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Two-dimensional flow of foam around a circular obstacle: local measurements of elasticity, plasticity and flow

Published online by Cambridge University Press:  07 August 2007

BENJAMIN DOLLET  and
FRANÇOIS GRANER
BENJAMIN DOLLET
Affiliation:
Laboratoire de Spectrométrie Physique, BP 87, 38402 Saint-Martin-d'Hères Cedex, France Physics of Fluids, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
FRANÇOIS GRANER
Affiliation:
Laboratoire de Spectrométrie Physique, BP 87, 38402 Saint-Martin-d'Hères Cedex, France
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Abstract

We investigate the two-dimensional flow of a liquid foam around a circular obstacle by measuring all the local fields necessary to describe this flow: velocity, pressure, and bubble deformations and rearrangements. We show how our experimental set-up, a quasi-two-dimensional ‘liquid pool’ system, is adapted to the determination of these fields: the velocity and bubble deformations are easy to measure from two-dimensional movies, and the pressure can be measured by exploiting a specific feature of this system, a two-dimensional effective compressibility. To describe accurately neighbour swapping (so-called ‘T1’ processes), we propose a new, tensorial descriptor. All these quantities are evaluated via an averaging procedure that we justify by showing that the fluctuations of the fields are essentially Gaussian. The flow is extensively studied in a reference experimental case; the velocity presents an overshoot in the wake of the obstacle, and the pressure is maximum at the leading side and minimal at the trailing side. The study of the elastic deformations and of the velocity gradients shows that the transition between plug flow and yielded regions is smooth. Our tensorial description of T1s highlights their correlation both with the bubble deformations and the velocity gradients. A salient feature of the flow, notably for the velocity and T1 distribution, is a marked fore–aft asymmetry, the signature of the elastic behaviour of the foam. We show that the results do not change qualitatively when various control parameters (flow rate, bubble area, fluid fraction, bulk viscosity, obstacle size and boundary conditions) vary, identifying a robust quasi-static regime. These results are discussed in the framework of the foam rheology literature. A movie is available with the online version of the paper.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 585 , 25 August 2007 , pp. 181 - 211
Copyright
Copyright © Cambridge University Press 2007

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Dollet and Graner supplementary movie

Movie 1. Flow of a monodisperse foam in a channel (width 10.0 cm) around a circular obstacle (diameter 3.0 cm). The parameters of the flow are the following: flow rate 176 ml/min, bubble area 16.0 mm$^2$, foam thickness 3.5 mm and solution viscosity 1.06 mm$^2$/s. This movie reveals the plastic character of the flow: the foam flows around the obstacle mainly thanks to multiple bubble rearrangements.

Download Dollet and Graner supplementary movie(Video)
Video 8.3 MB

Dollet and Graner supplementary movie

Movie 1. Flow of a monodisperse foam in a channel (width 10.0 cm) around a circular obstacle (diameter 3.0 cm). The parameters of the flow are the following: flow rate 176 ml/min, bubble area 16.0 mm$^2$, foam thickness 3.5 mm and solution viscosity 1.06 mm$^2$/s. This movie reveals the plastic character of the flow: the foam flows around the obstacle mainly thanks to multiple bubble rearrangements.

Download Dollet and Graner supplementary movie(Video)
Video 12.8 MB