A new method for the simulation of droplet motion due to interfacial tension gradients is developed, and the thermocapillary motion of deformable drops in the presence of convective transport of momentum and energy is studied numerically. Axisymmetric and two-dimensional problems are addressed, with the emphasis on the development of the method. Quad-tree adaptive refinement of the underlying cartesian grid is implemented in order to track the interface without the need for interface reconstruction. To verify the method the thermocapillary migration of a drop in the absence of momentum and energy convection is simulated; the results are in complete agreement with existing analytical solutions. A sample simulation of a drop in the presence of momentum and energy convection shows the importance of the deformation.
Shi, Q., Haj-Hariri, H., The Effects of Convection on the Motion of Deformable Drops, 32nd Aerospace Sciences Meeting & Exhibit, AIAA, Washington, DC, AIAA-94-0834, pp. 1-9, January 10, 1994.