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Film thickness distribution in gravity-driven pancake-shaped droplets rising in a Hele-Shaw cell

Published online by Cambridge University Press:  15 July 2019

Isha Shukla Open the ORCID record for Isha Shukla [Opens in a new window] ,
Nicolas Kofman ,
Gioele Balestra Open the ORCID record for Gioele Balestra [Opens in a new window] ,
Lailai Zhu Open the ORCID record for Lailai Zhu [Opens in a new window]  and
François Gallaire Open the ORCID record for François Gallaire [Opens in a new window]
Isha Shukla
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
Nicolas Kofman
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
Gioele Balestra
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
Lailai Zhu
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA Linné Flow Centre and Swedish e-Science Research Centre (SeRC), KTH Mechanics, SE-100 44 Stockholm, Sweden
François Gallaire*
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
*
†Email address for correspondence: francois.gallaire@epfl.ch
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Abstract

We study here experimentally, numerically and using a lubrication approach, the shape, velocity and lubrication film thickness distribution of a droplet rising in a vertical Hele-Shaw cell. The droplet is surrounded by a stationary immiscible fluid and moves purely due to buoyancy. A low density difference between the two media helps to operate in a regime with capillary number $Ca$ lying between $0.03$ and $0.35$, where $Ca=\unicode[STIX]{x1D707}_{o}U_{d}/\unicode[STIX]{x1D6FE}$ is built with the surrounding oil viscosity $\unicode[STIX]{x1D707}_{o}$, the droplet velocity $U_{d}$ and surface tension $\unicode[STIX]{x1D6FE}$. The experimental data show that in this regime the droplet velocity is not influenced by the thickness of the thin lubricating film and the dynamic meniscus. For iso-viscous cases, experimental and three-dimensional numerical results of the film thickness distribution agree well with each other. The mean film thickness is well captured by the Aussillous & Quéré (Phys. Fluids, vol. 12 (10), 2000, pp. 2367–2371) model with fitting parameters. The droplet also exhibits the ‘catamaran’ shape that has been identified experimentally for a pressure-driven counterpart (Huerre et al., Phys. Rev. Lett., vol. 115 (6), 2015, 064501). This pattern has been rationalized using a two-dimensional lubrication equation. In particular, we show that this peculiar film thickness distribution is intrinsically related to the anisotropy of the fluxes induced by the droplet’s motion.

JFM classification

Drops and Bubbles: Drops Low-Reynolds-number flows: Hele-Shaw flows Low-Reynolds-number flows: Lubrication theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 874 , 10 September 2019 , pp. 1021 - 1040
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Copyright
© 2019 Cambridge University Press 

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