Flow, onset and stability: Qualitative analysis of yield stress fluid flow in enclosures

Newtonian fluids initially at rest, begin to flow under the action of any force that creates a shear stress. The flow onset is immediate upon the action of such forces. Purely viscous generalised Newtonian fluids follow the same pattern. For such fluids stationary states are dynamically rather dull, being governed by the equations of hydrostatics. In contrast, yield stress fluids in the same situations display a rich variety of behaviours. Yield stress fluids allow stationary solutions while under shear. It is shown that such solutions are globally energy stable and that flow onset may be immediate, delayed or it may never take place. We identify the main dynamic features and illustrate how they depend upon the applied force, yield stress and purely viscous forces, for two classes of flows. First, we consider flows in enclosures driven by forces that are independent of the flow solution. Second we consider flows for which the body force is coupled with the flow field, taking natural convection as an example.