Viscoelastic effects on the stability of wall-bounded shear flows

Abstract

The dissolution of high molecular weight polymers and surfactants to wall-bounded shear flows of Newtonian liquids significantly modifies their stability characteristics. The critical Reynolds number Rec first decreases with increasing flow elasticity E until a critical value E=E* is reached and increases back again for E>E*. We explore the mechanisms that cause this behavior in the viscoelastic plane Poiseuille flow of an Oldroyd-B liquid. The minimum in the Rec−E curve arises from two competing contributions to the perturbation vorticity transport: The contribution from the viscoelastic shear stress perturbations that becomes more dissipative with increasing E and that from the viscoelastic normal stress perturbations that becomes more destabilizing with increasing E. Similar behavior is also exhibited by the contributions of the normal and the shear stress perturbations to the kinetic-energy budget. When a Deborah number based on the time scale of the critical disturbance becomes O(1) (≈1.6±0.1, irrespective of the solvent to total viscosity ratio), the dissipative influence of the shear stress perturbations becomes dominant. The elasticity value EC at which this occurs is approximately equal to E*. Moreover, both E* and EC exhibit similar asymptotic dependence on the solvent to total viscosity ratio. Furthermore, E* and EC are of the same order of magnitude as the elasticity values for which the onset of polymer-induced drag reduction is predicted by direct numerical simulations. Finally, we show that the perturbation velocity vector aligns progressively closer with the base flow velocity as E is increased for E<E*, contributing to the initial destabilization.