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Shear-thinning-induced chaos in taylor-couette flow
1Department of Mechanical and Materials Engineering, University of Western Ontario, London, Ontario, Canada N6A 5B9.
Summary
Weak shear thinning in fluids destabilizes Taylor-Couette flow, promoting Taylor vortex formation. This study reveals new bifurcations unique to shear-thinning fluids, impacting fluid dynamics understanding.
Area of Science:
- Fluid dynamics
- Non-Newtonian fluid mechanics
- Instability analysis
Background:
- Taylor-Couette flow is a fundamental problem in fluid dynamics.
- Shear-thinning fluids exhibit viscosity that decreases with shear rate.
- Understanding non-Newtonian fluid behavior is crucial in various industrial applications.
Purpose of the Study:
- To investigate the impact of weak shear thinning on Taylor-Couette flow stability.
- To analyze the transition dynamics in shear-thinning fluids using a low-order model.
- To identify novel bifurcations and stability phenomena in non-Newtonian flows.
Main Methods:
- Application of the Galerkin projection method to derive a dynamical system.
- Analysis of conservation of mass and momentum equations for a Carreau-Bird fluid.
- Comparison of results with Newtonian fluid behavior in the narrow-gap limit.
Main Results:
- Increased shear thinning lowers the critical Taylor number, advancing the onset of Taylor vortex flow.
- An exchange of stability occurs, leading to a supercritical bifurcation, similar to Newtonian fluids.
- A secondary instability and Hopf bifurcation emerge in the Taylor vortex structure, unique to shear-thinning fluids.
Conclusions:
- Shear thinning destabilizes the base Couette flow and promotes Taylor vortex formation.
- The study identifies a novel Hopf bifurcation in shear-thinning fluids, absent in Newtonian models.
- These findings enhance the understanding of non-Newtonian fluid instabilities and transitions.
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