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Home page > Research topics > Liquid foam rheology > Foam or emulsion: continuous tensorial rheological model.

Foam or emulsion: continuous tensorial rheological model

MSC : Cyprien Gay

Collaborations : François Molino (Montpellier) Sylvain Bénito, Thierry Colin, Charles-Henri Bruneau (Bordeaux), Isabelle Cantat (Rennes).

A foam (or an emulsion) is made of soft and round objects (the bubbles or the droplets) arranged in a dense manner, which are thus faceted. It is elastic on short time scales but rearranges and creeps on long time scales under weak stress, like a liquid. On intermediate time scales, a moderate stress, above some threshold value, triggers a series of discreet topological events (swapping of neighbours) allows the material to deform during the whole external action. That is a plastic behavior. Over the last years, the understanding of this type of materials has made a lot of progress. Beyond the purely mechanical experiments that exhibit the macroscopic behaviors, in situ observations, associated with new analysis tools (by François Graner and collaborators), have revealed the structure of the foam under flow. Furthermore, tensorial models have appeared to formalize the known rheological properties of these systems.

A plastic type of rhéologie is known for instance in metallurgy. But the specificity of a foam lies in the fact that the flow threshold corresponds to a large material deformation (of the order of 50 to 100%). Moreover, the stress also depends on the deformation rate like in a viscous liquid, as opposed to a purely plastic material in which the strain rate ajusts so that the stress should never exceed the threshold stress substantially.

-  We have built a rheological model that is equivalent to the (scalar and linear) Bingham model, but which accounts for the above properties. It is thus generic (non-linear both in its elastic response and in its rate of creep) and fully tensorial. [1]

-  We have compared the predictions of this model with the measurements obtained by Florence Rouyer and collaborators for a large amplitude oscillatory shear. We have also shown that the model predicts the possibility of stable shear bands affected by the initial conditions. [2]

- [1] Sylvain Bénito, Charles-Henri Bruneau, Thierry Colin, Cyprien Gay, and François Molino, "An elasto-visco-plastic model for immortal foams or emulsions" Eur. Phys. J. E 25 225-­251 (2008)

- [2] Sylvain Bénito, François Molino, Charles-Henri Bruneau, Thierry Colin, Cyprien Gay, "Non-linear oscillatory rheological properties of a generic continuum foam model: comparison with experiments and shear-banding predictions" Eur. Phys. J. E 35 51 (2012)

Contact : Published on / Publié le 29 October 2010

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