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# Instabilités thermoconvectives pour des fluides viscoplastiques

Abstract : The stability of the Poiseuille Rayleigh-Bénard flow for yield stress fluids is performed via linear, weakly non linear and non linear approaches. These fluids are widely used in industrial processes and at a larger scale in geophysics. It is assumed that the rheological behaviour of the material is described by the Bingham model. This model assumes that the material moves as a rigid solid when the applied stress is less than the yield stress and as a viscous fluid when the yield stress is exceeded. The aim of this study is to understand the influence of the yield stress on the stability conditions. It arises from the modification of the thickness of the yielded regions, the viscosity stratification inside these regions and the modification of the viscous dissipation. A fundamental difficulty by comparison with the Newtonian case lies in the description of the behaviour of the interface separating the gel-like" and fluid-like" phases. First, a linear analysis using modal and energetic approaches is developped. Results clearly highlight the stabilizing effect of the yield stress. Then, a weakly non linear analysis is performed to identify the nature of the bifurcation. Original results are obtained and show a change in the nature of the bifurcation at Péclet number. This is a consequence of the strong viscosity stratification. Finally, a non linear analysis was done using Reynolds-Orr type equation. The behaviour of the critical conditions as function of the yield stress is determined.
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• HAL Id : tel-01752783, version 1

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Christel Metivier. Instabilités thermoconvectives pour des fluides viscoplastiques. Autre. Institut National Polytechnique de Lorraine, 2006. Français. ⟨NNT : 2006INPL092N⟩. ⟨tel-01752783⟩

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