Understanding viscoelastic flow instabilities: Oldroyd-B and beyond

• Published in: Journal of non-Newtonian fluid mechanics Vol. 302; p. 104742
• Main Authors: Castillo Sánchez, Hugo A., Jovanović, Mihailo R., Kumar, Satish, Morozov, Alexander, Shankar, V., Subramanian, Ganesh, Wilson, Helen J.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.04.2022; Elsevier BV
• Subjects: Constitutive models; Elastic turbulence; Elasto-inertial turbulence; Laminar flow; Mathematical models; Multilayers; Nonlinear stability; Nonmodal stability; Oldroyd-B fluid; Purely elastic instability; Shearing; Stability analysis; Topology; Viscoelastic fluids; Viscoelasticity; Nonlinear stability; Elastic turbulence; Oldroyd-B fluid; Elasto-inertial turbulence; Nonmodal stability; Purely elastic instability
• ISSN: 0377-0257; 1873-2631; 1873-2631
• DOI: 10.1016/j.jnnfm.2022.104742

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. •State-of-the-art summary on the subject of viscoelastic flow instabilities.•Onset of elasto-inertial turbulence in rectilinear shearing flows.•Instabilities in curvilinear shear flows.•Elastic instabilities in nonviscometric flows.•Nonmodal and weakly nonlinear stability analyses.