The effect of surfactant redistribution on combined gravitational and thermocapillary interactions of deformable drops

Trajectories are calculated by the boundary-integral method for two contaminated deformable drops under the combined influence of buoyancy and a constant temperature gradient at low Reynolds number and with negligible thermal convection. The surfactant is bulk-insoluble, and its coverage is determined by solution of the time-dependent convective-diffusion equation. Two limits are considered. For small drops, the deformation is small, and thermocapillary and buoyant effects are of the same order of magnitude. In this case, comparison is made with incompressible surfactant results to determine when surfactant redistribution becomes important. Convection of surfactant can lead to elimination of interesting features, such as the possibility of two different-sized drops migrating with fixed separation and orientation, and can increase the difference between the drops' velocities. For larger drops, deformation can be significant, leading to smaller or larger drop breakup, and buoyant motion dominates thermocapillarity. In this case, convection of surfactant can increase deformation and offset previously observed inhibition of breakup for clean drops when the driving forces are opposed. This effect is less pronounced for larger size ratios. By extension, redistribution of surfactant can enhance deformation-increasing tendencies seen with driving forces aligned in the same direction.