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# Taylor-Couette flow for shear-thinning fluids

Abstract : This work deals with secondary instabilities in a Taylor-Couette flow with a wide gap in the case of shear-thinning fluids. Theoretical, experimental and numerical approaches are used. From theoretical point of view, a weakly nonlinear analysis has been done to account for the nonlinear effects of constitutive law on the flow structure of the Taylor Vortex Flow (TVF) regime. The shear-thinning behavior of the fluid are characterized by the Carreau model. Significant effects of shear-thinning have been demonstrated: Taylor vortices are smaller in size and shifted toward the inner cylinder. The radial outflow jet is thinner and stronger than the radial inflow jet. This asymmetry leads to an increase of the radial inflow zone. These changes in the flow structure are probably the origin of the secondary instabilities of Taylor vortices observed experimentally and numerically. The experimental setup consist of two coaxial cylinders where the inner cylinder is rotating and the outer one is at rest. The radius ratio is $eta = 0.4$ and the aspect ratio is $L = 32$. The fluids used are aqueous xanthan gum solutions at different concentrations and aqueous glycerol solution as a reference Newtonian fluid. The flow structure is analyzed through the visualization and by the 2D PIV velocity measurements. For the aqueous glycerol solution, once the primary bifurcation is reached at $Re = Re_c$, the stationary TVF regime remains stable up to practically $Re = 7 Re_c$. From this values the Taylor vortices lose its stability with respect to azimuthal disturbances. In the case of the aqueous xanthan gum solutions the values of the Reynolds number from which the Taylor vortices appear are in agreement with a linear theory as for the case of Newtonian fluid. By increasing the Reynolds number, the Taylor vortices become unstable, but with respect to axial disturbances. There instabilities can be considered as generalized Eckhaus instabilities. They are characterized by the continuous processes of creation and merging of vortices. The increase in the number of axial positions where these processes occur leads to the chaotic flow (phase turbulence). It should be noted that the stronger shear-thinning effects, the smaller the range of stable TVF regime. These results have been confirmed by a 2D numerical simulation of unsteady conservation equations, using PDE solver Freefem++. The case of shear-thinning with a stress-yield was started as well, focusing on the particular case when the unyielded zone is attached to the outer cylinder.
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Submitted on : Saturday, March 5, 2022 - 9:40:32 AM
Last modification on : Sunday, March 6, 2022 - 3:23:44 AM

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DDOC_T_2021_0301_TOPAYEV.pdf
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• HAL Id : tel-03598445, version 1

### Citation

S Topayev. Taylor-Couette flow for shear-thinning fluids. Fluid mechanics [physics.class-ph]. Université de Lorraine, 2021. English. ⟨NNT : 2021LORR0301⟩. ⟨tel-03598445⟩

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