Lumley 



2772 n' 

 — — d^ — 



where 



T] - and d = R, - R 



R 



In computing T we have used the value of viscosity, v, which corresponds to the 

 average shear stress in the gap. With this, somewhat arbitrary, choice of the 

 viscosity the primary motion of the non-Newtonian fluid appears less stable 

 than its Newtonian counterpart. (Fig. 3.) 



°o o 



^/L 



1.3 1.4 15 



% CONCENTRATION OF MILLING YELLOW —- 



Figure 3 



With respect to the second time dependent mode of instability, however, the 

 non-Newtonian fluid is relatively more stable as can be seen in Fig. 4, showing 

 the ratio between rotation rates for the appearance of the secondary and primary 

 (Taylor) instabilities. Thus we have the seemingly somewhat contradictory re- 

 sult that the primary motion is less stable in the non-Newtonian fluid, whereas 

 once the instability has occurred the resulting motion is relatively more stable, 

 when compared to a Newtonian fluid. 



Finally, Fig. 5 shows the variation with concentration of the Taylor cell 

 width, normalized with the gap width between the cylinders. This plot is 



942 



