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Quasi-static rheology of foams. Part 2. Continuous shear flow

Published online by Cambridge University Press:  31 August 2007

ALEXANDRE KABLA ,
JULIEN SCHEIBERT  and
GEORGES DEBREGEAS
ALEXANDRE KABLA
Affiliation:
Department of Engineering, University of Cambridge, Trumpington Street, Cambridge, CB2 1PZ, UK
JULIEN SCHEIBERT
Affiliation:
Laboratoire de Physique Statistique, Ecole Normale Supérieure, CNRS – UMR 8550, 24 Rue Lhomond, 75231 Paris Cedex 05, France
GEORGES DEBREGEAS
Affiliation:
Laboratoire de Physique Statistique, Ecole Normale Supérieure, CNRS – UMR 8550, 24 Rue Lhomond, 75231 Paris Cedex 05, France
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Abstract

The evolution of a bidimensional foam submitted to continuous quasi-static shearing isinvestigated both experimentally and numerically. We extract, from the images of the sheared foam, the plastic flow profiles as well as the local statistical properties of the stress field. When the imposed strain becomes larger than the yield strain, the plastic events develop large spatial and temporal correlations, and the plastic flow becomes confined to a narrow shear band. This transition and the steady-state regime of flow are investigated by first focusing on the elastic deformation produced by an elementary plastic event. This allows us to understand (i) the appearance of long-lived spatial heterogeneities of the stress field, which we believe are at the origin of the shear-banding transition, and (ii) the statistics of the dynamic fluctuations of the stress field induced by plastic rearrangements in the steady-state regime. Movies are available with the online versionof the paper.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 587 , 25 September 2007 , pp. 45 - 72
Copyright
Copyright © Cambridge University Press 2007

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Kabla et al. supplementary movie (Part 2)

Movie 1. A simulated two-dimensional polydisperse foam is subjected to a quasi-static continuous shear strain by incrementally moving the lower rigid boundary. The rapid local neighbour-switching events among the bubbles, called T1 events, can be localized by the colour flashes.

Download Kabla et al. supplementary movie (Part 2)(Video)
Video 41.4 MB

Kabla et al. supplementary movie (Part 2)

Movie 1. A simulated two-dimensional polydisperse foam is subjected to a quasi-static continuous shear strain by incrementally moving the lower rigid boundary. The rapid local neighbour-switching events among the bubbles, called T1 events, can be localized by the colour flashes.

Download Kabla et al. supplementary movie (Part 2)(Video)
Video 3.7 MB

Kabla et al. supplementary movie (Part 2)

Movie 2. Evolution of the displacement field (top) and variations of the shear stress (bottom) during the first of the two avalanches described in the paper (figure 10). Large circles show the location of T1 events that have already occurred, and small circles correspond to remaining T1 events until the avalanche is complete. The red colour in the stress variation map indicates an increase of the shear stress whereas the blue colour corresponds to a decrease of the shear stress.

Download Kabla et al. supplementary movie (Part 2)(Video)
Video 2.3 MB

Kabla et al. supplementary movie (Part 2)

Movie 2. Evolution of the displacement field (top) and variations of the shear stress (bottom) during the first of the two avalanches described in the paper (figure 10). Large circles show the location of T1 events that have already occurred, and small circles correspond to remaining T1 events until the avalanche is complete. The red colour in the stress variation map indicates an increase of the shear stress whereas the blue colour corresponds to a decrease of the shear stress.

Download Kabla et al. supplementary movie (Part 2)(Video)
Video 1.4 MB

Kabla et al. supplementary movie (Part 2)

Movie 3. Same as movie 2 but for the second avalanche.

Download Kabla et al. supplementary movie (Part 2)(Video)
Video 1.2 MB

Kabla et al. supplementary movie (Part 2)

Movie 3. Same as movie 2 but for the second avalanche.

Download Kabla et al. supplementary movie (Part 2)(Video)
Video 678.9 KB