Stress growth shearfree flow from the Oldroyd 8-constant framework

Abstract

Sudden inception of shearfree flows (also called stress growth in extension) is an extremely useful set of rheological measurement techniques for bringing out fluid nonlinearities. The previous predictions of these departures from linearity employed molecular simulation or finite difference solutions. In this work, we deepen our understanding of the physics of these departures by uncovering the exact solutions to a large and diverse framework of constitutive equations: the Oldroyd 8-constant framework. Specifically, we derive the exact analytical solutions for the first and second elongational viscosities in shearfree flow from the Oldroyd 8-constant framework including (I) uniaxial elongational flow, (II) biaxial stretching flow, and (III) planar elongational flow. We close our work with a worked example on analyzing a highly branched system.