Counter-current motion of a droplet levitated on a liquid film undergoing Marangoni convection

This paper experimentally and analytically investigates the motion of a levitated droplet against the Marangoni flow in an immiscible outer fluid. Based on our earlier experiments, when a droplet is released from a height ∼1.5-4 times its diameter from the liquid surface, it can overcome the impact and stay levitated at the liquid-air interface due to the existence of an air gap between the droplet and the liquid film. Surprisingly, such a levitated droplet, moves toward the heating source against the Marangoni convection. In order to explain this behavior, we propose a simple approach: first, the Marangoni convection inside the thin film is considered without the droplet floating on the surface. By using a level-set method and solving the Navier-Stokes equation, the free surface velocity and deformation are calculated. Then, these quantities are used to solve for droplet velocity and drag coefficient simultaneously using a force balance. In order to compare the simulation results, experiments with levitated water droplets on an immiscible carrier liquid, FC-43, are conducted for various temperature gradients and droplet velocities are measured at different locations using high-speed imaging. The experimental results are in good agreement with the developed theoretical model. For a Reynolds number range of 2-32, it is shown that the drag coefficients are up to 66% higher than those for the fully immersed sphere at the same Reynolds numbers. Finally, a correlation is proposed to calculate the drag coefficient of levitated droplets for various temperature drops across the channel.