Time-dependent elastic instabilities in a shear flow: spanning the entire Wi—Re phase plane

It is well known that the simple shear flow of a viscoelastic fluid, such as the torsional flow between a cone and plate in the low Reynolds number (Re) regime becomes unstable to a three-dimensional time-dependent instability. This elastically-driven instability emerges from the onset of a secondary motion resulting in a Bernoulli spiral-like flow at conditions just above critical. Here we present the effects of increasing Re on the critical conditions for the onset of elastic instabilities in a torsional shear flow between a cone and plate, thus, spanning the entire Weissenberg (Wi)-Reynolds (Re) number phase plane. Flow visualizations reveal the combined effects of varying Wi and Re on the secondary recirculation at the onset of instability. The results provide insight into non-Newtonian fluid mechanics and elevate our fundamental physical understanding of inertia-elastic coupling and the role of shear-thinning and second normal stresses on elastic instabilities.