Viscoelastic pipe flow is linearly unstable

TL;DR

This paper demonstrates for the first time that viscoelastic fluids in pipe flow can be linearly unstable at low Reynolds numbers, revealing a new pathway to turbulence in polymer solutions.

Contribution

It identifies a novel linear instability in viscoelastic pipe flow modeled by Oldroyd-B, contrasting with the stability of Newtonian flow, and explains experimental transition observations.

Findings

Instability occurs at lower Reynolds numbers than Newtonian turbulence.

Qualitative agreement with experimental transition to turbulence.

Analogous instability found in plane Poiseuille flow.

Abstract

Newtonian pipe flow is known to be linearly stable at all Reynolds numbers. We report, for the first time, a linear instability of pressure driven pipe flow of a viscoelastic fluid, obeying the Oldroyd-B constitutive equation commonly used to model dilute polymer solutions. The instability is shown to exist at Reynolds numbers significantly lower than those at which transition to turbulence is typically observed for Newtonian pipe flow. Our results qualitatively explain experimental observations of transition to turbulence in pipe flow of dilute polymer solutions at flow rates where Newtonian turbulence is absent. The instability discussed here should form the first stage in a hitherto unexplored dynamical pathway to turbulence in polymer solutions. An analogous instability exists for plane Poiseuille flow.