Publication

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

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 CaCa lying between 0.030.03 and 0.350.35 , where Ca=\unicode[STIX]x1D707oUd/\unicode[STIX]x1D6FECa=\unicode[STIX]{x1D707}_{o}U_{d}/\unicode[STIX]{x1D6FE} is built with the surrounding oil viscosity \unicode[STIX]x1D707o\unicode[STIX]{x1D707}_{o} , the droplet velocity UdU_{d} and surface tension \unicode[STIX]x1D6FE\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.

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Fluid bearings are bearings in which the load is supported by a thin layer of rapidly moving pressurized liquid or gas between the bearing surfaces. Since there is no contact between the moving parts, there is no sliding friction, allowing fluid bearings to have lower friction, wear and vibration than many other types of bearings. Thus, it is possible for some fluid bearings to have near-zero wear if operated correctly. They can be broadly classified into two types: fluid dynamic bearings (also known as hydrodynamic bearings) and hydrostatic bearings.
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