Kinematic and rheological equivalence of steady shearing and planar extensional flows

TL;DR

This paper demonstrates a rheological equivalence between steady shearing and planar extensional flows, allowing the prediction of extensional viscosity from shear measurements using derived effective extension rates.

Contribution

It introduces a method to reconstruct planar extensional viscosity from shear flow data by leveraging kinematic equivalence, supported by models and experiments.

Findings

Effective extension rate removes rotational component in shear flow

Extensional viscosity can be derived from shear measurements

Experimental validation with viscoelastic polymer solution

Abstract

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 experiments with a viscoelastic polymer solution.