Suppression of absolute instabilities in the flow inside a compliant tube

Abstract

AbstractThe 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. The temporal and spatial eigenvalues of the system are found. Influence of the material parameters of the layers and the Reynolds number on the spatial and temporal amplification rate of the most unstable mode is investigated. It is shown that the system can be in both absolute and convective unstable states. Effects of the rheological parameters of each layer on the amplification rate of the most unstable mode that represents an absolute instability are examined. 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. The rheological parameters of the tube layers influence the system stability in different ways. While some of those parameters destabilize the system, others stabilize it. 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. Copyright © 2009 John Wiley & Sons, Ltd.