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

Motion of an air bubble under the action of thermocapillary and buoyancy forces