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Film thickness distribution in gravity-driven pancake-shaped droplets rising in a Hele-Shaw cell
Ecole Polytech Fed Lausanne, Lab Fluid Mech & Instabil, CH-1015 Lausanne, Switzerland..
Ecole Polytech Fed Lausanne, Lab Fluid Mech & Instabil, CH-1015 Lausanne, Switzerland..
Ecole Polytech Fed Lausanne, Lab Fluid Mech & Instabil, CH-1015 Lausanne, Switzerland..
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. Ecole Polytech Fed Lausanne, Lab Fluid Mech & Instabil, CH-1015 Lausanne, Switzerland.;Princeton Univ, Dept Mech & Aerosp Engn, Princeton, NJ 08544 USA.
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2019 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 874, p. 1021-1040, article id PII S0022112019004531Article in journal (Refereed) Published
Abstract [en]

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 & Quere (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.

Place, publisher, year, edition, pages
Cambridge University Press, 2019. Vol. 874, p. 1021-1040, article id PII S0022112019004531
Keywords [en]
drops, Hele-Shaw flows, lubrication theory
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-255546DOI: 10.1017/jfm.2019.453ISI: 000475480700001OAI: oai:DiVA.org:kth-255546DiVA, id: diva2:1340406
Note

QC 20190805

Available from: 2019-08-05 Created: 2019-08-05 Last updated: 2019-08-05Bibliographically approved

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Zhu, Lailai

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MechanicsLinné Flow Center, FLOWSeRC - Swedish e-Science Research Centre
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