International audienceThe influence of rheological and interfacial properties of yield stress fluids is investigated on the onset of the Rayleigh-Bénard convection. Different Carbopol® (B.F. Goodrich) gels are used in a circular cell for Rayleigh-Bénard experimental setup. The influence of the boundary conditions is also investigated by controlling either slip or no-slip conditions. The onset of thermoconvection is shown by measuring temperature differences and also by using shadowgraph flow visualization. Experimental results show that convection occurs in the range of our experiments. Considering Carbopol gels as elasto-plastic materials with a yield stress τy, a generalized Rayleigh number is obtained: Rag = Y−1, with Y the yield number, which represents the balance between the yield stress of the gel and the buoyancy effects. The results show that the Rayleigh number is proportional to d, the height of the setup, and that the control parameter is the yield number at the onset of convection. Critical values of Y−1 have been determined for slip conditions 1/YSc≈40 as well as for no-slip conditions 1/YNSc≈80. It highlights that the change in surface conditions affect significantly the critical conditions

A linear and weakly nonlinear analysis of convection in a layer of shear-thinning fluids between two horizontal plates heated from below is performed. The objective is to examine the effects of the nonlinear variation of the viscosity with the shear rate on the nature of the bifurcation, the planform selection problem between rolls, squares and hexagons, and the consequences on the heat transfer coefficient. Navier’s slip boundary conditions are used at the top and bottom walls. The shear-thinning behaviour of the fluid is described by the Carreau model. By considering an infinitesimal perturbation, the critical conditions, corresponding to the onset of convection, are determined. At this stage, non-Newtonian effects do not come into play. The critical Rayleigh number decreases and the critical wavenumber increases when the slip increases. For a finite-amplitude perturbation, nonlinear effects enter in the dynamic. Analysis of the saturation coefficients at cubic order in the amplitude equations shows that the nature of the bifurcation depends on the rheological properties, i.e. the fluid characteristic time and shear-thinning index. For weakly shear-thinning fluids, the bifurcation is supercritical and the heat transfer coefficient increases, as compared with the Newtonian case. When the shear-thinning character is large enough, the bifurcation is subcritical, pointing out the destabilizing effect of the nonlinearities arising from the rheological law. Departing from the onset, the weakly nonlinear analysis is carried out up to fifth order in the amplitude expansion. The flow structure, the modification of the viscosity field and the Nusselt number are characterized. The competition between rolls, squares and hexagons is investigated. Unlike Albaalbaki & Khayat (J. Fluid. Mech., vol. 668, 2011, pp. 500–550), it is shown that in the supercritical regime, only rolls are stable near onset.

An experimental investigation of the Rayleigh-Bénard convection in shear-thinning fluids is presented by using MRI technics. The experimental setup consists on a cylindrical cavity defined by a finite aspect ratio A = D/d = 6. Qualitative and quantitative results are provided. Flow visualizations are presented via velocity mapping for a Newtonian fluid, the Glycerol and for shear-thinning fluids, Xanthan gum aqueous solutions with weight concentrations ranging from 0.1 to 0.2 %. In the case of the Glycerol and the Xanthan solution at 0.1 %, one recovers similar results in terms of criticality with Ra c = 1800 and patterns since the convection is characterized by rolls. When the Xanthan concentration is increased, the critical Rayleigh number is not modified, however the onset occurs with hexagonal pattern. Because the critical temperature differences increase with the concentrations due to an increase in viscosity, one can think that hexagonal patterns are due to variations of physical properties with temperature (non Oberbeck-Boussinesq effects). Similarities with some results obtained in the Newtonian case are highlighted. We have observed a transition from hexagonal patterns to rolls by increasing the Rayleigh number. This pattern transition is characterized by a discrepancy in the maximal velocity values. By using shearthinning fluids, results show an increase in the intensity of convection compared with the Newtonian case.