Non-linear oscillatory rheological properties of a generic continuum foam model: comparison with experiments and shear-banding predictions

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

The occurence of shear bands in a complex fluid is generally 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 related to the coexistence of different states of the material under shear. In this paper we present a scenario for shear-banding in a particular class of complex fluids, namely foams and concentrated emulsions, which differs from other scenarii in two important ways. First, the appearance of shear bands is shown to be possible both without any intrinsic physical evolution of the material (e.g. via a parameter coupled to the flow such as concentration or entanglements) and without any finite critical shear rate below which the flow does not remain stationary and homogeneous. Secondly, the appearance of shear bands depends on the initial conditions, i.e., the preparation of the material. In other words, it is history dependent. This behaviour relies on the tensorial character of the underlying model (2D or 3D) and is triggered by an initially inhomogeneous strain distribution in the material. The shear rate displays a discontinuity at the band boundary, whose amplitude is history dependent and thus depends on the sample preparation.

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. Non-linear oscillatory rheological properties of a generic continuum foam model: comparison with experiments and shear-banding predictions. European Physical Journal E: Soft matter and biological physics, 2012, 35, pp.51. ⟨10.1140/epje/i2012-12051-8⟩. ⟨hal-00530995v3⟩