STABILITY OF PLANAR STAGNATION FLOW OF A HIGHLY VISCOELASTIC FLUID

Linear stability analysis is used to predict the onset of instabilitie s in inertialess viscoelastic planar stagnation flow. Beyond a critica l value of the dimensionless flow rate, or Deborah number, the creepin g base flow of similarity type, which is valid in the limit of vanishi ngly small Reynolds numbers, becomes unstable to localized three-dimen sional disturbances. Stability calculations of the local similarity ty pe viscoelastic flow in a small region near the stagnation plane are r eported for the quasi-linear Oldroyd-B constitutive equation. The stab ility results for a range of Deborah numbers and viscosity ratio are p resented 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 viscoela stic hows in other simple and complex geometries with curved streamlin es. (C) 1997 Elsevier Science B.V.