The Asymptotic Behaviour of Oldroyd-B Fluids is Almost Newtonian

TL;DR

This paper demonstrates that Oldroyd-B viscoelastic fluids behave almost like Newtonian fluids at large times due to the decay rates of their stress and deformation tensors.

Contribution

It establishes the asymptotic decay rates of stress and deformation tensors in Oldroyd-B fluids, showing their near-Newtonian behavior over time.

Findings

Stress tensor and deformation tensor decay at the same rate.

Elastic part decays faster than stress and deformation tensors.

Viscoelastic fluid exhibits almost Newtonian behavior asymptotically.

Abstract

Consider a viscoelastic fluid of Oldroyd-B type. It is shown that its stress tensor $\tau$ and its Newtonian deformation tensor $D(u)$ decay at the same rate, while the elastic part $\varepsilon=\tau-2\omega D(u)$ decays faster. As a consequence, the stress tensor of a viscoelastic fluid exhibits an almost Newtonian behaviour for large times.