Levitation of a drop over a moving surface

Journal of Fluid Mechanics

Journal of Fluid Mechanics / Volume 733 / October 2013, R4 (14 pages)
©2013 Cambridge University Press
DOI: http://dx.doi.org/10.1017/jfm.2013.470 (About DOI), Published online: 25 September 2013

Table of Contents - Volume 733 - 2013

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Levitation of a drop over a moving surface

Article author query
lhuissier h [Google Scholar]
tagawa y [Google Scholar]
tran t [Google Scholar]
sun c [Google Scholar]

Henri Lhuissier^a1 ^c1, Yoshiyuki Tagawa^a1^a2 ^c1, Tuan Tran^a1 and Chao Sun^a1 ^c1

^a1 Physics of Fluids Group, Faculty of Science and Technology, J.M. Burgers Center for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands

^a2 Department of Mechanical Systems Engineering, Tokyo University of Agriculture and Technology, 2-24-16 Nakacho, Koganei-city, Tokyo, Japan

Abstract

We 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 ${h}_{0}$ \${h}_{0} \$: for large drops ${h}_{0} \sim {\mathit{Ca}}^{2/ 3} { \kappa }_{b}^{- 1}$ \${h}_{0} \sim {\mathit{Ca}}^{2/ 3} { \kappa }_{b}^{- 1} \$, as in the Bretherton problem, where $\mathit{Ca}$ \$\mathit{Ca}\$ is the capillary number based on the air viscosity and ${\kappa }_{b}$ \${\kappa }_{b} \$ is the curvature at the bottom of the drop; for small drops ${h}_{0} \sim {\mathit{Ca}}^{4/ 5} {(a{\kappa }_{b} )}^{4/ 5} { \kappa }_{b}^{- 1}$ \${h}_{0} \sim {\mathit{Ca}}^{4/ 5} {(a{\kappa }_{b} )}^{4/ 5} { \kappa }_{b}^{- 1} \$, where $a$ \$a\$ is the capillary length.