Stability of planar stagnation flow of a highly viscoelastic fluid

Linear stability analysis is used to predict the onset of instabilities in inertialess viscoelastic planar stagnation flow. Beyond a critical value of the dimensionless flow rate, or Deborah number, the creeping base flow of similarity type, which is valid in the limit of vanishingly small Reynolds numbers, becomes unstable to localized three-dimensional disturbances. Stability calculations of the local similarity type viscoelastic flow in a small region near the stagnation plane are reported for the quasi-linear Oldroyd-B constitutive equation. The stability results for a range of Deborah numbers and viscosity ratio are presented to explore systematically the effects of elasticity and other rheological properties. The onset of instability and the temporal and spatial characteristics of the secondary how predicted here resemble other purely elastic instabilities measured and predicted for viscoelastic hows in other simple and complex geometries with curved streamlines. (C) 1997 Elsevier Science B.V.