Stabilization of the flat Poiseuille-type flow for viscoelastic polymeric liquid

Abstract

The paper presents the numerical study for the problem of the <p>one-dimensional flow of viscoelastic liquid polymer between two parallel</p> <p>plates. The equations of rheological modified Vinogradov--Pokrovskii</p> <p>(mVP) model is used for the formulation of the problem. It is shown</p> <p>that the problem could have multiple steady-state solutions. The evaluation</p> <p>of non-steady solutions was performed to see if the time-dependent</p> <p>solutions got eventually attracted by the steady ones. Also for the</p> <p>case of multiple steady solutions it was checked which one attracts</p> <p>the non-steady solution if any. The evaluation of time-dependent solutions</p> <p>was used to estimate the stability of the equilibrium states. It is revealed that stable steady-state regimes of the problem exist under certain conditions and also that there could be no more than one stable regime for any given set of parameters. The calculations were performed to estimate the values of Reynolds and Weissenberg numbers corresponding to either stable or unstable steady regime. The result indicates that instability of the steady flow could possibly occur for arbitrarily low Reynolds number under certain balance of viscous and elastic forces.