Eur. Phys. J. E (2008) 25: 371-384
https://doi.org/10.1140/epje/i2007-10300-7

Regular Article

Discrete rearranging disordered patterns, part II: 2D plasticity, elasticity and flow of a foam

Laboratoire de Spectrométrie Physique, UMR5588, CNRS-Université Grenoble I, B.P. 87, F-38402, St Martin d'Hères Cedex, France

^* e-mail: philippe.marmottant@ujf-grenoble.fr

Received: 6 July 2007
Accepted: 15 February 2008
Published online: 30 April 2008

Abstract

The plastic flow of a foam results from bubble rearrangements. We study their occurrence in experiments where a foam is forced to flow in 2D: around an obstacle; through a narrow hole; or sheared between rotating disks. We describe their orientation and frequency using a topological matrix defined in the companion paper (F. Graner, B. Dollet, C. Raufaste, and P. Marmottant, this issue, 25 (2008) DOI 10.1140/epje/i2007-10298-8), which links them with continuous plasticity at large scale. We then suggest a phenomenological equation to predict the plastic strain rate: its orientation is determined from the foam's local elastic strain; and its rate is determined from the foam's local elongation rate. We obtain a good agreement with statistical measurements. This enables us to describe the foam as a continuous medium with fluid, elastic and plastic properties. We derive its constitutive equation, then test several of its terms and predictions.