Kinematic and rheological equivalence of steady shearing and planar extensional flows

Steady shearing and planar extension are commonly viewed as two distinct types of flow field, especially in the context of probing the rheology of complex fluids. By leveraging the kinematic equivalence between the two flows, we derive an effective extension rate experienced by a material element which removes the rotational component of the shearing flow. This enables reconstruction of the steady planar extensional viscosity of an unknown fluid using only material functions measured in a steady shearing flow, revealing a deep rheological equivalence between the two deformation histories. We demonstrate this equivalency through phenomenological and microscopically motivated frame-invariant constitutive models as well as using experimental data obtained with a viscoelastic polymer solution and a polymer melt.