Understanding viscoelastic flow instabilities: Oldroyd-B and beyond

TL;DR

This review discusses viscoelastic flow instabilities across various shearing flow types, focusing on the Oldroyd-B model's predictions, limitations, and how more realistic models can improve understanding of these complex phenomena.

Contribution

It provides a comprehensive overview of flow instabilities predicted by the Oldroyd-B model and discusses how to address its limitations with advanced constitutive models.

Findings

Oldroyd-B model qualitatively predicts most flow instabilities.

Various stability analysis tools are discussed with experimental support.

Open questions remain in viscoelastic flow stability research.

Abstract

The Oldroyd-B model has been used extensively to predict a host of instabilities in shearing flows of viscoelastic fluids, often realized experimentally using polymer solutions. The present review, written on the occasion of the birth centenary of James Oldroyd, provides an overview of instabilities found across major classes of shearing flows. These comprise (i) the canonical rectilinear shearing flows including plane Couette, plane and pipe Poiseuille flows; (ii) viscometric shearing flows with curved streamlines such as those in the Taylor-Couette, cone-and-plate and parallel-plate geometries; (iii) non-viscometric shearing flows with an underlying extensional flow topology such as the flow in a cross-slot device; and (iv) multilayer shearing flows. While the underlying focus in all these cases is on results obtained using the Oldroyd-B model, we also discuss their relation to the actual instability, and as to how the shortcomings of the Oldroyd-B model may be overcome by the use of more realistic constitutive models. All the three commonly used tools of stability analysis, viz., modal linear stability, nonmodal stability, and weakly nonlinear stability analyses are discussed, with supporting evidence from experiments and numerical simulations as appropriate. Despite only accounting for a shear-rate-independent viscosity and first normal stress coefficient, the Oldroyd-B model is able to qualitatively predict the majority of instabilities in the aforementioned shearing flows. The review also highlights, where appropriate, open questions in the area of viscoelastic stability.