Observations of purely elastic instabilities in the Taylor–Dean flow of a Boger fluid

Abstract

An experimental and theoretical investigation of the stability of the viscoelastic flow of a model Boger fluid between rotating cylinders with an applied pressure gradient is presented. In our theoretical study, a linear stability analysis based on the Oldroyd-B fluid model which predicts the critical conditions and the structure of the vortex flow at the onset of instability is developed. Our results reveal that certain non-axisymmetric modes are more unstable than the previously studied axisymmetric mode when the shearing by the cylinder rotation is the dominant flow-driving force. This is consistent with recent results presented by Beris & Avgousti (1992) on the stability of elastic Taylor–Couette flow. On the other hand, the axisymmetric mode is more unstable when the pressure gradient becomes dominant. Furthermore, we investigate the mechanism of purely elastic Taylor–Dean instability with respect to non-axisymmetric disturbances through an examination of the disturbance-energy equation. It is found that the mechanism of the elastic Taylor–Dean instability is associated with the coupling between the disturbance polymeric stresses due to the azimuthal variation of the disturbance flow and the base state velocity gradients. In our experimental study, evidence of non-inertial, cellular instabilities in the Taylor–Dean flow of a well-characterized polyisobutylene/polybutene Boger fluid is presented. A stationary, meridional obstruction is placed between independently rotating, concentric cylinders to generate an azimuthal pressure gradient in opposition to the shearing flow. Flow visualization experiments near the critical conditions show the transition from purely azimuthal flows to secondary vortex flows, and the development of evenly spaced, banded vortex structures. The critical wavenumber obtained from spectral image analysis of the visualizations, and the critical Deborah number are presented for various ratios of the pressure gradient to the shear driving force. Although there is a quantitative discrepancy between data and theory, the qualitative trends in the data are in agreement with our theoretical predictions. In addition, laser-Doppler velocimetry (LDV) measurements show that the instability is a stationary mode when the pressure gradient is the dominant flow-driving force, while it is an oscillatory instability when the shearing is dominant, again as predicted by the theory.