Quantitative characterization of the ribbons and elastic vortices in viscoelastic Taylor-Couette flow with Boger fluids

What is it about?

Instabilities modes in viscoelastic Taylor-Couette flow are investigated using space-time diagrams and particle image velocimetry (PIV) of flow patterns in the meridional cross-section. The working solution is an aqueous mixture of the polymer solution of Polyethylene oxide (PEO) and Polyethylene glycol (PEG). The concentrations of the PEG and the POE are chosen in such a way to obtain solutions with constant shear viscosities (characteristic of Boger fluids) and a wide spectrum of values of the molecular elastic number in a single Taylor-Couette system. The interplay between the elasticity of the polymer solution and the inertia forces induced by the rotation of the cylinders leads to different critical modes: stationary Taylor vortices for very small values of the elasticity, ribbons i.e. superposition of spirals of opposite helicity for intermediate values of the elasticity and elastic vortices for large values of the elasticity and weak inertia forces. The elasto-rotational Rayleigh discriminant and linear stability analysis show the role of elasticity in the destabilization of the base flow and on the threshold of critical modes. The elastic vortices are characterized by regions of strong inflows separated by outflows; they form flame patterns in the spatiotemporal diagrams. The amplitude of the radial velocity at the centre of vortices is used as the order parameter of the ribbons dynamics. The Ginzburg-Landau theory offers a framework to describe the destabilization of regular ribbons with the introduction of a dissymmetry parameter. Spatiotemporal properties of elastic vortices (such as the drift velocity, the fraction, the size and the lifetime of inflows) are measured for different values of the criticality. The scaling exponents of energy spectra for inertio-elastic turbulence are determined for viscoelastic Taylor-Couette flow with the inner or outer sole rotating cylinder ; the obtained values are compared with those from other experiments and from numerical simulations. PIV measurements have allowed to determine the power of the radial force at the inflow which shows that the driving mechanism of the elastic instability is active from the outer cylinder toward the inner cylinder.

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Why is it important?

We establish a universal phase diagram of critical states (E,Ta_c) or (E,K_c) which shows that the transition to elastic vortices has a constant threshold K_c for large values of elasticity E. The transition from base circular Couette flow to ribbons and to disordered ribbons is described in the framework of Ginzburg-Landau theory. We characterize the disorder nature of elastic vortices occuring at the threshold in large elasticity solutions. PIV measurements complement visualization data and allow to measure the radial force which is responsible of the formation of elastic vortices.

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