THE EFFECT OF FLUID RHEOLOGY ON THE ELASTIC TAYLOR-COUETTE INSTABILITY

The earlier theoretical and experimental work describing a non-inertia l purely elastic instability in the Taylor-Couette flow of ''ideal'' e lastic liquids is extended to fluids with a distribution of relaxation times and shear thinning in the shear viscosity and first normal stre ss coefficient. We find, both experimentally and theoretically, that a n elastic instability can occur even in highly shear-thinning entangle d polymer solutions. Using small-gap axisymmetric linear stability equ ations for a K-BKZ fluid with a zero value of the second normal stress difference, we show theoretically that a distribution of relaxation t imes, shear thinning, and a Newtonian solvent contribution to the visc osity end tend to increase the critical Deborah number, which is the s hear rate times the longest relaxation time, while decreasing the crit ical value of the ratio of first normal stress difference (N1) to the shear stress (tau12). Experiments with both shear-thinning and non-she ar-thinning polystyrene solutions, with viscosities and relaxation tim es differing by two orders of magnitude, show instabilities that occur at shear rates 20-45% lower than those predicted by the axisymmetric linear stability analysis. This discrepancy is readily attributable to non-axisymmetric modes, which in Oldroyd-B fluids have been shown to be unstable to shear rates 30-40% lower than the axisymmetric modes.