Levitation of a drop over a moving surface

Abstract

AbstractWe investigate the levitation of a drop gently deposited onto the inner wall of a rotating hollow cylinder. For a sufficiently large 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 measurements yield the three-dimensional (3D) air film thickness under the drop and reveal 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 {\mathit{Ca}}^{2/ 3} { \kappa }_{b}^{- 1} $, as in the Bretherton problem, where $\mathit{Ca}$ 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 {\mathit{Ca}}^{4/ 5} {(a{\kappa }_{b} )}^{4/ 5} { \kappa }_{b}^{- 1} $, where $a$ is the capillary length.