INSTABILITIES OF A STAGNATION POINT FLOW OF A DILUTE POLYMER-SOLUTION

The time-dependent planar flow of a dilute monodisperse polymer soluti on is considered in the limit where inertia is negligible. The polymer s are modelled as linear-locked dumbbells with non-linear hydrodynamic friction, and the flow field is chosen to contain an isolated stagnat ion point. For Weissenberg numbers We above a critical value, here tak en to be unity, the steady flow in this geometry contains a highly vis cous birefringent strand along the outgoing flow axis, of approximatel y uniform width, within which the polymers are fully extended. It is s hown that for sufficiently high polymer concentrations this steady flo w is subject to two modes of instability: for modest Weissenberg numbe rs (1 < We < 2) an oscillatory varicose disturbance of the strand is l inearly unstable; for higher Weissenberg numbers a strand-disturbance having a sinuous component gives rise to a finite amplitude instabilit y. The amplitude of initial disturbance required to trigger this insta bility is shown to be small. The parameter regimes for concentration, Weissenberg number and polymer extensibility within which each instabi lity occurs are found to be in qualitative agreement with the opposed jets experiments of A.J. Muller, J.A. Odell and J.P. Tatham, J. Non-Ne wtonian Fluid Mech., 35 (1990) 231-250. The mechanism of the instabili ty is kinematic in character: flow perturbations modify the polymer st retch and after a time delay, given by the time taken for polymers ent ering the flow to become fully stretched, the birefringent strand is a ffected. This in turn modifies the flow further, and if the polymer co ncentration is high enough gives an oscillation of increasing amplitud e.