Thermoconvective instabilities for microstructured fluids – ThIM

The non-Newtonian fluids mechanics represents a vast and active subject of research, for industrial problems with a broad active application field (cosmetic, food processes, oil industry), and for environmental questions such as geophysics. The majority of the fluids in the industrial processes are non-Newtonian. For example, fluids such as shear-thinning, or viscoplastic have a complex behavior insofar as the interactions related to their microscopic structure becomes sufficiently important to modify their macroscopic properties. The shear-thinning fluids present a nonlinear viscosity reduction with the deformation rate. If the concentration of the microstructures is sufficiently important, resistance to the flow is such as material does not flow under low stresses. These fluids are called yield stress or viscoplastic fluid.

Moreover, many industrial processes induce a heat transfer via the thermal convection. The studies of hydrodynamic stability are essential to understand the transition between the stable and unstable flows, because the instability is often accompanied by an important heat transfer increase. The chosen configuration is the academic configuration of Rayleigh-Bénard associated with shear-thinning, and viscoplastic fluids.

In spite many applications associated with the non-Newtonian fluids, and more particularly with the viscoplastic fluids, the stability studies of for these fluids remain very limited, probably because of the difficulties related to the treatment of the two phases.
In the Rayleigh-Bénard configuration, the convective instability origin is due to a vertical temperature gradient between two horizontal plates which induce a buoyancy force (Archimede buoyancy), characterized by the Rayleigh number , Ra the basic flow corresponds to a purely conductive static state.
For viscous fluids, as long as the Rayleigh number is sufficiently small, the buoyancy forces cannot overcome the stabilising effects of the viscous and thermal diffusion. From a criticalvalue Rac, thermo-convective rolls appear. In the case of the yield stress fluids, the onset of instability is possible if the buoyancy force is sufficiently important to overcome at the same time the yield stress, and the combined thermal and viscous dissipation effects.
The open flows closer to the industrial applications are relatively complex to study from the presence of a coupling between a complex rheology, a basic flow (Poiseuille flow for example), or an instability also depending on the centrifugal force (Dean flow), and a temperature gradient.
The idea thus was to retain a simpler configuration: The Rayleigh-Bénard configuration. The Rayleigh-Bénard convection system is the simplest configuration in which the effect of temperature gradient may be investigated without any base flow.
In this project, we propose to study the influence of the shear-thinnins, and the yield stress on the onset and the evolution of thermo-convectives instabilities. The main difficulties come from the nonlinear fluid behaviors (their properties can vary with the shearing rate, the temperature, and the time; the treatment of the two phases (liquid and solid) for the yield stress.
The project has the aim of overcoming these difficulties and more precisely to understand the behavior of these fluids. Work is divided into two principal parts. The first part consists in precisely understanding the effect of the viscosity stratification, for shear-thinnings fluids when thermo-convectives instabilities exist. The second part of the project has the aim of understanding the transition "fluid-gel" from the yield stress fluids and thus to be able to consider the two flow phases. This point will enable us to detect and explain the convection onset and the evolution of the thermo-convectives structures with the Rayleigh number, the control parameter.. Experimental, theoretical and numerical techniques will be developed throughout project.