Experimental study of the interactions of coupled counterpropagating spirals in a viscoelastic Couette – Taylor flow

The addition of small amounts of flexible polymer, with long linear chain, to a newtonian liquid gives to the resulting polymer solution viscoelastic or non-newtonian behaviors. Among the various nonnewtonian behaviors observed with polymer solutions, the reduction of the friction drag in turbulent flows is one of the features that had attracted much attention. Although this effect was discovered by Toms in 1949, there is no satisfactory theory available for its explanation. Research on the drag reduction problem requires the joint study of turbulence, which is not fully understood as itself, and viscoelastic flows, for which the lack of universal equations (like the Navier Stokes equations for newtonian flows) is a great flaw. These advocated the need for studies in hydrodynamic model systems like Couette–Taylor, for which various routes to turbulence were characterized for Newtonian flow [1]. Experimental studies of the viscoelastic Couette–Taylor flow reported various results depending of the fluid rheological properties [2]. For Boger fluids, which are very elastic and very viscous fluids, Larson et al. [3] showed that the base circular Couette flow could bifurcate to a nonstationary ”purely elastic” instability mode. Such mode is triggered by elastic effect only and can be observed for vanishing inertia. Inertio-elastic flow regimes result from an interplay between inertia and elastic effects. Of particular interest are flow patterns made of counterpropagating spirals. Such regimes were both observed and predicted for viscoelastic liquids with no or negligible shear-thinning [4,5,6]. With aqueous solutions of polyethylenoxide, we have observed a flow pattern made of strongly coupled counterpropagating spirals [7]. The present study provide further results on the interactions of coupled counterpropagating spirals with the help of complexe demodulation. The experimental setup consists of a Couette cell with coaxial horizontal cylinders. The inner cylinder is made of black Delrin with a radius a = 4.46 cm. The outer cylinder is made of Plexiglass with a radius b = 5.05 cm. The gap size between the cylinders is d = b − a = 0.59 cm and has a length L = 27.5 cm. The system radius ratio is thus a/b = 0.883 while the aspect ratio is L/d = 46.6. The inner cylinder is driven by a DC servomotor while the outer cylinder is kept at rest. Experiments are conducted at room temperature. The polymer solutions were prepared by mixing an initial suspension of polyethyleneoxide (Aldrich, 8 · 106 g/mol) in 40 ml of isopropyl alcohol with 760 ml of water. The concentration of POE in the resulting solution is 500 weight ppm. The solution is maintained 5 days at rest at 4C then approximately 14 h at room temperature. A final homogeneization stage is executed with a magnetic shaker. Viscosity measurements with an AR2000 Rheometer exhibit a shearthining behaviour. For flow visualization, 2% of Kalliroscope AQ 1000 are added. A linear 1024-pixels CCD camera recorded the reflected light intensity I(x) from a line along the axial direction with 8bits sampling. Collation of recorded lines at regular intervals (10 Hz) provide spatio-temporal diagrams I(x, t) of flow patterns. We define as Ωc the critical rotation speed for wich the base flow bifurcates, and = (Ω − Ωc)/Ωc is the criticality parameter. We observed a critical instability mode in the form of counterpropagating spirals. The spatio-temporal diagram (Fig. 1) however exhibits a rich dynamics and one may distinguish partialy stationnary waves