Flat Elastic Disc Suspensions Are Indistinguishable from Solutions of Long Flexible Polymers within Planar Incompressible Flows

We prove analytically that the two fundamental rheological equations for (elastic) disc suspensions and long flexible polymers, the so-called Oldroyd-A and-B models, respectively, predict the same flow and total stress fields in any planar incompressible flow. We illustrate this equivalence for creeping flow in a cross-slot channel and investigate differences arising from three-dimensional effects in a weakly elastic Taylor-Couette flow. Finally, we discuss implications for understanding elastic instabilities, controlling inertial turbulence, and deriving constitutive models for complex fluids.