The effect of shear thinning on the stability of the Taylor-Couette flow (TCF) is explored for a Carreau-Bird fluid in the narrow-gap limit to simulate shear-dependent viscosity of lubricants. Here, a low-order dynamical system is obtained from the conservation of mass and momentum equations. In comparison with the Newtonian system, the present equations include additional nonlinear coupling in the velocity components through the viscosity. It is found that the critical Taylor number, corresponding to the loss of stability of the base (Couette) flow becomes lower s the shear-thinning effect increases. Similar to Newtonian fluids, there is an exchange of stability between the Couette and Taylor vortex flows. However, unlike the Newtonian model, the Taylor vortex cellular structure loses its stability in turn as the Taylor number reaches a second critical value. At this point, A Hopf bifurcation emerges, which exists only for shear-thinning fluids.

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