Levitation of a drop over a moving surface

Abstract

We investigate the levitation of a drop gently deposited onto the inner wall of a rotating hollow cylinder. For a sufficient velocity of the wall, the drop steadily levitates over a thin air film and reaches a stable angular position in the cylinder, where the drag and lift balance the weight of the drop. Interferometric measurement yields the three-dimensional (3D) air film thickness under the drop and reveals the asymmetry of the profile along the direction of the wall motion. A two-dimensional (2D) model is presented which explains the levitation mechanism, captures the main characteristics of the air film shape and predicts two asymptotic regimes for the film thickness $h_0$: For large drops $h_0\sim\ca^{2/3}\kappa_b^{-1}$, as in the Bretherton problem, where $\ca$ is the capillary number based on the air viscosity and $\kappa_b$ is the curvature at the bottom of the drop. For small drops $h_0\sim\ca^{4/5}(a\kappa_b)^{4/5}\kappa_b^{-1}$, where $a$ is the capillary length.