ON PURELY ELASTIC INSTABILITIES IN ECCENTRIC CYLINDER FLOWS

An experimental and theoretical investigation of the stability of the viscoelastic flow of the Boger fluid between eccentric cylinders is co nsidered. In our theoretical study, a local linear stability analysis for the flow of an Oldroyd-B fluid suggests that the flow is elastical ly unstable for all eccentricities. It is shown that the linear stabil ity of eccentric cylinder flow, to leading order for small gap ratio, is very similar to that of Taylor-Dean flow (Y.L. Joo and E.S.G. Shaqf eh, Phys. Fluids A, 4(3) (1992) 524). Flow visualization experiments w ith a solution of high molecular polyisobutylene dissolved in a viscou s solvent clearly show the transition from a purely azimuthal to a sec ondary torodial flow. Comparison of these experimental results with th e local linear stability theory shows qualitative agreement with the p redicted critical conditions for the onset of the non-inertial cellula r instability when delta < 0.4, where delta is the eccentricity (made dimensionless with the average gap thickness). At higher eccentricitie s, experiment and theory cease to agree. Evidence is given that this d isagreement is due to the non-local streamwise extension rate which is not included in the present theory, and whose magnitude increases wit h increasing delta. We look forward to a comprehensive investigation o f this interesting phenomenon.