Inhomogeneous Flow in a One-Component Polymeric Fluid with a Nonmonotonic Constitutive Law

Abstract

We propose a phenomenological model of mechanical instability in a polymer melt having a nonmonotonic constitutive law. It relies on the fact that a nonmonotonic constitutive law is a result of shear-induced orientational ordering of polymers and this orientational order parameter has a common symmetry with that of liquid crystal. Our model shows that there exists gradient energy of “purely mechanical origin” associated with shear-rate inhomogeneity. We derive a “nonlocal” phenomenological equation describing shear banding, which is similar to the Cahn-Hilliard equation. The analogy of inhomogenization of flow fields to phase separation is discussed.