Axisymmetric and non-axisymmetric elastic and inertio-elastic instabilities in Taylor–Couette flow

Abstract

Flow visualization is performed on two highly elastic, non-shear-thinning dilute polymer solutions (polyisobutylene/polybutene) in a wide gap Couette cell ( R 1/ R 2=0.827) over a range of shear rates and choices of relative cylinder rotations. Axisymmetric structures of the type found in a narrow gap cell ( R 1/ R 2=0.912) [B.M Baumert, S.J. Muller, Rheol. Acta 34 (1995) 147–159; B.M. Baumert, S.J. Muller, Phys. Fluids 9 (1997) 566–586] were reproduced. Additionally, helical and non-axisymmetric standing wave patterns were visualized. In the more viscous, more elastic fluid ( ε=De/Re=15.0) transitions were found to be purely elastic. At the lowest shear rates at which transitions were observed, extremely slow-growing stationary axisymmetric counter-rotating vortices replace the purely azimuthal base flow. At rates more than twice the critical, axisymmetric oscillatory flow precedes the onset of steady vortices. Non-axisymmetric structures are first observed at rates more than 5 times the critical. The pattern is initially highly regular: two m=1 helices superpose to generate a non-axisymmetric standing wave pattern (`ribbons'). The ribbons quickly give way to intense merging structures with nearly axisymmetric cores. In the less viscous, less elastic fluid ( ε=0.0562) the lowest rate transitions are to weak axisymmetric counter-rotating vortices. At progressively higher rates in the presence of centrifugal destabilization several types of axially translating axisymmetric vortices are generated. Co-rotation of the cylinders gives rise to translating vortices at lower shear rates than rotation of the inner cylinder alone. At somewhat more than twice the critical rate, robust and hysteretic m=1 ribbons are produced. Brief periods of unpaired m=1 helices are also detectable very near the critical rate for the ribbons. The spectrum of spatial and temporal frequencies of the ribbons is found to broaden with further increases of shear rate. At the highest shear rates examined for this fluid, the flow is non-axisymmetric and highly disordered.