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Flat Elastic Disc Suspensions Are Indistinguishable from Solutions of Long Flexible Polymers within Planar
Fabian Hillebrand1, Rebecca J Hill2, Mahdi Davoodi3
1Okinawa Institute of Science and Technology Graduate University, 1919-1 Tancha, Onna, Okinawa 904-0495, Japan.
None:
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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