Order in chaotic pseudoplastic flow between coaxial cylinders

Order is found within the chaotic nonlinear flow between rotating coaxial cylinders. The flow stability analysis is carried out for a pseudoplastic fluid through bifurcation diagram and Lyapunov exponent histogram. The fluid is assumed to follow the Carreau-Bird model, and mixed boundary conditions are imposed. The low-order dynamical system, resulted from Galerkin projection of the conservation of mass and momentum equations, includes additional nonlinear terms in the velocity components originated from the shear-dependent viscosity. It is observed that the base flow loses its radial flow stability to the vortex structure at a lower critical Taylor number, as the shear-thinning effects increase. The emergence of the vortices corresponds to the onset of a supercritical bifurcation, which is also seen in the flow of a linear fluid. However, unlike the Newtonian case, shear-thinning Taylor vortices lose their stability as the Taylor number reaches a second critical number corresponding to the onset of a Hopf bifurcation. Complete flow field together with viscosity maps are given for different scenarios in the bifurcation diagram.