Taylor-Couette geometry

Problem 1.1 Compute the shear rate profile in the Taylor-Couette (or circular Couette) geometry (see Fig. Al-1) for a Newtonian fluid with negligible inertia and negligible gravity and for... 

Secondary flows in the Couette geometry have been well studied following Taylor s classic work (1923). Vfith the inno- cylinder rotating at some speed, inertial forces cause a small axisymmet-ric cellular secondary motion known as Taylor vortices or Taylor cells. These dissipate energy and cause an increase in the measured torque. Some data from Denn and Roisum (1969) for a glycerin-water solution are shown in Figure 5.3.8. For Newtcmian fluids and narrow gaps, the criterion for stability is... 

This is most easily achieved by rotating the inner cylinder and keeping the outer fixed in the laboratory frame. Note, however, that this geometry leads to the formation of Taylor vortex motion if inertial effects become important (Reynolds number Re 1). Most rheo-NMR experiments are actually performed at low Re. In the cylindrical Couette, the natural coordinates are cylindrical polar (q, <(>, z) so the shear stress is denoted and is radially dependent as q 2. The strain rate across the gap is given by [2]... 

---