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Inertial settling of a sphere through an interface. Part 1. From sphere flotation to wake fragmentation

Published online by Cambridge University Press:  28 November 2017

Jean-Lou Pierson
Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS, INPT, UPS, Toulouse, France
Jacques Magnaudet*
Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS, INPT, UPS, Toulouse, France
Email address for correspondence:


Experiments are performed to better understand the characteristics of the flow induced by the gravity-driven settling of a rigid sphere through a two-layer arrangement of immiscible Newtonian fluids, mostly in inertia-controlled regimes. High-speed video imaging is employed to follow the sphere motion and the deformation of the interface separating the two fluids. The viscosity ratio between the lower and upper fluids is varied by four orders of magnitude, making it possible to observe highly contrasting interface patterns. Depending on the properties of the sphere and the fluids, the sphere may either float steadily at the interface or cross it by pulling a column of the upper fluid into the lower one. This column, which may be axisymmetric or three-dimensional depending on the relative magnitude of inertia effects in the upper fluid, generally pinches off at some position located either close to the initial interface or, more frequently, close to the sphere. Its lower part then recedes towards the sphere, forming a drop which remains attached to its top half. However, when inertia effects in the lower fluid are large enough and the upper fluid is not ‘too’ viscous, the tail quickly undergoes a complete fragmentation, giving birth to a large quantity of filaments and droplets. These various interface configurations are qualitatively analysed using the five independent dimensionless parameters characterizing the system, and regime maps based on the most relevant of them are provided. The influence of several of these parameters on four specific features observed in the course of the experiments, namely the pinch-off position, the floating/sinking transition, the volume of the attached drops and the average size of the droplets formed during the fragmentation process, is examined in detail. A simple model providing qualitative or quantitative predictions is established in each case, and its validity and limitations are assessed against experimental observations.

JFM Papers
© 2017 Cambridge University Press 

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Present address: IFP Energies nouvelles, BP 3, 69360 Solaize, France.


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Pierson and Magnaudet supplementary movie 1a

A 14mm steel sphere is settling in a fluid setup with silicon oil on top of a water bath (lambda=0.21, corresponding to configuration 18(b) in figure 4). Massive fragmentation takes place in the tail.

Download Pierson and Magnaudet supplementary movie 1a(Video)
Video 2.8 MB

Pierson and Magnaudet supplementary movie 1b

Zooom of movie 1a allowing a better tracking of the tail dynamics.

Download Pierson and Magnaudet supplementary movie 1b(Video)
Video 1.6 MB

Pierson and Magnaudet supplementary movie 2a

Same as in Movie 1a-b, except that the silicon oil is ten times more viscous (lambda=0.02, corresponding to configuration 27(a) in figure 5). Again, massive fragmentation takes place in the tail.

Download Pierson and Magnaudet supplementary movie 2a(Video)
Video 2.4 MB

Pierson and Magnaudet supplementary movie 2b

Zooom of movie 2a.

Download Pierson and Magnaudet supplementary movie 2b(Video)
Video 935.2 KB

Pierson and Magnaudet supplementary movie 3a

Same as in Movie 1a-b, except that the silicon oil is a hundred times more viscous (lambda=0.002, corresponding to configuration 27(b) in figure 5).

Download Pierson and Magnaudet supplementary movie 3a(Video)
Video 2 MB

Pierson and Magnaudet supplementary movie 3b

Zooom of movie 3a.

Download Pierson and Magnaudet supplementary movie 3b(Video)
Video 1.1 MB