
robust one to investigate interfacial flows with variable surface tension. It
is well known that it is a challenging task to numerically model the tangential
and normal surface forces arising due to interfacial tension. We have shown
that the present method does not require the artificial smearing of surface
tension about the interface, and thus predicts the theoretical value of the
terminal velocity of bubble/drop migrating due to an imposed temperature
gradient very well. It is also demonstrated that the present solver provides
accurate results for problems exhibiting the gravity and thermocapillary forces
simultaneously, and useful for systems with high viscosity and density ratios.
