Global stability of Oldroyd-B fluids in plane Couette flow

TL;DR

This paper establishes conditions for the global nonlinear stability of Oldroyd-B viscoelastic fluids in plane Couette flow by introducing a novel perturbation entropy functional, extending classical Newtonian stability results.

Contribution

It introduces a new stability criterion based on a perturbation entropy functional for Oldroyd-B fluids in Couette flow, extending classical Newtonian results.

Findings

Conditions for global stability derived

Perturbation entropy functional introduced

Extension of classical stability results

Abstract

We prove conditions for global nonlinear stability of Oldroyd-B viscoelatic fluid flows in the Couette shear flow geometry. Global stability is inferred by analysing a new functional, called a perturbation entropy, to quantify the magnitude of the polymer perturbations from their steady-state values. The conditions for global stability extend, in a physically natural manner, classical results on global stability of Newtonian Couette flow.