Observations on the elastic instability in cone-and-plate and parallel-plate flows of a polyisobutylene Boger fluid

Experimental measurements of the shear stress and normal stresses in the viscometric flow of a well-characterized polyisobutylene/polybutene solution between a cone-and-plate and between parallel plates show the onset of an “anti-thixotropic” flow transition, which results in a time-dependent, apparent shear-thickening of the viscosity and first normal stress difference. Measurements of the critical conditions for the onset of the flow transition, made by systematically varying the plate separation in the parallel-plate geometry, demonstrate that this rotational instability is a function of the angular velocity in the flow and initially grows exponentially in time, in agreement with theoretical predictions for an Oldroyd-B model. However, experiments show that the disturbance which causes this flow transition is nonaxisymmetric, over-stable in time and subcritical in γ. Spectral analysis also shows that the nonlinear flow which ultimately develops is temporally aperiodic. These features of the flow transition do not agree with the existing theoretical analysis. The experimentally constructed flow-stability diagram shows that, for a given fluid, the instability occurs at a critical Deborah number which is insensitive to the specific geometrical parameters, temperature, and shear-rate of the flow. This interpretation of the elastic instability clarifies recent measurements of the flow stability for the Ml viscoelastic test fluid.