Stability of a Rayleigh-Bénard poiseuille flow for yield stress fluids - Comparison between Bingham and regularized models

Christel Métivier (1) , Chérif Nouar

1 LR - Laboratoire de rhéologie

A linear stability analysis of a Rayleigh-Bénard Poiseuille flow is performed for yield stress fluids whether we use the Bingham or regularized models. A fundamental difference between those models is that the effective viscosity is not defined in the plug zone for the Bingham model, while it is defined in the whole domain for the regularized models. For these models, the viscosity depends highly on a parameter ɛnear the axis and increases drastically in an intermediate region. The convergence of the critical conditions between the simple and the Bingham models is not obtained. However, we show that the Bercovier and Papanastasiou models can tend to the exact Bingham results.

Mots clés: Fluid mechanics

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]

Christel Métivier, Chérif Nouar. Stability of a Rayleigh-Bénard poiseuille flow for yield stress fluids - Comparison between Bingham and regularized models. International Journal of Non-Linear Mechanics, 2011, ⟨10.1016/j.ijnonlinmec.2011.05.017⟩. ⟨hal-00784918⟩