Bridging macromolecular theory of polymeric liquids to Oldroyd 8-constant constitutive framework

Abstract

The Oldroyd 8-constant continuum framework established a vision for constitutive equations for polymeric liquids—past, present, and future. In this Letter, we bridge a macromolecular theory for polymeric liquids to the continuum framework. Specifically, we bridge general rigid bead-rod theory (also called rotarance theory) to the Oldroyd 8-constant framework. In so doing, we arrive at a constitutive equation whose constants are known in terms of the macromolecular moments of inertia of axisymmetric macromolecules of otherwise arbitrary architecture. For any of the many polymer processing problems solved analytically for the Oldroyd 8-constant continuum theory, we can thus explore analytically the role of macromolecular architecture on the polymer processing.