Flat disc suspensions are indistinguishable from macromolecular solutions within planar incompressible flows

We prove analytically that the two fundamental rheological equations for flat disc suspensions and macromolecular solutions, the so-called Oldroyd-A and -B models, respectively, produce identical velocity fields in any planar incompressible flow. We demonstrate that this has significant implications for understanding and controlling nonlinear flow phenomena, such as elastic instabilities and elastoinertial turbulence. We use numerical simulations of Oldroyd-A/-B fluids to illustrate this equivalency in two benchmark flows: the creeping flow in a cross-slot channel and the onset of elastoinertial turbulence in a planar channel.