Rayleigh-Benard convection of carbopol microgels: Are viscoplastic models adequate?

We investigate the adequacy of viscoplastic models in describing the Rayleigh-Benard convection of yield stress fluids. We conduct numerical simulations of the steady two dimensional natural convection of viscoplastic fluids in a long rectangular cavity to explore how the uncertainties of the rheological properties and the temperature boundary conditions propagate to the uncertainties of steady flow features. A systematic compar-ison of different nondimensionalization approaches is conducted to motivate ou r choice of the dimensionless groups. The ratio of the yield stress and buoyancy stress, BY, governs momentu m transfer in natural convection flows and measurably improves the collapse of data. We show that the commonly used definitions of modified Rayleigh number can be similarly ineffective in revealing a master curve. For the ideal bounda r y conditions and BY > 0, the motionless state is a steady regime in Rayleigh-Benard settings irrespective of the value of the other dimensionless groups. The uncertainties in the temperature bounda r y conditions can eliminate this steady regime. Thus, the observation of flow development in experiments does not necessarily contradict the theoretical predictions based on viscoplastic models. Nevertheless, we show that the experimental estimates of the critical conditions challenge the predicted stabilizing effect of the yield stress: the estimates do not depend on BYin the manner predicted by viscoplastic models.