Shear bands in a continuum model of foams: how a 3D homogeneous material may seem inhomogeneous in 2D

Sylvain Bénito (1) , François Molino (2) , Charles-Henri Bruneau (3, 4) , Thierry Colin (3, 4) , Cyprien Gay (5)

1 MAB - Laboratoire de Mathématiques Appliquées de Bordeaux
2 IGF - Institut de Génomique Fonctionnelle
3 IMB - Institut de Mathématiques de Bordeaux
4 MC2 - Modélisation, contrôle et calcul
5 MSC - Matière et Systèmes Complexes

We describe possible conditions for stationnary inhomogeneous flow behaviour (sheared and blocked bands) in a continuous mechanical model of a soft visco-elasto-plastic material such as a foam or a concentrated emulsion under controled shear rate conditions. Usually, the occurence of shear bands in a complex fluid is understood as resulting from a structural evolution of the material under shear, which leads from a theoretical perspective to a non-monotonic stationnary flow curve. Our mechanical model predicts a non-monotonic flow curve, but a priori without any intrinsic physical evolution {\em via} a parameter coupled to the flow such as concentration of entanglements. Nevertheless, we predict the appearence of shear bands. In our case, the non-monotonic flow curve and the appearence of shear bands result specifically from the tensorial character of the underlying model (2D or 3D). For a Couette flow, a 3D tensorial formalism allows us to introduce an additional relaxtion freedom for the system in the third direction, which affects the material fluidity.

Mots clés: Foams; emulsions; Constitutive relations; Rheology; shear flow

Domaines: Matière Molle [cond-mat.soft]

Sylvain Bénito, François Molino, Charles-Henri Bruneau, Thierry Colin, Cyprien Gay. Shear bands in a continuum model of foams: how a 3D homogeneous material may seem inhomogeneous in 2D. 2010. ⟨hal-00530995v1⟩