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

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  • Tanaka Hajime
    Institute of Industrial Science, University of Tokyo, Meguro–ku, Tokyo 153–8505

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  • Inhomogeneous Flow in a One-Component Poly1meric Fluid with a Nonmonotonic Constitutive Law

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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.

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