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

Abstract

This paper presents a numerical study for the problem of the one-dimensional flow of viscoelastic liquid polymers between two parallel plates. The equations of a rheologically modified Vinogradov–Pokrovskii (mVP) model is used for the formulation of the problem. It is shown that the problem could have multiple steady-state solutions. The evaluation of non-steady solutions was performed to see if the time-dependent solutions got eventually attracted by the steady ones. Also for the case of multiple steady solutions, it was checked which one attracts the non-steady solution if any. The evaluation of time-dependent solutions was used to estimate the stability of equilibrium states. It is revealed that stable steady-state regimes of the problem exist under certain conditions, and also 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 regimes. The result indicates that instability of the steady flow could possibly occur for arbitrary low Reynolds numbers under certain balance of viscous and elastic forces.