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Inertial drag-out problem: sheets and films on a rotating disc

Published online by Cambridge University Press:  03 December 2020

J. John Soundar Jerome Open the ORCID record for J. John Soundar Jerome [Opens in a new window] ,
Sébastien Thevenin ,
Mickaël Bourgoin Open the ORCID record for Mickaël Bourgoin [Opens in a new window]  and
Jean-Philippe Matas Open the ORCID record for Jean-Philippe Matas [Opens in a new window]
J. John Soundar Jerome*
Affiliation:
Univ Lyon, Université Claude Bernard Lyon 1, Laboratoire de Mécanique des Fluides et d'Acoustique, CNRS UMR-5509, Boulevard 11 novembre 1918, F-69622 Villeurbanne CEDEX, LYON, France
Sébastien Thevenin
Affiliation:
Univ Lyon, Université Claude Bernard Lyon 1, Laboratoire de Mécanique des Fluides et d'Acoustique, CNRS UMR-5509, Boulevard 11 novembre 1918, F-69622 Villeurbanne CEDEX, LYON, France
Mickaël Bourgoin
Affiliation:
Laboratoire de Physique, Universite Lyon, ENS de Lyon, Universite Lyon 1, CNRS, F-69342Lyon, France
Jean-Philippe Matas
Affiliation:
Univ Lyon, Université Claude Bernard Lyon 1, Laboratoire de Mécanique des Fluides et d'Acoustique, CNRS UMR-5509, Boulevard 11 novembre 1918, F-69622 Villeurbanne CEDEX, LYON, France
*
†Email address for correspondence: [email protected]
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Abstract

The so-called Landau–Levich–Deryaguin problem treats the coating flow dynamics of a thin viscous liquid film entrained by a moving solid surface. In this context, we use a simple experimental set-up consisting of a partially immersed rotating disc in a liquid tank to study the role of inertia, and also curvature, on liquid entrainment. Using water and UCON$^{\textrm{TM} }$ mixtures, we point out a rich phenomenology in the presence of strong inertia: ejection of multiple liquid sheets on the emerging side of the disc, sheet fragmentation, ligament formation and atomization of the liquid flux entrained over the disc's rim. We focus our study on a single liquid sheet and the related average liquid flow rate entrained over a thin disc for various depth-to-radius ratio $h/R < 1$. We show that the liquid sheet is created via a ballistic mechanism as liquid is lifted out of the pool by the rotating disc. We then show that the flow rate in the entrained liquid film is controlled by both viscous and surface tension forces as in the classical Landau–Levich–Deryaguin problem, despite the three-dimensional, non-uniform and unsteady nature of the flow, and also despite the large values of the film thickness based flow Reynolds number. When the characteristic Froude and Weber numbers become significant, strong inertial effects influence the entrained liquid flux over the disc at large radius-to-immersion-depth ratio, namely via entrainment by the disc's lateral walls and via a contribution to the flow rate extracted from the three-dimensional liquid sheet itself, respectively.

JFM classification

Materials Processing Flows: Coating Interfacial Flows (free surface): Thin films Multiphase and Particle-laden Flows: Gas/liquid flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 908 , 10 February 2021 , A7
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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John Soundar Jerome et al. supplementary movie 1

A water sheet extending perpendicularly outward from the rim is ejected on the emerging side of a partially-submerged rotating wheel of radius 13.5 cm when depth-to-radius ratio of 0.2.

Download John Soundar Jerome et al. supplementary movie 1(Video)
Video 18.9 MB

John Soundar Jerome et al. supplementary movie 2

Holes nucleate, grow and disintegrate the water sheet on the emerging side of the wheel. This leads to ligaments and droplets ejected at the liquid rim.

Download John Soundar Jerome et al. supplementary movie 2(Video)
Video 39.9 MB

John Soundar Jerome et al. supplementary movie 3

Rim of the rotating disk for UCON (nearly 100 times more viscous than water) at 19 rpm and depth-to-radius ratio of 0.2.

Download John Soundar Jerome et al. supplementary movie 3(Video)
Video 15.4 MB

John Soundar Jerome et al. supplementary movie 4

A typical inertial liquid sheet for UCON (nearly 100 times more viscous than water) of a rotating wheel of radius 21 cm at 65 rpm and depth-to-radius ratio of 0.2.

Download John Soundar Jerome et al. supplementary movie 4(Video)
Video 7.6 MB

John Soundar Jerome et al. supplementary movie 5

Instantaneous visualization of sheet and entrained film thickness for a rotating wheel of diameter 42 cm and depth-to-radius ratio 0.43 at 3.5 m/s. The video shows relatively large variations of the film thickness, both locally and temporally.

Download John Soundar Jerome et al. supplementary movie 5(Video)
Video 32.3 MB