Zero-shear viscosity of Fraenkel dumbbell suspensions

Abstract

Whereas rigid dumbbell suspensions predict, at least qualitatively, most of the viscoelastic material functions measured in the laboratory, Hookean dumbbells predict few of these. For instance, whereas rigid dumbbells predict a shear-thinning viscosity curve, as they should, Hookean dumbbells yield a constant for the steady shear viscosity. In this paper, we explore the addition of a Hookean spring to the end of a rigid rod, a dumbbell attributed to Fraenkel. In this way, we focus our attention on how macromolecular extensibility affects the configuration distribution in steady shear flow. We arrive at the exact solution to this configuration distribution in steady shear flow at low shear rate and then insert it into the Giesekus expression for the stress tensor to arrive at an exact solution for the zero-shear viscosity and the zero-shear values of the normal stress differences.