Experimental studies of the onset of oscillatory instability in viscoelastic Taylor-Couette flow

Abstract

Laser Doppler velocimetry (LDV) measurements of the flow of a wellcharacterized viscoelastic fluid between concentric cylinders are presented. The results show that the viscoelastic Taylor-Couette instability at vanishing Reynolds number is oscillatory for a Boger fluid; the velocity undergoes a transition from steady to time periodic at a critical Deborah number, De c. The value of De c measured by LDV is in good agreement with earlier mechanical measurements and with the calculations of Shaqfeh et al. for an Oldroyd-B fluid. The frequency of oscillation of the velocity field, however, is considerably higher than the Oldroyd-B prediction. In addition, higher harmonics of the oscillation frequency appear in the power spectrum of the velocity just above the critical condition. This observation is consistent with the calculations of Northey et al. who predict that the flatness of the neutral stability curve with respect to changes in axial wavenumber will lead to nonlinear interactions between families of time-periodic states that are closely spaced in De. Finally, the temporal evolution of the local flow field in the present LDV studies appears qualitatively different from that observed in global flow-visualization studies. This suggests that the flow may depend on the history of the experiment as well as the Deborah number.