Tensorial rheological model for concentrated non-colloidal suspensions: normal-stress differences

Olivier Ozenda (1) , Pierre Saramito (1) , Guillaume Chambon (2)

1 EDP - Equations aux Dérivées Partielles
2 UR ETGR (ETNA) - Erosion torrentielle neige et avalanches

Most existing rheological models for non-colloidal suspensions fail to simultaneously capture the two main non-Newtonian trends of these systems, namely finite normal stress differences and transient effects. We address this issue by extending a previously-proposed minimal model accounting for microstructure anisotropy through a conformation tensor, and which was shown to correctly predict transient effects (Ozenda et al. 2018). The new model is compared to a large experimental dataset involving varying volume fractions, from dilute to concentrated cases. Both transient evolution of apparent viscosity during shear reversal, and normal stress differences in steady state, are quantitatively reproduced in the whole range of volume fraction. Furthermore, the model is validated against particle pressure measurements that were not used for parameter identification. Even if the proposed constitutive equation for the Cauchy stress tensor is more difficult to interpret than in the minimal model, this study opens way for the use of conformation tensor rheological models in applications where the effect of the second normal stress difference is prominent, like elongational flows or migration phenomenon.

Domaines: Mécanique des fluides [physics.class-ph]; Matière Molle [cond-mat.soft]; Equations aux dérivées partielles [math.AP]

Olivier Ozenda, Pierre Saramito, Guillaume Chambon. Tensorial rheological model for concentrated non-colloidal suspensions: normal-stress differences. 2019. ⟨hal-02138682v1⟩