Origin of the onset of Rayleigh-Bénard convection in a concentrated suspension of microgels with a yield stress behavior

Abstract

In this paper, we propose to explore experimentally the origin of the onset of motion in a well-known Carbopol gel, a concentrated suspension of microgels, when submitted to a vertical temperature gradient, namely, the Rayleigh-Bénard Convection (RBC). We consider three possible scenarios: (i) the gel behaves as an elasto-viscoplastic material, (ii) the gel presents a low-stress viscosity μ+ below the yield stress τy, and (iii) the gel can be considered as a two phase system, say the microgels and the solvent, i.e., a porous medium. We propose a complete rheological characterization of Carbopol 940. Creep measurements lead to obtain an instantaneous viscosity plateau μ+∼tm with m≈1. For the first time, we measure and provide permeability values k in the Carbopol gels. We show that k = O(10−14) m2 and k∝τy0.2. Our study focuses on the reference case of the RBC with no-slip conditions at walls, and new results are provided. The results lead to the conclusion that the control parameter is the (inverse) of the yield number Y, ratio between the yield stress and the buoyancy stress, and they show that the critical value is 1/Yc≈80 for no-slip conditions. One shows that both scenarios (i) and (ii) lead to recover 1/Y as the control parameter. By considering the Carbopol gels as porous media [scenario (iii)], one finds that the critical porous Rayleigh-Darcy number is Rap = O(10−4).