The critical wall velocity for stabilization of plane Couette-Poiseuille flow of viscoelastic fluids

In this paper we show numerically that the plane Couette-Poiseuille flow of Oldroyd-B and modified FENE Chilcott-Rallison fluids is stabilized at a critical wall velocity approximately 0.7 times the maximal velocity of the plane Poiseuille flow, independent of the elastic parameters investigated. This value is surprisingly close to the Newtonian critical value. A long wavelength analysis, following the distinguished limit method of Cowley and Smith [8], confirms that at leading order this stabilizing wall velocity is indeed independent of the elasticity number of the flow.