Levitation of a drop over a moving surface

TL;DR

This paper studies how drops levitate over a moving surface inside a rotating cylinder, combining experiments and a model to understand the air film dynamics and regimes.

Contribution

It introduces a 2D model explaining the levitation mechanism and predicts asymptotic regimes for the air film thickness based on drop size and flow parameters.

Findings

Stable levitation occurs at sufficient wall velocity.

Interferometry reveals asymmetric air film profiles.

The model predicts two asymptotic regimes for film thickness.

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.