Shear-thinning-induced chaos in Taylor-Couette flow

The effect of weak shear thinning on the stability of the Taylor-Couette fl ow is explored for a Carreau-Bird fluid in the narrow-gap limit. The Galerk in projection method is used to derive a low-order dynamical system from th e conservation of mass and momentum equations. In comparison with the Newto nian system, the present equations include additional nonlinear coupling in the velocity components through the viscosity. It is found that the critic al Taylor number, corresponding to the loss of stability of the base (Couet te) flow, becomes lower as the shear-thinning effect increases. That is, sh ear thinning tends to precipitate the onset of Taylor vortex flow. Similar to Newtonian fluids, there is an exchange of stability between the Couette and Taylor vortex flows, which coincides with the onset of a supercritical bifurcation. However, unlike the Newtonian model, the Taylor vortex cellula r structure loses its stability in turn as the Taylor number reaches a crit ical value. At this point, a Hopf bifurcation emerges, which exists only fo r shear-thinning fluids.