A constitutive equation for fiber suspensions in viscoelastic media

A viscosity overshoot of fibers filled in a polymer melt under a shear flow is much tougher to predict via the existing constitutive equations of suspension rheology in a viscous media, owing to the effect of fiber orientation on the viscoelastic behavior. The WMT-X (White-Metzner model eXtended by Tseng) viscoelastic fluid model coupled with the typical Dinh-Armstrong fiber suspension model, known as the suspended WMT-X model, is proposed herein. The primary procedure involves verifying the lower viscosity of the completely aligned suspension compared to that of the randomly oriented suspension. In addition, the viscosity overshoot depends on the off-diagonal orientation tensor component in the flow-gradient plane. As a validation, the numerical predictions of transient shear viscosity are in good agreement with the related experimental data.