Experimental investigation of the Rayleigh-Bénard convection in a yield stress fluid

An experimental study of the Rayleigh-Bénard convection in a yield stress fluid (Carbopol® 980) uniformly heated from below in a rectangular cavity with high aspect ratio is presented. By combined integral measurements of the temperature difference between two parallel plates and the local flow velocity within a wide range of heating powers P two distinct regimes are observed. For heating powers smaller then a critical value Pc a purely conductive regime is observed. A gradual increase of the heating power beyond this onset reveals a convective regime manifested through a nonlinear dependence of the temperature difference between plates on the heating power. Simultaneously with this, local measurements of the flow fields reveal a nonlinear increase of the roll pattern amplitude. Regardless the concentration of Carbopol® and in spite of a significant shear thinning behaviour, the Rayleigh-Bénard convection in the Carbopol® gel is found to emerge as an imperfect bifurcation that can be correctly modelled by the Landau theory of phase transitions. A critical slowing down phenomenon is observed corresponding to the onset of convection. The scaling laws of the convective onset Pc and of the corresponding temperature difference ΔTc with the relevant material properties are discussed. The onset of the instability can be described in terms of a critical yield number rather than in terms of a critical Rayleigh number. The paper closes with a comparison of our findings with existing previous works.