Finite-amplitude elastic instability of plane-Poiseuille flow of viscoelastic fluids

The purely elastic stability and bifurcation of the one-dimensional plane P oiseuille flow is determined for a large class of Oldroyd fluids with added viscosity which typically represent polymer solutions composed of a Newton ian solvent and a polymeric solute. The problem is reduced to a nonlinear d ynamical system using the Galerkin projection method. It is shown that elas tic normal stress effects can be solely responsible for the destabilization of the base (Poiseuille) flow. It is found drat the stability and bifurcat ion picture is dramatically influenced by the solvent-to-solute viscosity r atio, epsilon. As the flow deviates frost the Newtonian limit and epsilon d ecreases below a critical value, the base flow loses its stability. Two sta tic bifurcations emerge at two critical Weissenberg numbers, forming a clos ed diagram that widens the level of elasticity increases.