A Purely Elastic Instability in Taylor-Couette Flow.

A non-inertial (zero Taylor number) viscoelastic instability is discovered for Taylor-Couette flow of dilute polymer solutions. A linear stability analysis of the inertialess flow of an Oldroyd- B fluid (using both approximate Galerkin analysis and numerical solution of the relevant small-gap eigenvalue problem) show the growth of an overstable (oscillating) mode when the Deborah number exceeds f(S)epsilon sup (-1/2), where epsilon is the ratio of the gap to the inner cylinder radius, and f(S) is a function of the ratio of solvent to polymer contributions to the solution viscosity. Experiments with a 1000 ppm high molecular-weight polyisobutylene in a viscous solvent show an onset of secondary toroidal cells when the Deborah number reaches 20, for epsilon of 0.14, and a Taylor number of 10 sup (-6), in excellent agreement with the theoretical value of 21.