Suppression of Absolute Instabilities by Appropriate Choice of Rheological Parameters of Anisotropic Viscoelastic Tube Conveying Fluid

Abstract

The stability of the steady flow of a viscous liquid through a thick-wall, three-layer, viscoelastic tube with different rheological parameters for each layer is studied. It is shown that the system can be in both absolute and convective unstable states. It is shown that the absolute instability of the system can be converted into a convective instability, and in some cases the system can even be stabilized with an appropriate choice of the rheological parameters. It is found that an anisotropic tube composed of layers possessing distinct rheological values can completely eliminate all absolute instability modes. The present model can be applied to blood vessels that are composed of three viscoelastic layers with distinct rheological properties and to distensible tubes conveying fluids in different technical devices.