Concentric cylinders secondary flow

When the shear rate reaches a critical value, secondary flows occur. In the concentric cylinder, a stable secondary flow is set up with a rotational axis perpendicular to both the shear gradient direction and the vorticity axis, i.e. a rotation occurs around a streamline. Thus a series of rolling toroidal flow patterns occur in the annulus of the Couette. This of course enhances the energy dissipation and we see an increase in the stress over what we might expect. The critical value of the angular velocity of the moving cylinder, Qc, gives the Taylor number ... 

Secondary flow. This may rise when shearing low-viscosity fluids under high shear rates in concentric cylinders. The inconvenience of having secondary flow are two fold, i.e, the equations presented in Sec, II.C do not describe this type of flow behavior and a Newtonian fluid would show a false shear-thickening behavior. Strategies to avoid or minimize these experimental errors are found in Ref. 2. 

The main sources of error in the concentric cylinder type measuring geometry arise from end effects (see above), wall shp, inertia and secondary flows, viscous heating effects and eccentricities due to misahgnment of the geometry [Macosko, 1994],... 

For low-viscosity liquids flowing in concentric cylinders, with the inner cylinder rotating at high velocities, we see the appearance inertia-driven secondary flow cells called Taylor vortices, see figure 8. The onset of these vorhces is controlled by the Taylor number which is given by... 

Figure 8 Taylor vortex secondary flow pattern between rotating concentric cylinders.

High-speed testing of low-viscosity liquids can lead to secondary flows, as shown for cone-and-plate and concentric-cylinder geometries in figure 5. 

Figure S Inertial secondary flow patterns in concentric-cylinder and cone-and-plategeometries.

Taylor vortices A secondary fluid flow pattern that can occur in the gap or annulus of a concentric cylinder, or cup and bob system known as a Couette. For a rotating bob and stationary cup, a shear rate may reach a critical value such that a series of rolling toroidal flow patterns occur in the annulus of the Couette. In a cup and bob-type rheometer, this gives rise to inaccurate measurements of viscosity. 

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