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

Abstract

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.