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.

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• Non-Newtonian fluids