Understanding viscoelastic flow instabilities: Oldroyd-B and beyond

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