Effect of gap width on stability of non-Newtonian Taylor-Couette flow

The effect of gap width on the stability of non-Newtonian Taylor-Couette flow is studied. The fluid is assumed to follow the pseudo plastic Carreau-Bird model and mixed boundary conditions are imposed. The 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, depending on the gap width for certain fluid, the base flow loses its radial flow stability to the vortex structure known as Taylor vortices. The emergence of theses vortices corresponds to the onset of a supercritical bifurcation also seen in the flow of a linear fluid. A range of parameters is found in which the combination of shear thinning and gap effect leads to destabilizing the vortex structure indicated as the point of Hopf bifurcation. This is not observed in the Newtonian flow, in which the vortices remain stable regardless of the inertia. Furthermore, upon increase of gap width both the critical Taylor and Hopf bifurcation numbers also increase. The obtained results are in good agreement with the available studies carried out only for certain cases.