Planar extensional viscosity from Oldroyd 8-constant framework

Abstract

The Oldroyd 8-constant framework established a vision for constitutive equations for polymeric liquids past, present, and future. Though most canonical material functions for this framework are available, the expression for the steady planar extensional viscosity is not. In this work, we solve exactly for any steady homogeneous extensional (shearfree) flow field. Our results recover the well-known solution for the steady uniaxial extension, as they must. We next derive the steady planar extensional viscosity. Though this work has mainly been driven by curiosity, the planar extensional viscosity governs drawability in the film and sheet casting.